-
Notifications
You must be signed in to change notification settings - Fork 55
/
linplus.html
2402 lines (2368 loc) · 74.8 KB
/
linplus.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
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
<html>
<head>
<title>
LINPLUS - Linear Algebra Utilities
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
LINPLUS <br> Linear Algebra Utilities
</h1>
<hr>
<p>
<b>LINPLUS</b>
is a MATLAB library which
carries out operations such as matrix-vector products,
matrix factorization, linear solvers including Gauss-elimination,
Jacobi iteration, Gauss-Seidel iteration, Conjugate Gradient (CG),
for matrices in a
variety of formats, including banded, border-banded, circulant, lower
triangular, pentadiagonal, sparse, symmetric, toeplitz, tridiagonal,
upper triangular and vandermonde formats.
</p>
<p>
The routines are primarily organized by the storage format of
the matrix they operate on. Some of these formats were defined by
LINPACK, while others are new; I just made them up when I had to solve
problems involving such matrices. The formats include:
<ul>
<li>
<b>C83</b> - Double complex tridiagonal;
</li>
<li>
<b>C8CI</b> - Double complex circulant;
</li>
<li>
<b>C8GE</b> - Double complex general;
</li>
<li>
<b>C8TO</b> - Double complex Toeplitz;
</li>
<li>
<b>R83</b> - Real double precision tridiagonal;
</li>
<li>
<b>R83P</b> - Real double precision tridiagonal periodic;
</li>
<li>
<b>R83S</b> - Real double precision tridiagonal scalar;
</li>
<li>
<b>R85</b> - Real double precision pentadiagonal;
</li>
<li>
<b>R8BB</b> - Real double precision border-banded;
</li>
<li>
<b>R8BLT</b> - Real double precision banded lower triangular matrix;
</li>
<li>
<b>R8BTO</b> - Real double precision block Toeplitz;
</li>
<li>
<b>R8BUT</b> - Real double precision banded upper triangular matrix;
</li>
<li>
<b>R8CB</b> - Real double precision compact band;
</li>
<li>
<b>R8CBB</b> - Real double precision compact border-banded;
</li>
<li>
<b>R8CC</b> - Real double precision compressed column sparse
= Harwell Boeing Real Unsymmetric Assembled (RUA) format
= MATLAB sparse format;
</li>
<li>
<b>R8CI</b> - Real double precision circulant;
</li>
<li>
<b>R8GB</b> - Real double precision general band,
used by LINPACK and LAPACK;
</li>
<li>
<b>R8GD</b> - Real double precision general diagonal;
</li>
<li>
<b>R8GE</b> - Real double precision general, used by LINPACK and LAPACK;
</li>
<li>
<b>R8LT</b> - Real double precision lower triangular;
</li>
<li>
<b>R8NCF</b> - Real double precision Nonsymmetric Coordinate Format
(one of the formats used by NSPCG);
</li>
<li>
<b>R8PBL</b> - Real double precision positive-definite symmetric band
matrix, store diagonal and lower triangle;
</li>
<li>
<b>R8PBU</b> - Real double precision positive-definite symmetric band
matrix, store diagonal and upper triangle;
</li>
<li>
<b>R8PO</b> - Real double precision positive-definite symmetric,
used by LINPACK and LAPACK;
</li>
<li>
<b>R8PP</b> - Real double precision positive-definite symmetric Packed,
used by LINPACK and LAPACK;
</li>
<li>
<b>R8RI</b> - Real double precision Row-Indexed matrix,
used by Numerical Recipes;
</li>
<li>
<b>R8S3</b> - Real double precision sparse matrix stored by row,
column, value (used by SLAP/DLAP, symmetric or nonsymmetric);
</li>
<li>
<b>R8SD</b> - Real double precision symmetric diagonal;
</li>
<li>
<b>R8SM</b> - Real double precision Sherman Morrison system A - u * v';
</li>
<li>
<b>R8SP</b> - Real double precision sparse matrix stored by row,
column, value (used by CSPARSE ("sparse triplet"),
SLAP/DLAP (nonsymmetric SLAP triad format), MATLAB,
and SPARSEKIT ("COO" format));
</li>
<li>
<b>R8SR</b> - Real double precision sparse matrix stored by rows;
</li>
<li>
<b>R8SS</b> - Real double precision symmetric skyline;
</li>
<li>
<b>R8STO</b> - Real double precision symmetric Toeplitz;
</li>
<li>
<b>R8TO</b> - Real double precision Toeplitz;
</li>
<li>
<b>R8UT</b> - Real double precision upper triangular;
</li>
<li>
<b>R8UTP</b> - Real double precision upper triangular, packed
(only nonzeros are stored);
</li>
<li>
<b>R8VM</b> - Real double precision Vandermonde;
</li>
<li>
<b>R8VEC</b> - Real double precision vector, which in some cases
is used to store a matrix;
</li>
</ul>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>LINPLUS</b> is available in
<a href = "../../c_src/linplus/linplus.html">a C version </a> and
<a href = "../../cpp_src/linplus/linplus.html">a C++ version </a> and
<a href = "../../f77_src/linplus/linplus.html">a FORTRAN77 version </a> and
<a href = "../../f_src/linplus/linplus.html">a FORTRAN90 version </a> and
<a href = "../../m_src/linplus/linplus.html">a MATLAB version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../data/cc/cc.html">
CC</a>,
a data directory which
contains examples of the Compressed Column (CC)
sparse matrix file format;
</p>
<p>
<a href = "../../m_src/cg/cg.html">
CG</a>,
a MATLAB library which
implements a simple version of the conjugate gradient (CG) method
for solving a system of linear equations of the form A*x=b,
suitable for situations in which the matrix A is positive definite
(only real, positive eigenvalues) and symmetric.
</p>
<p>
<a href = "../../m_src/cg_rc/cg_rc.html">
CG_RC</a>,
a MATLAB library which
implements the conjugate gradient method for solving
a positive definite sparse linear system A*x=b, using reverse communication.
</p>
<p>
<a href = "../../data/cr/cr.html">
CR</a>,
a data directory which
contains examples of the Compressed Row (CR)
sparse matrix file format;
</p>
<p>
<a href = "../../m_src/linpack_d/linpack_d.html">
LINPACK_D</a>,
a MATLAB library which
is a linear algebra package to solve linear systems for a variety of
matrix storage formats.
</p>
<p>
<a href = "../../m_src/mgmres/mgmres.html">
MGMRES</a>,
a MATLAB library which
applies the restarted GMRES algorithm
to solve a sparse linear system.
</p>
<p>
<a href = "../../f_src/sparsekit/sparsekit.html">
SPARSEKIT</a>,
a FORTRAN90 library which
carries out operations on sparse matrices, including conversion between
various formats.
</p>
<p>
<a href = "../../c_src/superlu/superlu.html">
SUPERLU</a>,
a C library which
implements some very fast solvers
for systems of sparse linear equations.
</p>
<p>
<a href = "../../m_src/templates/templates.html">
TEMPLATES</a>,
a MATLAB library which
implements various iterative methods for solving a linear system.
</p>
<p>
<a href = "../../m_src/test_mat/test_mat.html">
TEST_MAT</a>,
a MATLAB library which
defines test matrices, some of
which have known determinants, eigenvalues and eigenvectors,
inverses and so on.
</p>
<p>
<a href = "../../m_src/toeplitz_cholesky/toeplitz_cholesky.html">
TOEPLITZ_CHOLESKY</a>,
a MATLAB library which
computes the Cholesky factorization of a nonnegative definite symmetric
Toeplitz matrix.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Edward Anderson, Zhaojun Bai, Christian Bischof, Susan Blackford,
James Demmel, Jack Dongarra, Jeremy Du Croz, Anne Greenbaum,
Sven Hammarling, Alan McKenney, Danny Sorensen,<br>
LAPACK User's Guide,<br>
Third Edition,<br>
SIAM, 1999,<br>
ISBN: 0898714478,<br>
LC: QA76.73.F25L36.
</li>
<li>
Frank Beckman,<br>
The Solution of Linear Equations by the Conjugate Gradient Method,<br>
in Mathematical Methods for Digital Computers,<br>
edited by John Ralston, Herbert Wilf,<br>
Wiley, 1967,<br>
ISBN: 0471706892.
</li>
<li>
Paul Bratley, Bennett Fox, Linus Schrage,<br>
A Guide to Simulation,<br>
Second Edition,<br>
Springer, 1987,<br>
ISBN: 0387964673.
</li>
<li>
Ward Cheney, David Kincaid,<br>
Numerical Mathematics and Computing,<br>
Brooks-Cole Publishing, 2004,<br>
ISBN: 0534201121.
</li>
<li>
Philip Davis,<br>
Circulant Matrices,<br>
Second Edition,<br>
Chelsea, 1994,<br>
ISBN: 0828403384,<br>
LC: QA188.D37.
</li>
<li>
Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,<br>
LINPACK User's Guide,<br>
SIAM, 1979,<br>
ISBN13: 978-0-898711-72-1,<br>
LC: QA214.L56.
</li>
<li>
Iain Duff, Roger Grimes, John Lewis,<br>
User's Guide for the Harwell-Boeing Sparse Matrix Collection,<br>
October 1992.
</li>
<li>
Bennett Fox,<br>
Algorithm 647:
Implementation and Relative Efficiency of Quasirandom
Sequence Generators,<br>
ACM Transactions on Mathematical Software,<br>
Volume 12, Number 4, December 1986, pages 362-376.
</li>
<li>
Gene Golub, Charles VanLoan,<br>
Matrix Computations,
Third Edition,<br>
Johns Hopkins, 1996,<br>
ISBN: 0-8018-4513-X,<br>
LC: QA188.G65.
</li>
<li>
Roger Hockney,<br>
A fast direct solution of Poisson's equation using Fourier Analysis,<br>
Journal of the ACM,<br>
Volume 12, Number 1, pages 95-113, January 1965.
</li>
<li>
David Kahaner, Cleve Moler, Steven Nash,<br>
Numerical Methods and Software,<br>
Prentice Hall, 1989,<br>
ISBN: 0-13-627258-4,<br>
LC: TA345.K34.
</li>
<li>
Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,<br>
Algorithm 539: Basic Linear Algebra Subprograms for Fortran Usage,<br>
ACM Transactions on Mathematical Software,<br>
Volume 5, Number 3, September 1979, pages 308-323.
</li>
<li>
Albert Nijenhuis, Herbert Wilf,<br>
Combinatorial Algorithms for Computers and Calculators,<br>
Second Edition,<br>
Academic Press, 1978,<br>
ISBN: 0-12-519260-6,<br>
LC: QA164.N54.
</li>
<li>
William Press, Brian Flannery, Saul Teukolsky, William Vetterling,<br>
Numerical Recipes in FORTRAN: The Art of Scientific Computing,<br>
Third Edition,<br>
Cambridge University Press, 2007,<br>
ISBN13: 978-0-521-88068-8,<br>
LC: QA297.N866.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "c8_le_l2.m">c8_le_l2.m</a>,
( X <= Y ) for C8 values and the L2 norm;
</li>
<li>
<a href = "c8_swap.m">c8_swap.m</a>,
swaps two C8 values;
</li>
<li>
<a href = "c83_cr_fa.m">c83_cr_fa.m</a>,
factors a C83 system using cyclic reduction;
</li>
<li>
<a href = "c83_cr_sl.m">c83_cr_sl.m</a>,
solves a C83 system factored by c83_cr_fa;
</li>
<li>
<a href = "c83_cr_sls.m">c83_cr_sls.m</a>,
solves multiple C83 systems factored by c83_cr_fa;
</li>
<li>
<a href = "c83_indicator.m">c83_indicator.m</a>,
sets up a C83 indicator matrix.
</li>
<li>
<a href = "c83_mxv.m">c83_mxv.m</a>,
multiplies a C83 matrix times a vector;
</li>
<li>
<a href = "c8mat_print.m">c8mat_print.m</a>,
prints a C8MAT.
</li>
<li>
<a href = "c8mat_print_some.m">c8mat_print_some.m</a>,
prints some of a C8MAT.
</li>
<li>
<a href = "c8vec_indicator.m">c8vec_indicator.m</a>,
sets a C8VEC to the indicator vector.
</li>
<li>
<a href = "c8vec_print.m">c8vec_print.m</a>,
prints a C8 vector.
</li>
<li>
<a href = "c8vec_print_some.m">c8vec_print_some.m</a>,
prints some of a C8VEC.
</li>
<li>
<a href = "c8vec_sort_a2.m">c8vec_sort_a2.m</a>,
sorts a C8 vector by L2 norm;
</li>
<li>
<a href = "c8vec_unity.m">c8vec_unity.m</a>,
returns the N roots of unity;
</li>
<li>
<a href = "r83_cr_fa.m">r83_cr_fa.m</a>,
factors an R83 system using cyclic reduction;
</li>
<li>
<a href = "r83_cr_sl.m">r83_cr_sl.m</a>,
solves an R83 system factored by r83_cr_fa;
</li>
<li>
<a href = "r83_cr_sls.m">r83_cr_sls.m</a>,
solves several R83 systems factored by r83_cr_fa;
</li>
<li>
<a href = "r83_gs_sl.m">r83_jac_sl.m</a>,
solves an R83 system using Gauss-Seidel iteration;
</li>
<li>
<a href = "r83_indicator.m">r83_indicator.m</a>,
sets up an R83 indicator matrix;
</li>
<li>
<a href = "r83_jac_sl.m">r83_jac_sl.m</a>,
solves an R83 system using Jacobi iteration;
</li>
<li>
<a href = "r83_mxv.m">r83_mxv.m</a>,
multiplies an R83 matrix times a vector;
</li>
<li>
<a href = "r83_np_det.m">r83_np_det.m</a>,
returns the determinant of a system factored by R83_NP_FA;
</li>
<li>
<a href = "r83_np_fa.m">r83_np_fa.m</a>,
factors an R83 linear system with no pivoting;
</li>
<li>
<a href = "r83_np_fs.m">r83_np_fs.m</a>,
factors and solves an R83 linear system with no pivoting;
</li>
<li>
<a href = "r83_np_ml.m">r83_np_ml.m</a>,
computes A * x or x * A, where A has been factored by R83_NP_FA;
</li>
<li>
<a href = "r83_np_sl.m">r83_np_sl.m</a>,
solves an R83 linear system factored by R83_NP_FA;
</li>
<li>
<a href = "r83_print.m">r83_print.m</a>,
prints an R83 matrix;
</li>
<li>
<a href = "r83_print_some.m">r83_print_some.m</a>,
prints some of an R83 matrix;
</li>
<li>
<a href = "r83_random.m">r83_random.m</a>,
randomizes an R83 matrix;
</li>
<li>
<a href = "r83_to_r8ge.m">r83_to_r8ge.m</a>,
copies an R83 matrix to an R8GE matrix;
</li>
<li>
<a href = "r83_vxm.m">r83_vxm.m</a>,
multiplies a vector times an R83 matrix;
</li>
<li>
<a href = "r83np_fs.m">r83np_fs.m</a>,
factors and solves an R83NP linear system with no pivoting;
</li>
<li>
<a href = "r83p_det.m">r83p_det.m</a>,
computes the determinant of an R83P matrix factored by
R83P_FA;
</li>
<li>
<a href = "r83p_fa.m">r83p_fa.m</a>,
factors an R83P matrix;
</li>
<li>
<a href = "r83p_indicator.m">r83p_indicator.m</a>,
returns an R83P indicator matrix;
</li>
<li>
<a href = "r83p_ml.m">r83p_ml.m</a>,
computes A*x or A'*x after A has been factored by R83P_FA;
</li>
<li>
<a href = "r83p_mxv.m">r83p_mxv.m</a>,
multiplies an R83P matrix times a vector;
</li>
<li>
<a href = "r83p_print.m">r83p_print.m</a>,
prints an R83P matrix;
</li>
<li>
<a href = "r83p_print_some.m">r83p_print_some.m</a>,
prints some of an R83P matrix;
</li>
<li>
<a href = "r83p_random.m">r83p_random.m</a>,
randomizes an R83P matrix;
</li>
<li>
<a href = "r83p_sl.m">r83p_sl.m</a>,
solves an R83P linear system factored by R83P_FA;
</li>
<li>
<a href = "r83p_to_r8ge.m">r83p_to_r8ge.m</a>,
copies an R83P matrix to an R8GE matrix;
</li>
<li>
<a href = "r83p_vxm.m">r83p_vxm.m</a>,
multiplies a vector times an R83P matrix;
</li>
<li>
<a href = "r83s_mxv.m">r83s_mxv.m</a>,
multiplies an R83S matrix times a vector;
</li>
<li>
<a href = "r83s_print.m">r83s_print.m</a>,
prints an R83S matrix;
</li>
<li>
<a href = "r83s_print_some.m">r83s_print_some.m</a>,
prints some of an R83S matrix;
</li>
<li>
<a href = "r83s_random.m">r83s_random.m</a>,
randomizes an R83S matrix;
</li>
<li>
<a href = "r85_indicator.m">r85_indicator.m</a>,
returns an R85 indicator matrix;
</li>
<li>
<a href = "r85_mxv.m">r85_mxv.m</a>,
multiplies an R85 matrix times a vector;
</li>
<li>
<a href = "r85_np_fs.m">r85_np_fs.m</a>,
factors and solves an R85 linear system with no pivoting;
</li>
<li>
<a href = "r85_print.m">r85_print.m</a>,
prints an R85 matrix;
</li>
<li>
<a href = "r85_print_some.m">r85_print_some.m</a>,
prints some of an R85 matrix;
</li>
<li>
<a href = "r85_random.m">r85_random.m</a>,
randomizes an R85 matrix;
</li>
<li>
<a href = "r85_to_r8ge.m">r85_to_r8ge.m</a>,
copies an R85 matrix to an R8GE matrix;
</li>
<li>
<a href = "r85_vxm.m">r85_vxm.m</a>,
multiplies a vector times an R85 matrix;
</li>
<li>
<a href = "daxpy.m">daxpy.m</a>,
adds a multiple of one real vector to another;
</li>
<li>
<a href = "r8bb_add.m">r8bb_add.m</a>,
adds a value to an entry in an R8BB matrix;
</li>
<li>
<a href = "r8bb_fa.m">r8bb_fa.m</a>,
factors an R8BB matrix;
</li>
<li>
<a href = "r8bb_get.m">r8bb_get.m</a>,
gets the value of an entry in an R8BB matrix;
</li>
<li>
<a href = "r8bb_indicator.m">r8bb_indicator.m</a>,
returns an R8BB indicator matrix;
</li>
<li>
<a href = "r8bb_mxv.m">r8bb_mxv.m</a>,
multiplies an R8BB matrix times a vector;
</li>
<li>
<a href = "r8bb_print.m">r8bb_print.m</a>,
prints an R8BB matrix;
</li>
<li>
<a href = "r8bb_print_some.m">r8bb_print_some.m</a>,
prints some of an R8BB matrix;
</li>
<li>
<a href = "r8bb_random.m">r8bb_random.m</a>,
returns a random R8BB matrix;
</li>
<li>
<a href = "r8bb_set.m">r8bb_set.m</a>,
sets one entry of an R8BB matrix;
</li>
<li>
<a href = "r8bb_sl.m">r8bb_sl.m</a>,
solves a linear system that was factored by R8BB_FA;
</li>
<li>
<a href = "r8bb_to_r8ge.m">r8bb_to_r8ge.m</a>,
copies an R8BB matrix to an R8GE matrix;
</li>
<li>
<a href = "r8bb_vxm.m">r8bb_vxm.m</a>,
multiplies a vector times an R8BB matrix;
</li>
<li>
<a href = "r8blt_det.m">r8blt_det.m</a>,
returns the determinant of an R8BLT matrix;
</li>
<li>
<a href = "r8blt_indicator.m">r8blt_indicator.m</a>,
returns an R8BLT indicator matrix;
</li>
<li>
<a href = "r8blt_mxv.m">r8blt_mxv.m</a>,
multiplies an R8BLT matrix times a vector;
</li>
<li>
<a href = "r8blt_print.m">r8blt_print.m</a>,
prints an R8BLT matrix;
</li>
<li>
<a href = "r8blt_print_some.m">r8blt_print_some.m</a>,
prints some of an R8BLT matrix;
</li>
<li>
<a href = "r8blt_random.m">r8blt_random.m</a>,
randomizes an R8BLT matrix;
</li>
<li>
<a href = "r8blt_sl.m">r8blt_sl.m</a>,
solves an R8BLT linear system;
</li>
<li>
<a href = "r8blt_to_r8ge.m">r8blt_to_r8ge.m</a>,
copies an R8BLT matrix to an R8GE matrix;
</li>
<li>
<a href = "r8blt_vxm.m">r8blt_vxm.m</a>,
multiplies a vector times an R8BLT matrix;
</li>
<li>
<a href = "r8bto_indicator.m">r8bto_indicator.m</a>,
returns an R8BTO indicator matrix;
</li>
<li>
<a href = "r8bto_mxv.m">r8bto_mxv.m</a>,
multiplies an R8BTO matrix times a vector;
</li>
<li>
<a href = "r8bto_print.m">r8bto_print.m</a>,
prints an R8BTO matrix;
</li>
<li>
<a href = "r8bto_print_some.m">r8bto_print_some.m</a>,
prints some of an R8BTO matrix;
</li>
<li>
<a href = "r8bto_random.m">r8bto_random.m</a>,
randomizes an R8BTO matrix;
</li>
<li>
<b>(r8bto_sl.m)</b>,
solves an R8BTO linear system (this routine is NOT available
in a MATLAB version);
</li>
<li>
<a href = "r8bto_vxm.m">r8bto_vxm.m</a>,
multiplies a vector times an R8BTO matrix;
</li>
<li>
<a href = "r8but_det.m">r8but_det.m</a>,
returns the determinant of an R8BUT matrix;
</li>
<li>
<a href = "r8but_indicator.m">r8but_indicator.m</a>,
returns an R8BUT indicator matrix;
</li>
<li>
<a href = "r8but_mxv.m">r8but_mxv.m</a>,
multiplies an R8BUT matrix times a vector;
</li>
<li>
<a href = "r8but_print.m">r8but_print.m</a>,
prints an R8BUT matrix;
</li>
<li>
<a href = "r8but_print_some.m">r8but_print_some.m</a>,
prints some of an R8BUT matrix;
</li>
<li>
<a href = "r8but_random.m">r8but_random.m</a>,
randomizes an R8BUT matrix;
</li>
<li>
<a href = "r8but_sl.m">r8but_sl.m</a>,
solves an R8BUT linear system;
</li>
<li>
<a href = "r8but_to_r8ge.m">r8but_to_r8ge.m</a>,
copies an R8BUT matrix to an R8GE matrix;
</li>
<li>
<a href = "r8but_vxm.m">r8but_vxm.m</a>,
multiplies a vector times an R8BUT matrix;
</li>
<li>
<a href = "r8cb_det.m">r8cb_det.m</a>,
returns the determinant of an R8CB matrix;
</li>
<li>
<a href = "r8cb_indicator.m">r8cb_indicator.m</a>,
returns an R8CB indicator matrix;
</li>
<li>
<a href = "r8cb_ml.m">r8cb_ml.m</a>,
computes A*x or A'*x after A has been factored by R8CB_NP_FA;
</li>
<li>
<a href = "r8cb_mxv.m">r8cb_mxv.m</a>,
multiplies an R8CB matrix times a vector;
</li>
<li>
<a href = "r8cb_np_fa.m">r8cb_np_fa.m</a>,
factors an R8CB linear system with no pivoting;
</li>
<li>
<a href = "r8cb_np_sl.m">r8cb_np_sl.m</a>,
solves an R8CB linear system;
</li>
<li>
<a href = "r8cb_print.m">r8cb_print.m</a>,
prints an R8CB matrix;
</li>
<li>
<a href = "r8cb_print_some.m">r8cb_print_some.m</a>,
prints some of an R8CB matrix;
</li>
<li>
<a href = "r8cb_random.m">r8cb_random.m</a>,
randomizes an R8CB matrix;
</li>
<li>
<a href = "r8cb_to_r8ge.m">r8cb_to_r8ge.m</a>,
copies an R8CB matrix to an R8GE matrix;
</li>
<li>
<a href = "r8cb_vxm.m">r8cb_vxm.m</a>,
multiplies a vector times an R8CB matrix;
</li>
<li>
<a href = "r8cbb_to_r8ge.m">r8cbb_to_r8ge.m</a>,
copies an R8CBB matrix to an R8GE matrix;
</li>
<li>
<a href = "r8cbb_add.m">r8cbb_add.m</a>,
adds a value to an entry of an R8CBB matrix;
</li>
<li>
<a href = "r8cbb_fa.m">r8cbb_fa.m</a>,
factors an R8CBB matrix;
</li>
<li>
<a href = "r8cbb_get.m">r8cbb_get.m</a>,
gets one entry of an R8CBB matrix;
</li>
<li>
<a href = "r8cbb_indicator.m">r8cbb_indicator.m</a>,
returns an R8CBB indicator matrix;
</li>
<li>
<a href = "r8cbb_mxv.m">r8cbb_mxv.m</a>,
multiplies a vector times an R8CBB matrix;
</li>
<li>
<a href = "r8cbb_print.m">r8cbb_print.m</a>,
print an R8CBB matrix;
</li>
<li>
<a href = "r8cbb_print_some.m">r8cbb_print_some.m</a>,
prints some of an R8CBB matrix;
</li>
<li>
<a href = "r8cbb_random.m">r8cbb_random.m</a>,
returns a random R8CBB matrix;
</li>
<li>
<a href = "r8cbb_set.m">r8cbb_set.m</a>,
sets one entry of an R8CBB matrix;
</li>
<li>
<a href = "r8cbb_sl.m">r8cbb_sl.m</a>,
solves a linear system factored by R8CBB_FA;
</li>
<li>
<a href = "r8cbb_vxm.m">r8cbb_vxm.m</a>,
multiplies a vector times an R8CBB matrix;
</li>
<li>
<a href = "r8cc_get.m">r8cc_get.m</a>,
gets an entry from an R8CC matrix.
</li>
<li>
<a href = "r8cc_ijk.m">r8cc_ijk.m</a>,
gets the sparse index from the full indices in an R8CC matrix.
</li>
<li>
<a href = "r8cc_inc.m">r8cc_inc.m</a>,
increments an entry from an R8CC matrix.
</li>
<li>
<a href = "r8cc_indicator.m">r8cc_indicator.m</a>,
returns an R8CC indicator matrix;
</li>
<li>
<a href = "r8cc_kij.m">r8cc_kij.m</a>,
gets the full indices from the sparse index in an R8CC matrix.
</li>
<li>
<a href = "r8cc_mxv.m">r8cc_mxv.m</a>,
multiplies an R8CC matrix times a vector;
</li>
<li>
<a href = "r8cc_print.m">r8cc_print.m</a>,
prints an R8CC matrix;
</li>
<li>
<a href = "r8cc_print_some.m">r8cc_print_some.m</a>,
prints some of an R8CC matrix;
</li>
<li>
<a href = "r8cc_random.m">r8cc_random.m</a>,
randomizes an R8CC matrix;
</li>
<li>
<a href = "r8cc_read.m">r8cc_read.m</a>,
reads an R8CC matrix from three files;
</li>
<li>
<a href = "r8cc_read_size.m">r8cc_read_size.m</a>,
reads the sizes associated with an R8CC matrix stored in three files;
</li>
<li>
<a href = "r8cc_set.m">r8cc_set.m</a>,
sets an entry in an R8CC matrix.
</li>
<li>
<a href = "r8cc_to_r8ge.m">r8cc_to_r8ge.m</a>,
solves an R8CC linear system;
</li>
<li>
<a href = "r8cc_vxm.m">r8cc_vxm.m</a>,
multiplies a vector times an R8CC matrix;
</li>
<li>
<a href = "r8cc_write.m">r8cc_write.m</a>,
writes an R8CC matrix to three files;
</li>
<li>
<a href = "r8ci_eval.m">r8ci_eval.m</a>,
returns the eigenvalues of an R8CI matrix;
</li>
<li>
<a href = "r8ci_indicator.m">r8ci_indicator.m</a>,
returns an R8CI indicator matrix;
</li>
<li>
<a href = "r8ci_mxv.m">r8ci_mxv.m</a>,
multiplies an R8CI matrix times a vector;
</li>
<li>
<a href = "r8ci_print.m">r8ci_print.m</a>,
prints an R8CI matrix;
</li>
<li>
<a href = "r8ci_print_some.m">r8ci_print_some.m</a>,
prints some of an R8CI matrix;
</li>
<li>
<a href = "r8ci_random.m">r8ci_random.m</a>,
randomizes an R8CI matrix;
</li>
<li>
<a href = "r8ci_sl.m">r8ci_sl.m</a>,
solves an R8CI linear system;
</li>
<li>
<a href = "r8ci_to_r8ge.m">r8ci_to_r8ge.m</a>,
copies an R8CI matrix to an R8GE matrix;
</li>
<li>
<a href = "r8ci_vxm.m">r8ci_vxm.m</a>,
multiplies a vector times an R8CI matrix;
</li>
<li>
<a href = "r8gb_det.m">r8gb_det.m</a>,
computes the determinant of an R8GB matrix factored by
R8GB_FA or R8GB_TRF;
</li>
<li>
<a href = "r8gb_fa.m">r8gb_fa.m</a>,
performs a LINPACK style PLU factorization of an R8GB matrix;
</li>
<li>
<a href = "r8gb_indicator.m">r8gb_indicator.m</a>,
returns an R8GB indicator matrix;
</li>
<li>
<a href = "r8gb_ml.m">r8gb_ml.m</a>,
computes A*x or A'*x after A has been factored by R8GB_FA;
</li>
<li>
<a href = "r8gb_mu.m">r8gb_mu.m</a>,
computes A*x or A'*x after A has been factored by R8GB_TRF;
</li>
<li>
<a href = "r8gb_mxv.m">r8gb_mxv.m</a>,
multiplies an R8GB matrix times a vector;
</li>
<li>
<a href = "r8gb_nz_num.m">r8gb_nz_num.m</a>,
counts the nonzeroes in an R8GB matrix;
</li>
<li>
<a href = "r8gb_print.m">r8gb_print.m</a>,
prints an R8GB matrix.;
</li>
<li>
<a href = "r8gb_print_some.m">r8gb_print_some.m</a>,
prints some of an R8GB matrix;
</li>
<li>