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
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
|
<!DOCTYPE html>
<html lang="en" data-content_root="../../" >
<head>
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Additional Information — SLEPc 3.24.1 documentation</title>
<script data-cfasync="false">
document.documentElement.dataset.mode = localStorage.getItem("mode") || "";
document.documentElement.dataset.theme = localStorage.getItem("theme") || "";
</script>
<!--
this give us a css class that will be invisible only if js is disabled
-->
<noscript>
<style>
.pst-js-only { display: none !important; }
</style>
</noscript>
<!-- Loaded before other Sphinx assets -->
<link href="../../_static/styles/theme.css?digest=8878045cc6db502f8baf" rel="stylesheet" />
<link href="../../_static/styles/pydata-sphinx-theme.css?digest=8878045cc6db502f8baf" rel="stylesheet" />
<link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=8f2a1f02" />
<link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
<link rel="stylesheet" type="text/css" href="../../_static/togglebutton.css?v=13237357" />
<link rel="stylesheet" type="text/css" href="../../_static/sphinx-design.min.css?v=95c83b7e" />
<link rel="stylesheet" type="text/css" href="../../_static/css/slepc.css?v=d285b177" />
<!-- So that users can add custom icons -->
<script src="../../_static/scripts/fontawesome.js?digest=8878045cc6db502f8baf"></script>
<!-- Pre-loaded scripts that we'll load fully later -->
<link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=8878045cc6db502f8baf" />
<link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=8878045cc6db502f8baf" />
<script src="../../_static/documentation_options.js?v=d1c46438"></script>
<script src="../../_static/doctools.js?v=9a2dae69"></script>
<script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
<script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
<script src="../../_static/copybutton.js?v=a56c686a"></script>
<script>let toggleHintShow = 'Click to show';</script>
<script>let toggleHintHide = 'Click to hide';</script>
<script>let toggleOpenOnPrint = 'true';</script>
<script src="../../_static/togglebutton.js?v=4a39c7ea"></script>
<script src="../../_static/design-tabs.js?v=f930bc37"></script>
<script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
<script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
<script>window.MathJax = {"options": {"processHtmlClass": "tex2jax_process|mathjax_process|math|output_area"}}</script>
<script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<script>DOCUMENTATION_OPTIONS.pagename = 'documentation/manual/extra';</script>
<link rel="icon" href="../../_static/favicon-slepc.ico"/>
<link rel="index" title="Index" href="../../genindex.html" />
<link rel="search" title="Search" href="../../search.html" />
<link rel="next" title="Hands-on exercises" href="../hands-on/index.html" />
<link rel="prev" title="Auxiliary Classes" href="aux.html" />
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<meta name="docsearch:language" content="en"/>
<meta name="docsearch:version" content="3.24" />
</head>
<body data-bs-spy="scroll" data-bs-target=".bd-toc-nav" data-offset="180" data-bs-root-margin="0px 0px -60%" data-default-mode="">
<div id="pst-skip-link" class="skip-link d-print-none"><a href="#main-content">Skip to main content</a></div>
<div id="pst-scroll-pixel-helper"></div>
<button type="button" class="btn rounded-pill" id="pst-back-to-top">
<i class="fa-solid fa-arrow-up"></i>Back to top</button>
<dialog id="pst-search-dialog">
<form class="bd-search d-flex align-items-center"
action="../../search.html"
method="get">
<i class="fa-solid fa-magnifying-glass"></i>
<input type="search"
class="form-control"
name="q"
placeholder="Search the docs ..."
aria-label="Search the docs ..."
autocomplete="off"
autocorrect="off"
autocapitalize="off"
spellcheck="false"/>
<span class="search-button__kbd-shortcut"><kbd class="kbd-shortcut__modifier">Ctrl</kbd>+<kbd>K</kbd></span>
</form>
</dialog>
<div class="pst-async-banner-revealer d-none">
<aside id="bd-header-version-warning" class="d-none d-print-none" aria-label="Version warning"></aside>
</div>
<header class="bd-header navbar navbar-expand-lg bd-navbar d-print-none">
<div class="bd-header__inner bd-page-width">
<button class="pst-navbar-icon sidebar-toggle primary-toggle" aria-label="Site navigation">
<span class="fa-solid fa-bars"></span>
</button>
<div class="col-lg-3 navbar-header-items__start">
<div class="navbar-item">
<a class="navbar-brand logo" href="../../index.html">
<img src="../../_static/logo-slepc.gif" class="logo__image only-light" alt="SLEPc Home"/>
<img src="../../_static/logo-slepc.gif" class="logo__image only-dark pst-js-only" alt="SLEPc Home"/>
</a></div>
</div>
<div class="col-lg-9 navbar-header-items">
<div class="me-auto navbar-header-items__center">
<div class="navbar-item">
<nav>
<ul class="bd-navbar-elements navbar-nav">
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../about/index.html">
About
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../installation/index.html">
Installation
</a>
</li>
<li class="nav-item current active">
<a class="nav-link nav-internal" href="../index.html">
Documentation
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../manualpages/index.html">
C/Fortran API
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../slepc4py/index.html">
slepc4py API
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../material/index.html">
Material
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../contact/index.html">
Contact
</a>
</li>
</ul>
</nav></div>
</div>
<div class="navbar-header-items__end">
<div class="navbar-item navbar-persistent--container">
<button class="btn search-button-field search-button__button pst-js-only" title="Search" aria-label="Search" data-bs-placement="bottom" data-bs-toggle="tooltip">
<i class="fa-solid fa-magnifying-glass"></i>
<span class="search-button__default-text">Search</span>
<span class="search-button__kbd-shortcut"><kbd class="kbd-shortcut__modifier">Ctrl</kbd>+<kbd class="kbd-shortcut__modifier">K</kbd></span>
</button>
</div>
<div class="navbar-item">
<button class="btn btn-sm nav-link pst-navbar-icon theme-switch-button pst-js-only" aria-label="Color mode" data-bs-title="Color mode" data-bs-placement="bottom" data-bs-toggle="tooltip">
<i class="theme-switch fa-solid fa-sun fa-lg" data-mode="light" title="Light"></i>
<i class="theme-switch fa-solid fa-moon fa-lg" data-mode="dark" title="Dark"></i>
<i class="theme-switch fa-solid fa-circle-half-stroke fa-lg" data-mode="auto" title="System Settings"></i>
</button></div>
<div class="navbar-item"><ul class="navbar-icon-links"
aria-label="Icon Links">
<li class="nav-item">
<a href="https://gitlab.com/slepc/slepc" title="GitLab" class="nav-link pst-navbar-icon" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><i class="fa-brands fa-square-gitlab fa-lg" aria-hidden="true"></i>
<span class="sr-only">GitLab</span></a>
</li>
<li class="nav-item">
<a href="https://www.upv.es" title="UPV" class="nav-link pst-navbar-icon" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><img src="https://www.upv.es/favicon.ico" class="icon-link-image" alt="UPV"/></a>
</li>
<li class="nav-item">
<a href="https://slepc.upv.es/release/_static/rss/slepc-news.xml" title="Feed" class="nav-link pst-navbar-icon" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><i class="fa-solid fa-square-rss fa-lg" aria-hidden="true"></i>
<span class="sr-only">Feed</span></a>
</li>
</ul></div>
</div>
</div>
<div class="navbar-persistent--mobile">
<button class="btn search-button-field search-button__button pst-js-only" title="Search" aria-label="Search" data-bs-placement="bottom" data-bs-toggle="tooltip">
<i class="fa-solid fa-magnifying-glass"></i>
<span class="search-button__default-text">Search</span>
<span class="search-button__kbd-shortcut"><kbd class="kbd-shortcut__modifier">Ctrl</kbd>+<kbd class="kbd-shortcut__modifier">K</kbd></span>
</button>
</div>
<button class="pst-navbar-icon sidebar-toggle secondary-toggle" aria-label="On this page">
<span class="fa-solid fa-outdent"></span>
</button>
</div>
</header>
<div class="bd-container">
<div class="bd-container__inner bd-page-width">
<dialog id="pst-primary-sidebar-modal"></dialog>
<div id="pst-primary-sidebar" class="bd-sidebar-primary bd-sidebar">
<div class="sidebar-header-items sidebar-primary__section">
<div class="sidebar-header-items__center">
<div class="navbar-item">
<nav>
<ul class="bd-navbar-elements navbar-nav">
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../about/index.html">
About
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../installation/index.html">
Installation
</a>
</li>
<li class="nav-item current active">
<a class="nav-link nav-internal" href="../index.html">
Documentation
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../manualpages/index.html">
C/Fortran API
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../slepc4py/index.html">
slepc4py API
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../material/index.html">
Material
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../contact/index.html">
Contact
</a>
</li>
</ul>
</nav></div>
</div>
<div class="sidebar-header-items__end">
<div class="navbar-item">
<button class="btn btn-sm nav-link pst-navbar-icon theme-switch-button pst-js-only" aria-label="Color mode" data-bs-title="Color mode" data-bs-placement="bottom" data-bs-toggle="tooltip">
<i class="theme-switch fa-solid fa-sun fa-lg" data-mode="light" title="Light"></i>
<i class="theme-switch fa-solid fa-moon fa-lg" data-mode="dark" title="Dark"></i>
<i class="theme-switch fa-solid fa-circle-half-stroke fa-lg" data-mode="auto" title="System Settings"></i>
</button></div>
<div class="navbar-item"><ul class="navbar-icon-links"
aria-label="Icon Links">
<li class="nav-item">
<a href="https://gitlab.com/slepc/slepc" title="GitLab" class="nav-link pst-navbar-icon" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><i class="fa-brands fa-square-gitlab fa-lg" aria-hidden="true"></i>
<span class="sr-only">GitLab</span></a>
</li>
<li class="nav-item">
<a href="https://www.upv.es" title="UPV" class="nav-link pst-navbar-icon" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><img src="https://www.upv.es/favicon.ico" class="icon-link-image" alt="UPV"/></a>
</li>
<li class="nav-item">
<a href="https://slepc.upv.es/release/_static/rss/slepc-news.xml" title="Feed" class="nav-link pst-navbar-icon" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><i class="fa-solid fa-square-rss fa-lg" aria-hidden="true"></i>
<span class="sr-only">Feed</span></a>
</li>
</ul></div>
</div>
</div>
<div class="sidebar-primary-items__start sidebar-primary__section">
<div class="sidebar-primary-item">
<nav class="bd-docs-nav bd-links"
aria-label="Section Navigation">
<p class="bd-links__title" role="heading" aria-level="1">Section Navigation</p>
<div class="bd-toc-item navbar-nav"><ul class="current nav bd-sidenav">
<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">SLEPc Users Manual</a><details open="open"><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul class="current">
<li class="toctree-l2"><a class="reference internal" href="intro.html">Getting Started</a></li>
<li class="toctree-l2"><a class="reference internal" href="eps.html">EPS: Eigenvalue Problem Solver</a></li>
<li class="toctree-l2"><a class="reference internal" href="st.html">ST: Spectral Transformation</a></li>
<li class="toctree-l2"><a class="reference internal" href="svd.html">SVD: Singular Value Decomposition</a></li>
<li class="toctree-l2"><a class="reference internal" href="pep.html">PEP: Polynomial Eigenvalue Problems</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep.html">NEP: Nonlinear Eigenvalue Problems</a></li>
<li class="toctree-l2"><a class="reference internal" href="mfn.html">MFN: Matrix Function</a></li>
<li class="toctree-l2"><a class="reference internal" href="lme.html">LME: Linear Matrix Equation</a></li>
<li class="toctree-l2"><a class="reference internal" href="aux.html">Auxiliary Classes</a></li>
<li class="toctree-l2 current active"><a class="current reference internal" href="#">Additional Information</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../hands-on/index.html">Hands-on exercises</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../hands-on/hands-on0.html">Exercise 0: Hello World</a></li>
<li class="toctree-l2"><a class="reference internal" href="../hands-on/hands-on1.html">Exercise 1: Standard Symmetric Eigenvalue Problem</a></li>
<li class="toctree-l2"><a class="reference internal" href="../hands-on/hands-on2.html">Exercise 2: Standard Non-Symmetric Eigenvalue Problem</a></li>
<li class="toctree-l2"><a class="reference internal" href="../hands-on/hands-on3.html">Exercise 3: Generalized Eigenvalue Problem Stored in a File</a></li>
<li class="toctree-l2"><a class="reference internal" href="../hands-on/hands-on4.html">Exercise 4: Singular Value Decomposition</a></li>
<li class="toctree-l2"><a class="reference internal" href="../hands-on/hands-on5.html">Exercise 5: Problem without Explicit Matrix Storage</a></li>
<li class="toctree-l2"><a class="reference internal" href="../hands-on/hands-on6.html">Exercise 6: Parallel Execution</a></li>
<li class="toctree-l2"><a class="reference internal" href="../hands-on/hands-on7.html">Exercise 7: Use of Deflation Subspaces</a></li>
<li class="toctree-l2"><a class="reference internal" href="../hands-on/hands-on8.html">Exercise 8: Quadratic Eigenvalue Problem</a></li>
</ul>
</details></li>
<li class="toctree-l1"><a class="reference internal" href="../faq.html">Frequently Asked Questions</a></li>
<li class="toctree-l1"><a class="reference internal" href="../presentations.html">Presentations</a></li>
<li class="toctree-l1"><a class="reference internal" href="../license.html">License</a></li>
</ul>
</div>
</nav></div>
</div>
<div class="sidebar-primary-items__end sidebar-primary__section">
<div class="sidebar-primary-item">
<div id="ethical-ad-placement"
class="flat"
data-ea-publisher="readthedocs"
data-ea-type="readthedocs-sidebar"
data-ea-manual="true">
</div></div>
</div>
</div>
<main id="main-content" class="bd-main" role="main">
<div class="bd-content">
<div class="bd-article-container">
<div class="bd-header-article d-print-none">
<div class="header-article-items header-article__inner">
<div class="header-article-items__start">
<div class="header-article-item">
<nav aria-label="Breadcrumb" class="d-print-none">
<ul class="bd-breadcrumbs">
<li class="breadcrumb-item breadcrumb-home">
<a href="../../index.html" class="nav-link" aria-label="Home">
<i class="fa-solid fa-home"></i>
</a>
</li>
<li class="breadcrumb-item"><a href="../index.html" class="nav-link">Documentation</a></li>
<li class="breadcrumb-item"><a href="index.html" class="nav-link">SLEPc Users Manual</a></li>
<li class="breadcrumb-item active" aria-current="page"><span class="ellipsis">Additional Information</span></li>
</ul>
</nav>
</div>
</div>
</div>
</div>
<div id="searchbox"></div>
<article class="bd-article">
<section class="tex2jax_ignore mathjax_ignore" id="additional-information">
<span id="ch-add"></span><h1>Additional Information<a class="headerlink" href="#additional-information" title="Link to this heading">#</a></h1>
<p>This chapter contains miscellaneous information as a complement to the previous chapters, that can be regarded as less important.</p>
<section id="supported-petsc-features">
<h2>Supported PETSc Features<a class="headerlink" href="#supported-petsc-features" title="Link to this heading">#</a></h2>
<p>SLEPc relies on PETSc for most features that are not directly related to eigenvalue problems. All functionality associated with vectors and matrices as well as systems of linear equations is provided by PETSc. Also, low level details are inherited directly from PETSc. In particular, the parallelism within SLEPc methods is handled almost completely by PETSc’s vector and matrix modules.</p>
<p>SLEPc mainly contains high level objects, as depicted in figure <a class="reference internal" href="intro.html#fig-slepc"><span class="std std-ref">Numerical components of PETSc and SLEPc</span></a>. These object classes have been designed and implemented following the philosophy of other high level objects in PETSc. In this way, SLEPc benefits from a number of PETSc’s good properties such as the following (see <a class="reference external" href="https://petsc.org/release/manual/" target="_blank">PETSc Users Guide</a> for details):</p>
<ul class="simple">
<li><p>Portability and scalability in a wide range of platforms. Different architecture builds can coexist in the same installation. Where available, shared libraries are used to reduce disk space of executable files.</p></li>
<li><p>Support for profiling of programs:</p>
<ul>
<li><p>Display performance statistics with <code class="docutils notranslate"><span class="pre">-log_view</span></code>, including also SLEPc’s objects. The collected data are <em>flops</em>, memory usage and execution times as well as information about parallel performance, for individual subroutines and the possibility of user-defined stages.</p></li>
<li><p>Event logging, including user-defined events.</p></li>
<li><p>Direct wall-clock timing with <a class="reference external" href="https://petsc.org/release/manualpages/Sys/PetscTime/" title="(in PETSc v3.24)"><span class="xref std std-doc">PetscTime</span></a>().</p></li>
<li><p>Display detailed profile information and trace of events.</p></li>
</ul>
</li>
<li><p>Convergence monitoring, both textual and graphical.</p></li>
<li><p>Support for debugging of programs:</p>
<ul>
<li><p>Debugger startup and attachment of parallel processes.</p></li>
<li><p>Automatic generation of back-traces of the call stack.</p></li>
<li><p>Detection of memory leaks.</p></li>
</ul>
</li>
<li><p>A number of viewers for visualization of data, including built-in graphics capabilities that allow for sparse pattern visualization, graphic convergence monitoring, operator’s spectrum visualization and display of regions of the complex plane.</p></li>
<li><p>Easy handling of runtime options.</p></li>
<li><p>Support for Fortran programming using Fortran modules. See section <a class="reference internal" href="#sec-fortran"><span class="std std-ref">Fortran Interface</span></a> for details.</p></li>
</ul>
</section>
<section id="sec-supported">
<h2>Supported Matrix Types<a class="headerlink" href="#sec-supported" title="Link to this heading">#</a></h2>
<p>Methods implemented in SLEPc merely require vector operations and matrix-vector products. In PETSc, mathematical objects such as vectors and matrices have an interface that is independent of the underlying data structures. SLEPc manipulates vectors and matrices via this interface and, therefore, it can be used with any of the matrix representations provided by PETSc, including dense, sparse, and symmetric formats, either sequential or parallel.</p>
<p>The above statement must be reconsidered when using <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/EPS/EPS.html">EPS</a></span></code> in combination with <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/ST/ST.html">ST</a></span></code>. As explained in chapter <a class="reference internal" href="st.html#ch-st"><span class="std std-ref">ST: Spectral Transformation</span></a>, in many cases the operator associated with a spectral transformation not only consists in pure matrix-vector products but also other operations may be required as well, most notably a linear system solve (see Table <a class="reference internal" href="st.html#tab-op"><span class="std std-ref">Operators used in each spectral transformation mode</span></a>). In this case, the limitation is that there must be support for the requested operation for the selected matrix representation.</p>
<section id="shell-matrices">
<h3>Shell Matrices<a class="headerlink" href="#shell-matrices" title="Link to this heading">#</a></h3>
<p>In many applications, the matrices that define the eigenvalue problem are not available explicitly. Instead, the user knows a way of applying these matrices to a vector.</p>
<p>An intermediate case is when the matrices have some block structure and the different blocks are stored separately. There are numerous situations in which this occurs, such as the discretization of equations with a mixed finite-element scheme. An example is the eigenproblem arising in the stability analysis associated with Stokes problems,</p>
<div class="math notranslate nohighlight" id="equation-eq-stokes">
<span class="eqno">(1)<a class="headerlink" href="#equation-eq-stokes" title="Link to this equation">#</a></span>\[\begin{split}\begin{bmatrix}A & C\\C^* & 0\end{bmatrix}\begin{bmatrix}x\\p\end{bmatrix}
=\lambda\begin{bmatrix}B & 0\\0 & 0\end{bmatrix}\begin{bmatrix}x\\p\end{bmatrix}\;\;,\end{split}\]</div>
<p>where <span class="math notranslate nohighlight">\(x\)</span> and <span class="math notranslate nohighlight">\(p\)</span> denote the velocity and pressure fields. Similar formulations also appear in many other situations.</p>
<p>In some cases, these problems can be solved by reformulating them as a reduced-order standard or generalized eigensystem, in which the matrices are equal to certain operations of the blocks. These matrices are not computed explicitly to avoid losing sparsity.</p>
<p>All these cases can be easily handled in SLEPc by means of shell matrices. These are matrices that do not require explicit storage of the matrix entries. Instead, the user must provide subroutines for all the necessary matrix operations, typically only the application of the linear operator to a vector.</p>
<p>Shell matrices, also called matrix-free matrices, are created in PETSc with the function <a class="reference external" href="https://petsc.org/release/manualpages/Mat/MatCreateShell/" title="(in PETSc v3.24)"><span class="xref std std-doc">MatCreateShell</span></a>(). Then, the function <a class="reference external" href="https://petsc.org/release/manualpages/Mat/MatShellSetOperation/" title="(in PETSc v3.24)"><span class="xref std std-doc">MatShellSetOperation</span></a>() is used to provide any user-defined shell matrix operations (see the <a class="reference external" href="https://petsc.org/release/manual/mat/#application-specific-custom-matrices" target="_blank">PETSc Users Guide</a> for additional details). Several examples are available in SLEPc that illustrate how to solve a matrix-free eigenvalue problem.</p>
<p>In the simplest case, defining matrix-vector product operations (<code class="docutils notranslate"><span class="pre">MATOP_MULT</span></code>) is enough for using <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/EPS/EPS.html">EPS</a></span></code> with shell matrices. However, in the case of generalized problems, if matrix <span class="math notranslate nohighlight">\(B\)</span> is also a shell matrix then it may be necessary to define other operations in order to be able to solve the linear system successfully, for example <code class="docutils notranslate"><span class="pre">MATOP_GET_DIAGONAL</span></code> to use an iterative linear solver with Jacobi preconditioning. On the other hand, if the shift-and-invert <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/ST/ST.html">ST</a></span></code> is to be used, then in addition it may also be necessary to define <code class="docutils notranslate"><span class="pre">MATOP_SHIFT</span></code> or <code class="docutils notranslate"><span class="pre">MATOP_AXPY</span></code> (see section <a class="reference internal" href="st.html#sec-explicit"><span class="std std-ref">Explicit Computation of the Coefficient Matrix</span></a> for discussion).</p>
<p>In the case of <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/SVD/SVD.html">SVD</a></span></code>, both <span class="math notranslate nohighlight">\(A\)</span> and <span class="math notranslate nohighlight">\(A^*\)</span> are required to solve the problem. So when computing the SVD, the shell matrix needs to have the <code class="docutils notranslate"><span class="pre">MATOP_MULT_TRANSPOSE</span></code> operation (or <code class="docutils notranslate"><span class="pre">MATOP_MULT_HERMITIAN_TRANSPOSE</span></code> in the case of complex scalars) in addition to <code class="docutils notranslate"><span class="pre">MATOP_MULT</span></code>. Alternatively, if <span class="math notranslate nohighlight">\(A^*\)</span> is to be built explicitly, <code class="docutils notranslate"><span class="pre">MATOP_TRANSPOSE</span></code> is then the required operation. For details, see the manual page for <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/SVD/SVDSetImplicitTranspose.html">SVDSetImplicitTranspose</a>()</span></code>.</p>
</section>
</section>
<section id="sec-gpu">
<h2>GPU Computing<a class="headerlink" href="#sec-gpu" title="Link to this heading">#</a></h2>
<p>Support for graphics processing unit (GPU) computing is included in SLEPc. This is related to section <a class="reference internal" href="#sec-supported"><span class="std std-ref">Supported Matrix Types</span></a> because GPU support in PETSc is based on using special types of <a class="reference external" href="https://petsc.org/release/manualpages/Mat/Mat/" title="(in PETSc v3.24)"><span class="xref std std-doc">Mat</span></a> and <a class="reference external" href="https://petsc.org/release/manualpages/Vec/Vec/" title="(in PETSc v3.24)"><span class="xref std std-doc">Vec</span></a>. GPU support in SLEPc has been tested in all solver classes and most solvers should work, although the performance gain to be expected depends on the particular algorithm. Regarding PETSc, all iterative linear solvers are prepared to run on the GPU, but this is not the case for direct solvers and preconditioners. The user must not expect a spectacular performance boost, but in general moderate gains can be achieved by running the eigensolver on the GPU instead of the CPU (in some cases a 10-fold improvement).</p>
<p>SLEPc currently provides support for NVIDIA GPUs using CUDA<a class="footnote-reference brackets" href="#cuda" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> as well as AMD GPUs using HIP and ROCm<a class="footnote-reference brackets" href="#rocm" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>.</p>
<p>CUDA provides a C/C++ compiler with CUDA extensions as well as the cuBLAS and cuSPARSE libraries that implement dense and sparse linear algebra operations. For instance, to configure PETSc with GPU support in single precision arithmetic use the following options:</p>
<div class="highlight-console notranslate"><div class="highlight"><pre><span></span><span class="gp">$ </span>./configure<span class="w"> </span>--with-precision<span class="o">=</span>single<span class="w"> </span>--with-cuda
</pre></div>
</div>
<p><a class="reference external" href="https://petsc.org/release/manualpages/Vec/VECCUDA/" title="(in PETSc v3.24)"><span class="xref std std-doc">VECCUDA</span></a> and <a class="reference external" href="https://petsc.org/release/manualpages/Mat/MATAIJCUSPARSE/" title="(in PETSc v3.24)"><span class="xref std std-doc">MATAIJCUSPARSE</span></a> are currently the mechanism in PETSc to run a computation on the GPU. <a class="reference external" href="https://petsc.org/release/manualpages/Vec/VECCUDA/" title="(in PETSc v3.24)"><span class="xref std std-doc">VECCUDA</span></a> is a special type of <a class="reference external" href="https://petsc.org/release/manualpages/Vec/Vec/" title="(in PETSc v3.24)"><span class="xref std std-doc">Vec</span></a> whose array is mirrored in the GPU (and similarly for <a class="reference external" href="https://petsc.org/release/manualpages/Mat/MATAIJCUSPARSE/" title="(in PETSc v3.24)"><span class="xref std std-doc">MATAIJCUSPARSE</span></a>). PETSc takes care of keeping memory coherence between the two copies of the array, and performs the computation on the GPU when possible, trying to avoid unnecessary copies between the host and the device. For maximum efficiency, the user has to make sure that all vectors and matrices are of these types. If they are created in the standard way (<a class="reference external" href="https://petsc.org/release/manualpages/Vec/VecCreate/" title="(in PETSc v3.24)"><span class="xref std std-doc">VecCreate</span></a>() plus <a class="reference external" href="https://petsc.org/release/manualpages/Vec/VecSetFromOptions/" title="(in PETSc v3.24)"><span class="xref std std-doc">VecSetFromOptions</span></a>()) then it is sufficient to run the SLEPc program with</p>
<div class="highlight-console notranslate"><div class="highlight"><pre><span></span><span class="gp">$ </span>./program<span class="w"> </span>-vec_type<span class="w"> </span>cuda<span class="w"> </span>-mat_type<span class="w"> </span>aijcusparse
</pre></div>
</div>
<p>Note that the first option is unnecessary if no <a class="reference external" href="https://petsc.org/release/manualpages/Vec/Vec/" title="(in PETSc v3.24)"><span class="xref std std-doc">Vec</span></a> is created in the main program, or if all vectors are created via <a class="reference external" href="https://petsc.org/release/manualpages/Mat/MatCreateVecs/" title="(in PETSc v3.24)"><span class="xref std std-doc">MatCreateVecs</span></a>() from a <a class="reference external" href="https://petsc.org/release/manualpages/Mat/MATAIJCUSPARSE/" title="(in PETSc v3.24)"><span class="xref std std-doc">MATAIJCUSPARSE</span></a>.</p>
<p>For AMD GPUs the procedure is very similar, with HIP providing the compiler and ROCm providing the analogue libraries hipBLAS and hipSPARSE. To configure PETSc with HIP do:</p>
<div class="highlight-console notranslate"><div class="highlight"><pre><span></span><span class="gp">$ </span>./configure<span class="w"> </span>--with-precision<span class="o">=</span>single<span class="w"> </span>--with-hip
</pre></div>
</div>
<p>Then the equivalent vector and matrix types are <a class="reference external" href="https://petsc.org/release/manualpages/Vec/VECHIP/" title="(in PETSc v3.24)"><span class="xref std std-doc">VECHIP</span></a> and <a class="reference external" href="https://petsc.org/release/manualpages/Mat/MATAIJHIPSPARSE/" title="(in PETSc v3.24)"><span class="xref std std-doc">MATAIJHIPSPARSE</span></a>, which can be used in the command line with</p>
<div class="highlight-console notranslate"><div class="highlight"><pre><span></span><span class="gp">$ </span>./program<span class="w"> </span>-vec_type<span class="w"> </span>hip<span class="w"> </span>-mat_type<span class="w"> </span>aijhipsparse
</pre></div>
</div>
</section>
<section id="sec-shell">
<h2>Extending SLEPc<a class="headerlink" href="#sec-shell" title="Link to this heading">#</a></h2>
<p>Shell matrices, presented in section <a class="reference internal" href="#sec-supported"><span class="std std-ref">Supported Matrix Types</span></a>, are a simple mechanism of extensibility, in the sense that the package is extended with new user-defined matrix objects. Once the new matrix has been defined, it can be used by SLEPc in the same way as the rest of the matrices as long as the required operations are provided.</p>
<p>A similar mechanism is available in SLEPc also for extending the system incorporating new spectral transformations (<code class="docutils notranslate"><span class="pre"><a href="../../manualpages/ST/ST.html">ST</a></span></code>). This is done by using the <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/ST/STSHELL.html">STSHELL</a></span></code> spectral transformation type, in a similar way as shell matrices or shell preconditioners. In this case, the user defines how the operator is applied to a vector and optionally how the computed eigenvalues are transformed back to the solution of the original problem. This tool is intended for simple spectral transformations. For more sophisticated transformations, the user should register a new <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/ST/ST.html">ST</a></span></code> type (see below).</p>
<p>The following function:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../../manualpages/ST/STShellSetApply.html">STShellSetApply</a></span><span class="p">(</span><span class="n"><a href="../../manualpages/ST/ST.html">ST</a></span><span class="w"> </span><span class="n">st</span><span class="p">,</span><span class="n"><a href="../../manualpages/ST/STShellApplyFn.html">STShellApplyFn</a></span><span class="w"> </span><span class="o">*</span><span class="n">apply</span><span class="p">)</span>
</pre></div>
</div>
<p>has to be invoked after the creation of the <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/ST/ST.html">ST</a></span></code> object in order to provide a routine that applies the operator to a vector. And this function:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../../manualpages/ST/STShellSetBackTransform.html">STShellSetBackTransform</a></span><span class="p">(</span><span class="n"><a href="../../manualpages/ST/ST.html">ST</a></span><span class="w"> </span><span class="n">st</span><span class="p">,</span><span class="n"><a href="../../manualpages/ST/STShellBackTransformFn.html">STShellBackTransformFn</a></span><span class="w"> </span><span class="o">*</span><span class="n">backtr</span><span class="p">)</span>
</pre></div>
</div>
<p>can be used optionally to specify the routine for the back-transformation of eigenvalues. The two functions provided by the user can make use of any required user-defined information via a context that can be retrieved with <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/ST/STShellGetContext.html">STShellGetContext</a>()</span></code>. The example program <a class="reference external" href="https://slepc.upv.es/release/src/eps/tutorials/ex10.c.html" target="_blank">ex10.c</a> illustrates the use of shell transformations.</p>
<p>SLEPc further supports extensibility by allowing application programmers to code their own subroutines for unimplemented features such as new eigensolvers or new spectral transformations. It is possible to register these new methods to the system and use them as the rest of standard subroutines. For example, to implement a variant of the Subspace Iteration method, one could copy the SLEPc code associated with the <code class="docutils notranslate"><span class="pre">subspace</span></code> solver, modify it and register a new <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/EPS/EPS.html">EPS</a></span></code> type with the following line of code:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="n"><a href="../../manualpages/EPS/EPSRegister.html">EPSRegister</a></span><span class="p">(</span><span class="s">"newsubspace"</span><span class="p">,</span><span class="n">EPSCreate_NEWSUB</span><span class="p">);</span>
</pre></div>
</div>
<p>After this call, the new solver could be used in the same way as the rest of SLEPc solvers, e.g. with <code class="docutils notranslate"><span class="pre">-eps_type</span> <span class="pre">newsubspace</span></code> in the command line. A similar mechanism is available for registering new types of the other classes.</p>
</section>
<section id="directory-structure">
<h2>Directory Structure<a class="headerlink" href="#directory-structure" title="Link to this heading">#</a></h2>
<p>The directory structure of the SLEPc software is very similar to that of PETSc. The root directory of SLEPc contains the following directories:</p>
<ul class="simple">
<li><p><code class="docutils notranslate"><span class="pre">lib/slepc/conf</span></code> - Directory containing the base SLEPc makefile, to be included in application makefiles.</p></li>
<li><p><code class="docutils notranslate"><span class="pre">config</span></code> - SLEPc configuration scripts.</p></li>
<li><p><code class="docutils notranslate"><span class="pre">doc</span></code> - Directory containing the source from which all documentation of SLEPc is generated, including the manual and the website.</p></li>
<li><p><code class="docutils notranslate"><span class="pre">include</span></code> - All include files for SLEPc. The following subdirectories exist:</p>
<ul>
<li><p><code class="docutils notranslate"><span class="pre">slepc/finclude</span></code> - include files for Fortran programmers.</p></li>
<li><p><code class="docutils notranslate"><span class="pre">slepc/private</span></code> - include files containing implementation details, for developer use only.</p></li>
</ul>
</li>
<li><p><code class="docutils notranslate"><span class="pre">share/slepc</span></code> - Common files, including:</p>
<ul>
<li><p><code class="docutils notranslate"><span class="pre">datafiles</span></code> - data files used by some examples.</p></li>
</ul>
</li>
<li><p><code class="docutils notranslate"><span class="pre">src</span></code> - The source code for all SLEPc components, which currently includes:</p>
<ul>
<li><p><code class="docutils notranslate"><span class="pre">sys</span></code> - system-related routines and auxiliary classes <code class="docutils notranslate"><span class="pre">bv</span></code>, <code class="docutils notranslate"><span class="pre">ds</span></code>, <code class="docutils notranslate"><span class="pre">fn</span></code>, <code class="docutils notranslate"><span class="pre">rg</span></code>, <code class="docutils notranslate"><span class="pre">st</span></code>.</p></li>
<li><p><code class="docutils notranslate"><span class="pre">eps</span></code> - eigenvalue problem solver.</p></li>
<li><p><code class="docutils notranslate"><span class="pre">svd</span></code> - singular value decomposition solver.</p></li>
<li><p><code class="docutils notranslate"><span class="pre">pep</span></code> - polynomial eigenvalue problem solver.</p></li>
<li><p><code class="docutils notranslate"><span class="pre">nep</span></code> - nonlinear eigenvalue problem solver.</p></li>
<li><p><code class="docutils notranslate"><span class="pre">mfn</span></code> - matrix function.</p></li>
<li><p><code class="docutils notranslate"><span class="pre">lme</span></code> - linear matrix equations.</p></li>
<li><p><code class="docutils notranslate"><span class="pre">binding</span></code> - source code of slepc4py</p></li>
</ul>
</li>
<li><p><code class="docutils notranslate"><span class="pre">$PETSC_ARCH</span></code> - For each value of <code class="docutils notranslate"><span class="pre">PETSC_ARCH</span></code>, a directory exists containing files generated during installation of that particular configuration. Among others, it includes the following subdirectories:</p>
<ul>
<li><p><code class="docutils notranslate"><span class="pre">lib</span></code> - all the generated libraries.</p></li>
<li><p><code class="docutils notranslate"><span class="pre">lib/slepc/conf</span></code> - configuration parameters and log files.</p></li>
<li><p><code class="docutils notranslate"><span class="pre">include</span></code> - automatically generated include files, such as Fortran <code class="docutils notranslate"><span class="pre">*.mod</span></code> files.</p></li>
</ul>
</li>
</ul>
<p>Each SLEPc source code component directory has the following subdirectories:</p>
<ul class="simple">
<li><p><code class="docutils notranslate"><span class="pre">interface</span></code>: The calling sequences for the abstract interface to the components. Code here does not know about particular implementations.</p></li>
<li><p><code class="docutils notranslate"><span class="pre">impls</span></code>: Source code for the different implementations.</p></li>
<li><p><code class="docutils notranslate"><span class="pre">tutorials</span></code>: Example programs intended for learning to use SLEPc.</p></li>
<li><p><code class="docutils notranslate"><span class="pre">tests</span></code>: Example programs used by testing scripts.</p></li>
</ul>
</section>
<section id="sec-wrap">
<h2>Wrappers to External Libraries<a class="headerlink" href="#sec-wrap" title="Link to this heading">#</a></h2>
<p>SLEPc interfaces to several external libraries for the solution of eigenvalue problems. This section provides a short description of each of these packages as well as some hints for using them with SLEPc, including pointers to the respective websites from which the software can be downloaded. The description may also include method-specific parameters, that can be set in the same way as other SLEPc options, either procedurally or via the command-line.</p>
<p>In order to use SLEPc together with an external library such as ARPACK, one needs to do the following.</p>
<ol class="arabic simple">
<li><p>Install the external software, with the same compilers and MPI that will be used for PETSc/SLEPc.</p></li>
<li><p>Enable the utilization of the external software from SLEPc by specifying configure options as explained in section <a class="reference internal" href="intro.html#sec-opt-inst"><span class="std std-ref">Configuration Options</span></a>.</p></li>
<li><p>Build the SLEPc libraries.</p></li>
<li><p>Use the runtime option <code class="docutils notranslate"><span class="pre">-eps_type</span> <span class="pre"><type></span></code> to select the solver.</p></li>
</ol>
<p>Exceptions to the above rule are LAPACK, which should be enabled during PETSc’s configuration, and BLOPEX, that must be installed with <code class="docutils notranslate"><span class="pre">--download-blopex</span></code> in SLEPc’s configure. Other packages also support the download option.</p>
<section id="list-of-external-libraries">
<h3>List of External Libraries<a class="headerlink" href="#list-of-external-libraries" title="Link to this heading">#</a></h3>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>This list might be incomplete. Check the output of <code class="docutils notranslate"><span class="pre">./configure</span> <span class="pre">--help</span></code> for other libraries not listed here.</p>
</div>
<section id="lapack">
<h4>LAPACK<a class="headerlink" href="#lapack" title="Link to this heading">#</a></h4>
<p><a class="reference external" href="https://www.netlib.org/lapack" target="_blank">https://www.netlib.org/lapack</a></p>
<p>LAPACK <span id="id3">[<a class="reference internal" href="../../manualpages/EPS/EPSLAPACK.html#id3" title="E. Anderson, Z. Bai, C. Bischof, L. S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen. LAPACK Users' Guide. Society for Industrial and Applied Mathematics, Philadelphia, PA, third edition, 1999.">Anderson <em>et al.</em>, 1999</a>]</span> is a software package for the solution of many different dense linear algebra problems, including various types of eigenvalue problems and singular value decompositions. SLEPc explicitly creates the operator matrix in dense form and then the appropriate LAPACK driver routine is invoked. Therefore, this interface should be used only for testing and validation purposes and not in a production code. The operator matrix is created by applying the operator to the columns of the identity matrix.</p>
<p><strong>Installation</strong>: PETSc already depends on LAPACK. The SLEPc interface to LAPACK can be used directly. If SLEPc’s <code class="docutils notranslate"><span class="pre">configure</span></code> script complains about missing LAPACK functions, then reconfigure PETSc with option <code class="docutils notranslate"><span class="pre">--download-f2cblaslapack</span></code>.</p>
</section>
<section id="arpack">
<h4>ARPACK<a class="headerlink" href="#arpack" title="Link to this heading">#</a></h4>
<p><a class="reference external" href="https://www.arpack.org" target="_blank">https://www.arpack.org</a></p>
<p><a class="github reference external" href="https://github.com/opencollab/arpack-ng" target="_blank">opencollab/arpack-ng</a></p>
<p>ARPACK <span id="id4">[<a class="reference internal" href="../../manualpages/EPS/EPSARPACK.html#id8" title="R. B. Lehoucq, D. C. Sorensen, and C. Yang. ARPACK Users' Guide, Solution of Large-Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods. Society for Industrial and Applied Mathematics, Philadelphia, PA, 1998.">Lehoucq <em>et al.</em>, 1998</a>, <a class="reference internal" href="#id21" title="K. J. Maschhoff and D. C. Sorensen. PARPACK: an efficient portable large scale eigenvalue package for distributed memory parallel architectures. Lect. Notes Comp. Sci., 1184:478–486, 1996.">Maschhoff and Sorensen, 1996</a>]</span> is a software package for the computation of a few eigenvalues and corresponding eigenvectors of a general <span class="math notranslate nohighlight">\(n\times n\)</span> matrix <span class="math notranslate nohighlight">\(A\)</span>. It is most appropriate for large sparse matrices. ARPACK is based upon an algorithmic variant of the Arnoldi process called the Implicitly Restarted Arnoldi Method (IRAM). When the matrix <span class="math notranslate nohighlight">\(A\)</span> is symmetric it reduces to a variant of the Lanczos process called the Implicitly Restarted Lanczos Method (IRLM). These variants may be viewed as a synthesis of the Arnoldi/Lanczos process with the Implicitly Shifted QR technique that is suitable for large scale problems. It can be used for standard and generalized eigenvalue problems, both in real and complex arithmetic. It is implemented in Fortran 77 and it is based on the reverse communication interface. A parallel version, PARPACK, is available with support for both MPI and BLACS.</p>
<p><strong>Installation</strong>: To install ARPACK we recommend using the <em>arpack-ng</em> distribution, available in <code class="docutils notranslate"><span class="pre">github.com</span></code>, that supports <code class="docutils notranslate"><span class="pre">configure</span></code>+<code class="docutils notranslate"><span class="pre">make</span></code> for installation. Also, SLEPc’s <code class="docutils notranslate"><span class="pre">configure</span></code> allows to download this version automatically via the <code class="docutils notranslate"><span class="pre">--download-arpack</span></code> option. It is also possible to configure SLEPc with the serial version of ARPACK. For this, you have to configure PETSc with the option <code class="docutils notranslate"><span class="pre">--with-mpi=0</span></code>.</p>
</section>
<section id="primme">
<h4>PRIMME<a class="headerlink" href="#primme" title="Link to this heading">#</a></h4>
<p><a class="reference external" href="https://www.cs.wm.edu/~andreas/software" target="_blank">https://www.cs.wm.edu/~andreas/software</a></p>
<p>PRIMME <span id="id5">[<a class="reference internal" href="../../manualpages/EPS/EPSPRIMMESetBlockSize.html#id25" title="A. Stathopoulos and J. R. McCombs. PRIMME: PReconditioned Iterative MultiMethod Eigensolver: methods and software description. ACM Trans. Math. Software, 37(2):21:1–21:30, 2010. doi:10.1145/1731022.1731031.">Stathopoulos and McCombs, 2010</a>]</span> is a C library for finding a number of eigenvalues and their corresponding eigenvectors of a real symmetric (or complex Hermitian) matrix. This library provides a multimethod eigensolver, based on Davidson/Jacobi-Davidson. Particular methods include GD+1, JDQMR, and LOBPCG. It supports preconditioning as well as the computation of interior eigenvalues.</p>
<p><strong>Installation</strong>: Type <code class="docutils notranslate"><span class="pre">make</span> <span class="pre">lib</span></code> after customizing the file <code class="docutils notranslate"><span class="pre">Make_flags</span></code> appropriately. Alternatively, the <code class="docutils notranslate"><span class="pre">--download-primme</span></code> option is also available in SLEPc’s <code class="docutils notranslate"><span class="pre">configure</span></code>.</p>
<p><strong>Specific options</strong>: Since PRIMME contains preconditioned solvers, the SLEPc interface uses <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/ST/STPRECOND.html">STPRECOND</a></span></code>, as described in section <a class="reference internal" href="st.html#sec-precond"><span class="std std-ref">Preconditioner</span></a>. The SLEPc interface to this package allows the user to specify the maximum allowed block size with the function <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/EPS/EPSPRIMMESetBlockSize.html">EPSPRIMMESetBlockSize</a>()</span></code> or at run time with the option <code class="docutils notranslate"><span class="pre">-eps_primme_blocksize</span> <span class="pre"><size></span></code>. For changing the particular algorithm within PRIMME, use the function <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/EPS/EPSPRIMMESetMethod.html">EPSPRIMMESetMethod</a>()</span></code>. PRIMME also provides a solver for the singular value decomposition that is interfaced in SLEPc’s <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/SVD/SVD.html">SVD</a></span></code>, see <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/SVD/SVDPRIMMESetMethod.html">SVDPRIMMESetMethod</a>()</span></code>.</p>
</section>
<section id="evsl">
<h4>EVSL<a class="headerlink" href="#evsl" title="Link to this heading">#</a></h4>
<p><a class="reference external" href="https://www-users.cse.umn.edu/~saad/software/EVSL/" target="_blank">https://www-users.cse.umn.edu/~saad/software/EVSL/</a></p>
<p>EVSL <span id="id6">[<a class="reference internal" href="../../manualpages/EPS/EPSEVSLSetSlices.html#id49" title="R. Li, Y. Xi, L. Erlandson, and Y. Saad. The eigenvalues slicing library (EVSL): algorithms, implementation, and software. SIAM J. Sci. Comput., 41(4):C393–C415, 2019. doi:10.1137/18M1170935.">Li <em>et al.</em>, 2019</a>]</span> is a sequential library that implements methods for computing all eigenvalues located in a given interval for real symmetric (standard or generalized) eigenvalue problems. Currently SLEPc only supports standard problems.</p>
<p><strong>Installation</strong>: The option <code class="docutils notranslate"><span class="pre">--download-evsl</span></code> is available in SLEPc’s <code class="docutils notranslate"><span class="pre">configure</span></code> for easy installation. Alternatively, one can use an already installed version.</p>
</section>
<section id="blopex">
<h4>BLOPEX<a class="headerlink" href="#blopex" title="Link to this heading">#</a></h4>
<p><a class="github reference external" href="https://github.com/lobpcg/blopex" target="_blank">lobpcg/blopex</a></p>
<p>BLOPEX <span id="id7">[<a class="reference internal" href="../../manualpages/EPS/EPSBLOPEX.html#id17" title="A. V. Knyazev, M. E. Argentati, I. Lashuk, and E. E. Ovtchinnikov. Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in HYPRE and PETSc. SIAM J. Sci. Comput., 29(5):2224–2239, 2007. doi:10.1137/060661624.">Knyazev <em>et al.</em>, 2007</a>]</span> is a package that implements the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) method for computing several extreme eigenpairs of symmetric positive generalized eigenproblems. Numerical comparisons suggest that this method is a genuine analog for eigenproblems of the standard preconditioned conjugate gradient method for symmetric linear systems.</p>
<p><strong>Installation</strong>: In order to use BLOPEX from SLEPc, it necessary to install it during SLEPc’s configuration: <code class="docutils notranslate"><span class="pre">./configure</span> <span class="pre">--download-blopex</span></code>.</p>
<p><strong>Specific options</strong>: Since BLOPEX contains preconditioned solvers, the SLEPc interface uses <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/ST/STPRECOND.html">STPRECOND</a></span></code>, as described in section <a class="reference internal" href="st.html#sec-precond"><span class="std std-ref">Preconditioner</span></a>.</p>
</section>
<section id="scalapack">
<h4>ScaLAPACK<a class="headerlink" href="#scalapack" title="Link to this heading">#</a></h4>
<p><a class="reference external" href="https://www.netlib.org/scalapack" target="_blank">https://www.netlib.org/scalapack</a></p>
<p>ScaLAPACK <span id="id8">[<a class="reference internal" href="../../manualpages/EPS/EPSSCALAPACK.html#id6" title="L. S. Blackford, J. Choi, A. Cleary, E. D'Azevedo, J. Demmel, I. Dhillon, J. Dongarra, S. Hammarling, G. Henry, A. Petitet, K. Stanley, D. Walker, and R. C. Whaley. ScaLAPACK Users' Guide. Society for Industrial and Applied Mathematics, Philadelphia, PA, 1997.">Blackford <em>et al.</em>, 1997</a>]</span> is a library of high-performance linear algebra routines for parallel distributed memory machines. It contains eigensolvers for dense Hermitian eigenvalue problems, as well as solvers for the (dense) SVD.</p>
<p><strong>Installation</strong>: For using ScaLAPACK from SLEPc it is necessary to select it during configuration of PETSc.</p>
</section>
<section id="elpa">
<h4>ELPA<a class="headerlink" href="#elpa" title="Link to this heading">#</a></h4>
<p><a class="reference external" href="https://elpa.mpcdf.mpg.de/" target="_blank">https://elpa.mpcdf.mpg.de/</a></p>
<p>ELPA <span id="id9">[<a class="reference internal" href="../../manualpages/EPS/EPSELPA.html#id50" title="T. Auckenthaler, V. Blum, H.-J. Bungartz, T. Huckle, R. Johanni, L. Krämer, B. Lang, H. Lederer, and P.R. Willems. Parallel solution of partial symmetric eigenvalue problems from electronic structure calculations. Parallel Comput., 37(12):783–794, 2011. doi:10.1016/j.parco.2011.05.002.">Auckenthaler <em>et al.</em>, 2011</a>]</span> is a high-performance library for the parallel solution of dense symmetric (or Hermitian) eigenvalue problems on distributed memory computers. It uses a ScaLAPACK-compatible matrix distribution.</p>
<p><strong>Installation</strong>: The SLEPc wrapper to ELPA can be activated at configure time with the option <code class="docutils notranslate"><span class="pre">--download_elpa</span></code>, in which case ScaLAPACK support must have been enabled during the configuration of PETSc.</p>
</section>
<section id="ksvd">
<h4>KSVD<a class="headerlink" href="#ksvd" title="Link to this heading">#</a></h4>
<p><a class="github reference external" href="https://github.com/ecrc/ksvd/" target="_blank">ecrc/ksvd</a></p>
<p>KSVD <span id="id10">[<a class="reference internal" href="../../manualpages/SVD/SVDKSVDPolarMethod.html#id51" title="D. Sukkari, H. Ltaief, A. Esposito, and D. Keyes. A QDWH-based SVD software framework on distributed-memory manycore systems. ACM Trans. Math. Software, 2019. doi:10.1145/3309548.">Sukkari <em>et al.</em>, 2019</a>]</span> is a high performance software framework for computing a dense SVD on distributed-memory manycore systems. The KSVD solver relies on the polar decomposition (PD) based on the QR Dynamically-Weighted Halley (QDWH) and ZOLO-PD algorithms.</p>
<p><strong>Installation</strong>: The option <code class="docutils notranslate"><span class="pre">--download-ksvd</span></code> is available in SLEPc’s <code class="docutils notranslate"><span class="pre">configure</span></code> for easy installation, which in turn requires adding <code class="docutils notranslate"><span class="pre">--download-polar</span></code> and <code class="docutils notranslate"><span class="pre">--download-elpa</span></code>.</p>
</section>
<section id="elemental">
<h4>ELEMENTAL<a class="headerlink" href="#elemental" title="Link to this heading">#</a></h4>
<p><a class="github reference external" href="https://github.com/elemental/Elemental" target="_blank">elemental/Elemental</a></p>
<p>ELEMENTAL <span id="id11">[<a class="reference internal" href="../../manualpages/EPS/EPSELEMENTAL.html#id52" title="J. Poulson, B. Marker, R. A. van de Geijn, J. R. Hammond, and N. A. Romero. Elemental: a new framework for distributed memory dense matrix computations. ACM Trans. Math. Software, 2013. doi:10.1145/2427023.2427030.">Poulson <em>et al.</em>, 2013</a>]</span> is a distributed-memory, dense and sparse-direct linear algebra package. It contains eigensolvers for dense Hermitian eigenvalue problems, as well as solvers for the SVD.</p>
<p><strong>Installation</strong>: For using ELEMENTAL from SLEPc it is necessary to select it during configuration of PETSc.</p>
</section>
<section id="feast">
<h4>FEAST<a class="headerlink" href="#feast" title="Link to this heading">#</a></h4>
<p><a class="reference external" href="https://feast-solver.org/" target="_blank">https://feast-solver.org/</a></p>
<p>FEAST <span id="id12">[<a class="reference internal" href="../../manualpages/EPS/EPSFEAST.html#id29" title="E. Polizzi. Density-matrix-based algorithm for solving eigenvalue problems. Phys. Rev. B, 79(11):115112, 2009. doi:10.1103/PhysRevB.79.115112.">Polizzi, 2009</a>]</span> is a numerical library for solving the standard or generalized symmetric eigenvalue problem, and obtaining all the eigenvalues and eigenvectors within a given search interval. It is based on an innovative fast and stable numerical algorithm which deviates fundamentally from the traditional Krylov subspace based iterations or Davidson-Jacobi techniques. The FEAST algorithm takes its inspiration from the density-matrix representation and contour integration technique in quantum mechanics. Latest versions also support non-symmetric problems.</p>
<p><strong>Installation</strong>: We only support the FEAST implementation included in Intel MKL. For using it from SLEPc it is necessary to configure PETSc with MKL by adding the corresponding option, e.g., <code class="docutils notranslate"><span class="pre">--with-blas-lapack-dir=$MKLROOT</span></code>.</p>
<p><strong>Specific options</strong>: The SLEPc interface to FEAST allows the user to specify the number of contour integration points with the function <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/EPS/EPSFEASTSetNumPoints.html">EPSFEASTSetNumPoints</a>()</span></code> or at run time with the option <code class="docutils notranslate"><span class="pre">-eps_feast_num_points</span> <span class="pre"><n></span></code>.</p>
</section>
<section id="chase">
<h4>CHASE<a class="headerlink" href="#chase" title="Link to this heading">#</a></h4>
<p><a class="github reference external" href="https://github.com/ChASE-library/ChASE" target="_blank">ChASE-library/ChASE</a></p>
<p>CHASE <span id="id13">[<a class="reference internal" href="../../manualpages/EPS/EPSCHASESetDegree.html#id53" title="J. Winkelmann, P. Springer, and E. Di Napoli. ChASE: Chebyshev accelerated subspace iteration eigensolver for sequences of hermitian eigenvalue problems. ACM Trans. Math. Software, 2019. doi:10.1145/3313828.">Winkelmann <em>et al.</em>, 2019</a>]</span> is a modern and scalable library based on subspace iteration with polynomial acceleration to solve dense Hermitian (symmetric) algebraic eigenvalue problems, especially solving dense Hermitian eigenproblems arranged in a sequence. Novel to ChASE is the computation of the spectral estimates that enter in the filter and an optimization of the polynomial degree that further reduces the necessary floating-point operations.</p>
<p><strong>Installation</strong>: Currently, the CHASE interface in SLEPc is based on the MPI version with block-cyclic distribution, i.e., ScaLAPACK matrix storage, so it is necessary to enable ScaLAPACK during configuration of PETSc.</p>
</section>
<section id="slicot">
<h4>SLICOT<a class="headerlink" href="#slicot" title="Link to this heading">#</a></h4>
<p><a class="reference external" href="https://www.slicot.org" target="_blank">https://www.slicot.org</a></p>
<p>SLICOT provides Fortran 77 implementations of numerical algorithms for computations in systems and control theory. In SLEPc, they are used in the <code class="docutils notranslate"><span class="pre"><a href="../../manualpages/LME/LME.html">LME</a></span></code> module only, for solving Lyapunov equations of small size.</p>
<p><strong>Installation</strong>: The option <code class="docutils notranslate"><span class="pre">--download-slicot</span></code> is available in SLEPc’s <code class="docutils notranslate"><span class="pre">configure</span></code> for easy installation.</p>
</section>
</section>
</section>
<section id="sec-fortran">
<h2>Fortran Interface<a class="headerlink" href="#sec-fortran" title="Link to this heading">#</a></h2>
<p>SLEPc provides an interface for Fortran programmers, very much like PETSc. As in the case of PETSc, there are slight differences between the C and Fortran SLEPc interfaces, due to differences in Fortran syntax. For instance, the error checking variable is the final argument of all the routines in the Fortran interface, in contrast to the C convention of providing the error variable as the routine’s return value.</p>
<p>A detailed discussion can be found in the <a class="reference external" href="https://petsc.org/release/manual/fortran/" target="_blank">PETSc Users Guide</a>.</p>
<p>The following is a Fortran example. It is the Fortran equivalent of the program given in section <a class="reference internal" href="intro.html#sec-simpleex"><span class="std std-ref">Simple SLEPc Example</span></a> and can be found in <code class="docutils notranslate"><span class="pre">${SLEPC_DIR}/src/eps/tutorials</span></code> (file <code class="docutils notranslate"><span class="pre">ex1f.F90</span></code>).</p>
<div class="highlight-fortran notranslate" id="ex1f-f90"><div class="highlight"><pre><span></span><span class="w"> </span><span class="k">program </span><span class="n">main</span>
<span class="cp">#include <slepc/finclude/slepceps.h></span>
<span class="w"> </span><span class="k">use </span><span class="n">slepceps</span>
<span class="w"> </span><span class="k">implicit none</span>
<span class="c">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</span>
<span class="c">! Declarations</span>
<span class="c">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</span>
<span class="c">!</span>
<span class="c">! Variables:</span>
<span class="c">! A operator matrix</span>
<span class="c">! eps eigenproblem solver context</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Mat/Mat/">Mat</a></span><span class="w"> </span><span class="n">A</span>
<span class="w"> </span><span class="n"><a href="../../manualpages/EPS/EPS.html">EPS</a></span><span class="w"> </span><span class="n">eps</span>
<span class="w"> </span><span class="n"><a href="../../manualpages/EPS/EPSType.html">EPSType</a></span><span class="w"> </span><span class="n">tname</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscInt/">PetscInt</a></span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">Istart</span><span class="p">,</span><span class="w"> </span><span class="n">Iend</span><span class="p">,</span><span class="w"> </span><span class="n">one</span><span class="p">,</span><span class="w"> </span><span class="n">two</span><span class="p">,</span><span class="w"> </span><span class="n">three</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscInt/">PetscInt</a></span><span class="w"> </span><span class="n">nev</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscInt/">PetscInt</a></span><span class="w"> </span><span class="n">row</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="n">col</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscMPIInt/">PetscMPIInt</a></span><span class="w"> </span><span class="n">rank</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscErrorCode/">PetscErrorCode</a></span><span class="w"> </span><span class="n">ierr</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscBool/">PetscBool</a></span><span class="w"> </span><span class="n">flg</span><span class="p">,</span><span class="w"> </span><span class="n">terse</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscScalar/">PetscScalar</a></span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<span class="c">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</span>
<span class="c">! Beginning of program</span>
<span class="c">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</span>
<span class="w"> </span><span class="n">one</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span>
<span class="w"> </span><span class="n">two</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span>
<span class="w"> </span><span class="n">three</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="../../manualpages/Sys/SlepcInitialize.html">SlepcInitialize</a></span><span class="p">(</span><span class="n">PETSC_NULL_CHARACTER</span><span class="p">,</span><span class="s2">"ex1f test"</span><span class="o">//</span><span class="nb">c_new_line</span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ierr</span><span class="w"> </span><span class="p">.</span><span class="n">ne</span><span class="p">.</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="k">then</span>
<span class="k"> print</span><span class="o">*</span><span class="p">,</span><span class="s1">'<a href="../../manualpages/Sys/SlepcInitialize.html">SlepcInitialize</a> failed'</span>
<span class="w"> </span><span class="k">stop</span>
<span class="k"> endif</span>
<span class="k"> </span><span class="n">PetscCallMPIA</span><span class="p">(</span><span class="n"><a href="http://www.mpich.org/static/docs/latest/www3/MPI_Comm_rank.html#MPI_Comm_rank">MPI_Comm_rank</a></span><span class="p">(</span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PETSC_COMM_WORLD/">PETSC_COMM_WORLD</a></span><span class="p">,</span><span class="n">rank</span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">30</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscOptionsGetInt/">PetscOptionsGetInt</a></span><span class="p">(</span><span class="n">PETSC_NULL_OPTIONS</span><span class="p">,</span><span class="n">PETSC_NULL_CHARACTER</span><span class="p">,</span><span class="s1">'-n'</span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="n">flg</span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">rank</span><span class="w"> </span><span class="p">.</span><span class="n">eq</span><span class="p">.</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="k">then</span>
<span class="k"> write</span><span class="p">(</span><span class="o">*</span><span class="p">,</span><span class="mi">100</span><span class="p">)</span><span class="w"> </span><span class="n">n</span>
<span class="w"> </span><span class="k">endif</span>
<span class="k"> </span><span class="mi">100</span><span class="w"> </span><span class="k">format</span><span class="w"> </span><span class="p">(</span><span class="o">/</span><span class="s1">'1-D Laplacian Eigenproblem, n ='</span><span class="p">,</span><span class="n">I4</span><span class="p">,</span><span class="s1">' (Fortran)'</span><span class="p">)</span>
<span class="c">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</span>
<span class="c">! Compute the operator matrix that defines the eigensystem, Ax=kx</span>
<span class="c">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="https://petsc.org/release/manualpages/Mat/MatCreate/">MatCreate</a></span><span class="p">(</span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PETSC_COMM_WORLD/">PETSC_COMM_WORLD</a></span><span class="p">,</span><span class="n">A</span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="https://petsc.org/release/manualpages/Mat/MatSetSizes/">MatSetSizes</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PETSC_DECIDE/">PETSC_DECIDE</a></span><span class="p">,</span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PETSC_DECIDE/">PETSC_DECIDE</a></span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="https://petsc.org/release/manualpages/Mat/MatSetFromOptions/">MatSetFromOptions</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="https://petsc.org/release/manualpages/Mat/MatGetOwnershipRange/">MatGetOwnershipRange</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n">Istart</span><span class="p">,</span><span class="n">Iend</span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">Istart</span><span class="w"> </span><span class="p">.</span><span class="n">eq</span><span class="p">.</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="k">then</span>
<span class="k"> </span><span class="n">row</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<span class="w"> </span><span class="n">col</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<span class="w"> </span><span class="n">col</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span>
<span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span>
<span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="mf">1.0</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="https://petsc.org/release/manualpages/Mat/MatSetValues/">MatSetValues</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n">one</span><span class="p">,</span><span class="n">row</span><span class="p">,</span><span class="n">two</span><span class="p">,</span><span class="n">col</span><span class="p">,</span><span class="n">val</span><span class="p">,</span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/INSERT_VALUES/">INSERT_VALUES</a></span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="n">Istart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Istart</span><span class="o">+</span><span class="mi">1</span>
<span class="w"> </span><span class="k">endif</span>
<span class="k"> if</span><span class="w"> </span><span class="p">(</span><span class="n">Iend</span><span class="w"> </span><span class="p">.</span><span class="n">eq</span><span class="p">.</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="k">then</span>
<span class="k"> </span><span class="n">row</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="o">-</span><span class="mi">1</span>
<span class="w"> </span><span class="n">col</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="o">-</span><span class="mi">2</span>
<span class="w"> </span><span class="n">col</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="o">-</span><span class="mi">1</span>
<span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="mf">1.0</span>
<span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="https://petsc.org/release/manualpages/Mat/MatSetValues/">MatSetValues</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n">one</span><span class="p">,</span><span class="n">row</span><span class="p">,</span><span class="n">two</span><span class="p">,</span><span class="n">col</span><span class="p">,</span><span class="n">val</span><span class="p">,</span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/INSERT_VALUES/">INSERT_VALUES</a></span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="n">Iend</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Iend</span><span class="o">-</span><span class="mi">1</span>
<span class="w"> </span><span class="k">endif</span>
<span class="k"> </span><span class="n">val</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="mf">1.0</span>
<span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span>
<span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="mf">1.0</span>
<span class="w"> </span><span class="k">do </span><span class="n">i</span><span class="o">=</span><span class="n">Istart</span><span class="p">,</span><span class="n">Iend</span><span class="o">-</span><span class="mi">1</span>
<span class="w"> </span><span class="n">row</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span>
<span class="w"> </span><span class="n">col</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="o">-</span><span class="mi">1</span>
<span class="w"> </span><span class="n">col</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span>
<span class="w"> </span><span class="n">col</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="o">+</span><span class="mi">1</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="https://petsc.org/release/manualpages/Mat/MatSetValues/">MatSetValues</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n">one</span><span class="p">,</span><span class="n">row</span><span class="p">,</span><span class="n">three</span><span class="p">,</span><span class="n">col</span><span class="p">,</span><span class="n">val</span><span class="p">,</span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/INSERT_VALUES/">INSERT_VALUES</a></span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="k">enddo</span>
<span class="k"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="https://petsc.org/release/manualpages/Mat/MatAssemblyBegin/">MatAssemblyBegin</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n">MAT_FINAL_ASSEMBLY</span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="https://petsc.org/release/manualpages/Mat/MatAssemblyEnd/">MatAssemblyEnd</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n">MAT_FINAL_ASSEMBLY</span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="c">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</span>
<span class="c">! Create the eigensolver and display info</span>
<span class="c">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</span>
<span class="c">! ** Create eigensolver context</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="../../manualpages/EPS/EPSCreate.html">EPSCreate</a></span><span class="p">(</span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PETSC_COMM_WORLD/">PETSC_COMM_WORLD</a></span><span class="p">,</span><span class="n">eps</span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="c">! ** Set operators. In this case, it is a standard eigenvalue problem</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="../../manualpages/EPS/EPSSetOperators.html">EPSSetOperators</a></span><span class="p">(</span><span class="n">eps</span><span class="p">,</span><span class="n">A</span><span class="p">,</span><span class="n">PETSC_NULL_MAT</span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="../../manualpages/EPS/EPSSetProblemType.html">EPSSetProblemType</a></span><span class="p">(</span><span class="n">eps</span><span class="p">,</span><span class="n"><a href="../../manualpages/EPS/EPS_HEP.html">EPS_HEP</a></span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="c">! ** Set solver parameters at runtime</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="../../manualpages/EPS/EPSSetFromOptions.html">EPSSetFromOptions</a></span><span class="p">(</span><span class="n">eps</span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="c">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</span>
<span class="c">! Solve the eigensystem</span>
<span class="c">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="../../manualpages/EPS/EPSSolve.html">EPSSolve</a></span><span class="p">(</span><span class="n">eps</span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="c">! ** Optional: Get some information from the solver and display it</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="../../manualpages/EPS/EPSGetType.html">EPSGetType</a></span><span class="p">(</span><span class="n">eps</span><span class="p">,</span><span class="n">tname</span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">rank</span><span class="w"> </span><span class="p">.</span><span class="n">eq</span><span class="p">.</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="k">then</span>
<span class="k"> write</span><span class="p">(</span><span class="o">*</span><span class="p">,</span><span class="mi">120</span><span class="p">)</span><span class="w"> </span><span class="n">tname</span>
<span class="w"> </span><span class="k">endif</span>
<span class="k"> </span><span class="mi">120</span><span class="w"> </span><span class="k">format</span><span class="w"> </span><span class="p">(</span><span class="s1">' Solution method: '</span><span class="p">,</span><span class="n">A</span><span class="p">)</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="../../manualpages/EPS/EPSGetDimensions.html">EPSGetDimensions</a></span><span class="p">(</span><span class="n">eps</span><span class="p">,</span><span class="n">nev</span><span class="p">,</span><span class="n">PETSC_NULL_INTEGER</span><span class="p">,</span><span class="n">PETSC_NULL_INTEGER</span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">rank</span><span class="w"> </span><span class="p">.</span><span class="n">eq</span><span class="p">.</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="k">then</span>
<span class="k"> write</span><span class="p">(</span><span class="o">*</span><span class="p">,</span><span class="mi">130</span><span class="p">)</span><span class="w"> </span><span class="n">nev</span>
<span class="w"> </span><span class="k">endif</span>
<span class="k"> </span><span class="mi">130</span><span class="w"> </span><span class="k">format</span><span class="w"> </span><span class="p">(</span><span class="s1">' Number of requested eigenvalues:'</span><span class="p">,</span><span class="n">I4</span><span class="p">)</span>
<span class="c">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</span>
<span class="c">! Display solution and clean up</span>
<span class="c">! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</span>
<span class="c">! ** show detailed info unless -terse option is given by user</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscOptionsHasName/">PetscOptionsHasName</a></span><span class="p">(</span><span class="n">PETSC_NULL_OPTIONS</span><span class="p">,</span><span class="n">PETSC_NULL_CHARACTER</span><span class="p">,</span><span class="s1">'-terse'</span><span class="p">,</span><span class="n">terse</span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">terse</span><span class="p">)</span><span class="w"> </span><span class="k">then</span>
<span class="k"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="../../manualpages/EPS/EPSErrorView.html">EPSErrorView</a></span><span class="p">(</span><span class="n">eps</span><span class="p">,</span><span class="n"><a href="../../manualpages/EPS/EPSErrorType.html">EPS_ERROR_RELATIVE</a></span><span class="p">,</span><span class="n">PETSC_NULL_VIEWER</span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="k">else</span>
<span class="k"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="https://petsc.org/release/manualpages/Viewer/PetscViewerPushFormat/">PetscViewerPushFormat</a></span><span class="p">(</span><span class="n"><a href="https://petsc.org/release/manualpages/Viewer/PETSC_VIEWER_STDOUT_WORLD/">PETSC_VIEWER_STDOUT_WORLD</a></span><span class="p">,</span><span class="n">PETSC_VIEWER_ASCII_INFO_DETAIL</span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="../../manualpages/EPS/EPSConvergedReasonView.html">EPSConvergedReasonView</a></span><span class="p">(</span><span class="n">eps</span><span class="p">,</span><span class="n"><a href="https://petsc.org/release/manualpages/Viewer/PETSC_VIEWER_STDOUT_WORLD/">PETSC_VIEWER_STDOUT_WORLD</a></span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="../../manualpages/EPS/EPSErrorView.html">EPSErrorView</a></span><span class="p">(</span><span class="n">eps</span><span class="p">,</span><span class="n"><a href="../../manualpages/EPS/EPSErrorType.html">EPS_ERROR_RELATIVE</a></span><span class="p">,</span><span class="n"><a href="https://petsc.org/release/manualpages/Viewer/PETSC_VIEWER_STDOUT_WORLD/">PETSC_VIEWER_STDOUT_WORLD</a></span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="https://petsc.org/release/manualpages/Viewer/PetscViewerPopFormat/">PetscViewerPopFormat</a></span><span class="p">(</span><span class="n"><a href="https://petsc.org/release/manualpages/Viewer/PETSC_VIEWER_STDOUT_WORLD/">PETSC_VIEWER_STDOUT_WORLD</a></span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="k">endif</span>
<span class="k"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="../../manualpages/EPS/EPSDestroy.html">EPSDestroy</a></span><span class="p">(</span><span class="n">eps</span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="https://petsc.org/release/manualpages/Mat/MatDestroy/">MatDestroy</a></span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="n"><a href="https://petsc.org/release/manualpages/Sys/PetscCallA/">PetscCallA</a></span><span class="p">(</span><span class="n"><a href="../../manualpages/Sys/SlepcFinalize.html">SlepcFinalize</a></span><span class="p">(</span><span class="n">ierr</span><span class="p">))</span>
<span class="w"> </span><span class="k">end</span>
</pre></div>
</div>
<p class="rubric">References</p>
<div class="docutils container" id="id14">
<div role="list" class="citation-list">
<div class="citation" id="id15" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id3">And99</a><span class="fn-bracket">]</span></span>
<p>E. Anderson, Z. Bai, C. Bischof, L. S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen. <em>LAPACK Users' Guide</em>. Society for Industrial and Applied Mathematics, Philadelphia, PA, third edition, 1999.</p>
</div>
<div class="citation" id="id62" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id9">Auc11</a><span class="fn-bracket">]</span></span>
<p>T. Auckenthaler, V. Blum, H.-J. Bungartz, T. Huckle, R. Johanni, L. Krämer, B. Lang, H. Lederer, and P.R. Willems. Parallel solution of partial symmetric eigenvalue problems from electronic structure calculations. <em>Parallel Comput.</em>, 37(12):783–794, 2011. <a class="reference external" href="https://doi.org/10.1016/j.parco.2011.05.002">doi:10.1016/j.parco.2011.05.002</a>.</p>
</div>
<div class="citation" id="id18" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id8">Bla97</a><span class="fn-bracket">]</span></span>
<p>L. S. Blackford, J. Choi, A. Cleary, E. D'Azevedo, J. Demmel, I. Dhillon, J. Dongarra, S. Hammarling, G. Henry, A. Petitet, K. Stanley, D. Walker, and R. C. Whaley. <em>ScaLAPACK Users' Guide</em>. Society for Industrial and Applied Mathematics, Philadelphia, PA, 1997.</p>
</div>
<div class="citation" id="id29" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id7">Kny07</a><span class="fn-bracket">]</span></span>
<p>A. V. Knyazev, M. E. Argentati, I. Lashuk, and E. E. Ovtchinnikov. Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in HYPRE and PETSc. <em>SIAM J. Sci. Comput.</em>, 29(5):2224–2239, 2007. <a class="reference external" href="https://doi.org/10.1137/060661624">doi:10.1137/060661624</a>.</p>
</div>
<div class="citation" id="id20" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id4">Leh98</a><span class="fn-bracket">]</span></span>
<p>R. B. Lehoucq, D. C. Sorensen, and C. Yang. <em>ARPACK Users' Guide, Solution of Large-Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods</em>. Society for Industrial and Applied Mathematics, Philadelphia, PA, 1998.</p>
</div>
<div class="citation" id="id61" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id6">Li19</a><span class="fn-bracket">]</span></span>
<p>R. Li, Y. Xi, L. Erlandson, and Y. Saad. The eigenvalues slicing library (EVSL): algorithms, implementation, and software. <em>SIAM J. Sci. Comput.</em>, 41(4):C393–C415, 2019. <a class="reference external" href="https://doi.org/10.1137/18M1170935">doi:10.1137/18M1170935</a>.</p>
</div>
<div class="citation" id="id21" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id4">Mas96</a><span class="fn-bracket">]</span></span>
<p>K. J. Maschhoff and D. C. Sorensen. PARPACK: an efficient portable large scale eigenvalue package for distributed memory parallel architectures. <em>Lect. Notes Comp. Sci.</em>, 1184:478–486, 1996.</p>
</div>
<div class="citation" id="id41" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id12">Pol09</a><span class="fn-bracket">]</span></span>
<p>E. Polizzi. Density-matrix-based algorithm for solving eigenvalue problems. <em>Phys. Rev. B</em>, 79(11):115112, 2009. <a class="reference external" href="https://doi.org/10.1103/PhysRevB.79.115112">doi:10.1103/PhysRevB.79.115112</a>.</p>
</div>
<div class="citation" id="id64" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id11">Pou13</a><span class="fn-bracket">]</span></span>
<p>J. Poulson, B. Marker, R. A. van de Geijn, J. R. Hammond, and N. A. Romero. Elemental: a new framework for distributed memory dense matrix computations. <em>ACM Trans. Math. Software</em>, 2013. <a class="reference external" href="https://doi.org/10.1145/2427023.2427030">doi:10.1145/2427023.2427030</a>.</p>
</div>
<div class="citation" id="id37" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id5">Sta10</a><span class="fn-bracket">]</span></span>
<p>A. Stathopoulos and J. R. McCombs. PRIMME: PReconditioned Iterative MultiMethod Eigensolver: methods and software description. <em>ACM Trans. Math. Software</em>, 37(2):21:1–21:30, 2010. <a class="reference external" href="https://doi.org/10.1145/1731022.1731031">doi:10.1145/1731022.1731031</a>.</p>
</div>
<div class="citation" id="id63" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id10">Suk19</a><span class="fn-bracket">]</span></span>
<p>D. Sukkari, H. Ltaief, A. Esposito, and D. Keyes. A QDWH-based SVD software framework on distributed-memory manycore systems. <em>ACM Trans. Math. Software</em>, 2019. <a class="reference external" href="https://doi.org/10.1145/3309548">doi:10.1145/3309548</a>.</p>
</div>
<div class="citation" id="id65" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id13">Win19</a><span class="fn-bracket">]</span></span>
<p>J. Winkelmann, P. Springer, and E. Di Napoli. ChASE: Chebyshev accelerated subspace iteration eigensolver for sequences of hermitian eigenvalue problems. <em>ACM Trans. Math. Software</em>, 2019. <a class="reference external" href="https://doi.org/10.1145/3313828">doi:10.1145/3313828</a>.</p>
</div>
</div>
</div>
<p class="rubric">Footnotes</p>
</section>
</section>
<hr class="footnotes docutils" />
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="cuda" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
<p><a class="reference external" href="https://developer.nvidia.com/cuda-zone" target="_blank">https://developer.nvidia.com/cuda-zone</a></p>
</aside>
<aside class="footnote brackets" id="rocm" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
<p><a class="reference external" href="https://rocm.docs.amd.com" target="_blank">https://rocm.docs.amd.com</a></p>
</aside>
</aside>
</article>
<footer class="prev-next-footer d-print-none">
<div class="prev-next-area">
<a class="left-prev"
href="aux.html"
title="previous page">
<i class="fa-solid fa-angle-left"></i>
<div class="prev-next-info">
<p class="prev-next-subtitle">previous</p>
<p class="prev-next-title">Auxiliary Classes</p>
</div>
</a>
<a class="right-next"
href="../hands-on/index.html"
title="next page">
<div class="prev-next-info">
<p class="prev-next-subtitle">next</p>
<p class="prev-next-title">Hands-on exercises</p>
</div>
<i class="fa-solid fa-angle-right"></i>
</a>
</div>
</footer>
</div>
<dialog id="pst-secondary-sidebar-modal"></dialog>
<div id="pst-secondary-sidebar" class="bd-sidebar-secondary bd-toc"><div class="sidebar-secondary-items sidebar-secondary__inner">
<div class="sidebar-secondary-item">
<div
id="pst-page-navigation-heading-2"
class="page-toc tocsection onthispage">
<i class="fa-solid fa-list"></i> On this page
</div>
<nav class="bd-toc-nav page-toc" aria-labelledby="pst-page-navigation-heading-2">
<ul class="visible nav section-nav flex-column">
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#supported-petsc-features">Supported PETSc Features</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#sec-supported">Supported Matrix Types</a><ul class="nav section-nav flex-column">
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#shell-matrices">Shell Matrices</a></li>
</ul>
</li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#sec-gpu">GPU Computing</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#sec-shell">Extending SLEPc</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#directory-structure">Directory Structure</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#sec-wrap">Wrappers to External Libraries</a><ul class="nav section-nav flex-column">
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#list-of-external-libraries">List of External Libraries</a><ul class="nav section-nav flex-column">
<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#lapack">LAPACK</a></li>
<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#arpack">ARPACK</a></li>
<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#primme">PRIMME</a></li>
<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#evsl">EVSL</a></li>
<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#blopex">BLOPEX</a></li>
<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#scalapack">ScaLAPACK</a></li>
<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#elpa">ELPA</a></li>
<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#ksvd">KSVD</a></li>
<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#elemental">ELEMENTAL</a></li>
<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#feast">FEAST</a></li>
<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#chase">CHASE</a></li>
<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#slicot">SLICOT</a></li>
</ul>
</li>
</ul>
</li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#sec-fortran">Fortran Interface</a></li>
</ul>
</nav></div>
<div class="sidebar-secondary-item">
<div class="tocsection editthispage">
<a href="https://gitlab.com/slepc/slepc/-/edit/release/doc/source/documentation/manual/extra.md">
<i class="fa-solid fa-pencil"></i>
Edit on GitLab
</a>
</div>
</div>
<div class="sidebar-secondary-item">
<div role="note" aria-label="source link">
<h3>This Page</h3>
<ul class="this-page-menu">
<li><a href="../../_sources/documentation/manual/extra.md.txt"
rel="nofollow">Show Source</a></li>
</ul>
</div></div>
</div></div>
</div>
<footer class="bd-footer-content">
</footer>
</main>
</div>
</div>
<!-- Scripts loaded after <body> so the DOM is not blocked -->
<script defer src="../../_static/scripts/bootstrap.js?digest=8878045cc6db502f8baf"></script>
<script defer src="../../_static/scripts/pydata-sphinx-theme.js?digest=8878045cc6db502f8baf"></script>
<footer class="bd-footer">
<div class="bd-footer__inner bd-page-width">
<div class="footer-items__start">
<div class="footer-item">
<p class="copyright">
© Copyright 2002-2025, Universitat Politecnica de Valencia, Spain.
<br/>
</p>
</div>
<div class="footer-item">
<p class="sphinx-version">
Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.3.7.
<br/>
</p>
</div>
</div>
<div class="footer-items__end">
<div class="footer-item">
<p class="theme-version">
<!-- # L10n: Setting the PST URL as an argument as this does not need to be localized -->
Built with the <a href="https://pydata-sphinx-theme.readthedocs.io/en/stable/index.html">PyData Sphinx Theme</a> 0.16.1.
</p></div>
</div>
</div>
</footer>
</body>
</html>
|
