forked from johannesgerer/jburkardt-cpp
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathtest_mat.html
2500 lines (2462 loc) · 79.3 KB
/
test_mat.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>
TEST_MAT - Test Matrices
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TEST_MAT <br> Test Matrices
</h1>
<hr>
<p>
<b>TEST_MAT</b>
is a C++ library which
defines test matrices for which some of the determinant, eigenvalues,
inverse, null vectors, P*L*U factorization or linear system solution
are already known, including the Vandermonde and Wathen matrix.
</p>
<p>
A wide range of matrix
dimensions, forms and properties are available. These matrices may be
useful in testing an algorithm for correctness on a variety of problems.
</p>
<p>
Many of the matrices can be rectangular, with the user specifying
the number of rows and columns. Almost all the matrices can be
made of arbitrary size, with the user specifying the dimension.
</p>
<p>
Many different matrix zero structures are available, including diagonal,
bidiagonal, tridiagonal, pentadiagonal, banded, upper and lower
triangular, and Hessenberg.
</p>
<p>
Many different matrix symmetry patterns are available, including
symmetric, antisymmetric, persymmetric, circulant, Toeplitz, and
Hankel.
</p>
<p>
Matrices are available with known inverses, condition numbers,
determinants, rank, eigenvalues, and characteristic polynomials.
Other matrix properties include positive definiteness, positivity,
zero/one, and adjacency matrices.
</p>
<p>
Many of the matrices come from a MATLAB M file collection developed by
Nicholas Higham, Department of Mathematics, University of Manchester.
</p>
<p>
An earlier version of the collection is available, again as MATLAB
M files, in ACM TOMS Algorithm 694, in the TOMS directory of
<a href = "http://www.netlib.org/">the NETLIB web site</a>.
</p>
<p>
Many of these matrices, and many other matrices, are available at
<a href = "http://math.nist.gov/">
http://math.nist.gov</a>,
the Matrix Market web site.
</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>TEST_MAT</b> is available in
<a href = "../../c_src/test_mat/test_mat.html">a C version</a> and
<a href = "../../cpp_src/test_mat/test_mat.html">a C++ version</a> and
<a href = "../../f77_src/test_mat/test_mat.html">a FORTRAN77 version</a> and
<a href = "../../f_src/test_mat/test_mat.html">a FORTRAN90 version</a> and
<a href = "../../m_src/test_mat/test_mat.html">a MATLAB version</a> and
<a href = "../../py_src/test_mat/test_mat.html">a Python version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/cg/cg.html">
CG</a>,
a C++ 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 = "../../cpp_src/condition/condition.html">
CONDITION</a>,
a C++ library which
implements methods of computing or estimating the condition number of a matrix.
</p>
<p>
<a href = "../../cpp_src/eispack/eispack.html">
EISPACK</a>,
a C++ library which
carries out eigenvalue computations.
It includes a function to compute the singular value decomposition (SVD)
of a rectangular matrix.
superseded by LAPACK;
</p>
<p>
<a href = "../../cpp_src/jacobi_eigenvalue/jacobi_eigenvalue.html">
JACOBI_EIGENVALUE</a>,
a C++ library which
implements the Jacobi iteration for the iterative determination
of the eigenvalues and eigenvectors of a real symmetric matrix.
</p>
<p>
<a href = "../../cpp_src/linpack_d/linpack_d.html">
LINPACK_D</a>,
a C++ library which
solves linear systems using double precision real arithmetic;
</p>
<p>
<a href = "../../cpp_src/linplus/linplus.html">
LINPLUS</a>,
a C++ library which
contains routines for factoring matrices,
computing determinants and inverses, solving linear systems,
for real arithmetic for a variety of matrix storage formats.
</p>
<p>
<a href = "../../cpp_src/test_matrix_exponential/test_matrix_exponential.html">
TEST_MATRIX_EXPONENTIAL</a>,
a C++ library which
defines a set of test cases for computing the matrix exponential.
</p>
<p>
<a href = "../../cpp_src/wathen/wathen.html">
WATHEN</a>,
a C++ library which
compares storage schemes (full, banded, sparse triplet) and
solution strategies (Linpack full, Linpack banded,
conjugate gradient (CG)) for linear systems involving the Wathen matrix,
which can arise when solving a problem using the
finite element method (FEM).
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "test_mat.cpp>test_mat.cpp</a>, the source code.
</li>
<li>
<a href = "test_mat.hpp">test_mat.hpp</a>, the include file.
</li>
<li>
<a href = "test_mat.sh">test_mat.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "test_mat_prb.cpp">test_mat_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "test_mat_prb.sh">test_mat_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "test_mat_prb_output.txt">test_mat_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>AEGERTER</b> returns the AEGERTER matrix.
</li>
<li>
<b>AEGERTER_CONDITION</b> returns the L1 condition of the AEGERTER matrix.
</li>
<li>
<b>AEGERTER_DETERMINANT</b> returns the determinant of the AEGERTER matrix.
</li>
<li>
<b>AEGERTER_EIGENVALUES</b> returns the eigenvalues of the AEGERTER matrix.
</li>
<li>
<b>AEGERTER_INVERSE</b> returns the inverse of the AEGERTER matrix.
</li>
<li>
<b>ANTICIRCULANT</b> returns an ANTICIRCULANT matrix.
</li>
<li>
<b>ANTICIRCULANT_DETERMINANT:</b> determinant of the ANTICIRCULANT matrix.
</li>
<li>
<b>ANTIHADAMARD</b> returns an approximate ANTIHADAMARD matrix.
</li>
<li>
<b>ANTIHADAMARD_DETERMINANT</b> returns the determinant of the ANTIHADAMARD matrix.
</li>
<li>
<b>ANTISYMM_RANDOM</b> returns an ANTISYMMETRIC matrix.
</li>
<li>
<b>ARCHIMEDES</b> returns the ARCHIMEDES matrix.
</li>
<li>
<b>ARCHIMEDES_NULL</b> returns a null vector for the ARCHIMEDES matrix.
</li>
<li>
<b>BAB</b> returns the BAB matrix.
</li>
<li>
<b>BAB_CONDITION</b> returns the L1 condition of the BAB matrix.
</li>
<li>
<b>BAB_DETERMINANT</b> returns the determinant of the BAB matrix.
</li>
<li>
<b>BAB_EIGENVALUES</b> returns the eigenvalues of the BAB matrix.
</li>
<li>
<b>BAB_INVERSE</b> returns the inverse of the BAB matrix.
</li>
<li>
<b>BERNSTEIN</b> returns the Bernstein matrix.
</li>
<li>
<b>BERNSTEIN_INVERSE</b> returns the inverse Bernstein matrix.
</li>
<li>
<b>BIMARKOV_RANDOM</b> returns a BIMARKOV matrix.
</li>
<li>
<b>BIS</b> returns the BIS matrix.
</li>
<li>
<b>BIS_DETERMINANT</b> returns the determinant of the BIS matrix.
</li>
<li>
<b>BIS_EIGENVALUES</b> returns the eigenvalues of the BIS matrix.
</li>
<li>
<b>BIS_INVERSE</b> returns the inverse of the BIS matrix.
</li>
<li>
<b>BODEWIG</b> returns the BODEWIG matrix.
</li>
<li>
<b>BODEWIG_CONDITION</b> returns the L1 condition of the BODEWIG matrix.
</li>
<li>
<b>BODEWIG_DETERMINANT</b> returns the determinant of the BODEWIG matrix.
</li>
<li>
<b>BODEWIG_EIGENVALUES</b> returns the eigenvalues of the BODEWIG matrix.
</li>
<li>
<b>BODEWIG_INVERSE</b> returns the inverse of the BODEWIG matrix.
</li>
<li>
<b>BODEWIG_PLU</b> returns the PLU factors of the BODEWIG matrix.
</li>
<li>
<b>BODEWIG_RHS</b> returns the BODEWIG right hand side.
</li>
<li>
<b>BODEWIG_RIGHT</b> returns the right eigenvectors of the BODEWIG matrix.
</li>
<li>
<b>BODEWIG_SOLUTION</b> returns the BODEWIG_SOLUTION
</li>
<li>
<b>BOOTHROYD</b> returns the BOOTHROYD matrix.
</li>
<li>
<b>BOOTHROYD_DETERMINANT</b> returns the determinant of the BOOTHROYD matrix.
</li>
<li>
<b>BOOTHROYD_INVERSE</b> returns the inverse of the BOOTHROYD matrix.
</li>
<li>
<b>BORDERBAND</b> returns the BORDERBAND matrix.
</li>
<li>
<b>BORDERBAND_DETERMINANT</b> returns the determinant of the BORDERBAND matrix.
</li>
<li>
<b>BORDERBAND_INVERSE</b> returns the inverse of the BORDERBAND matrix.
</li>
<li>
<b>BORDERBAND_PLU</b> returns the PLU factors of the BORDERBAND matrix.
</li>
<li>
<b>C8_ABS</b> returns the absolute value of a C8.
</li>
<li>
<b>C8_I</b> returns the value of the imaginary unit, i as a C8.
</li>
<li>
<b>C8_LE_L2</b> := X <= Y for C8 values, and the L2 norm.
</li>
<li>
<b>C8_NORMAL_01</b> returns a unit pseudonormal C8.
</li>
<li>
<b>C8_ONE</b> returns the value of complex 1.
</li>
<li>
<b>C8_SWAP</b> swaps two C8's.
</li>
<li>
<b>C8_UNIFORM_01</b> returns a unit pseudorandom C8.
</li>
<li>
<b>C8_ZERO</b> returns the value of 0 as a C8.
</li>
<li>
<b>C8MAT_COPY_NEW</b> copies one C8MAT to a "new" C8MAT.
</li>
<li>
<b>C8MAT_IDENTITY</b> sets a C8MAT to the identity.
</li>
<li>
<b>C8MAT_MM_NEW</b> multiplies two C8MAT's.
</li>
<li>
<b>C8MAT_NORM_FRO</b> returns the Frobenius norm of a C8MAT.
</li>
<li>
<b>C8MAT_PRINT</b> prints a C8MAT.
</li>
<li>
<b>C8MAT_PRINT_SOME</b> prints some of a C8MAT.
</li>
<li>
<b>C8MAT_UNIFORM_01</b> returns a unit pseudorandom C8MAT.
</li>
<li>
<b>C8MAT_ZERO_NEW</b> returns a new zeroed C8MAT.
</li>
<li>
<b>C8VEC_COPY_NEW</b> copies a C8VEC to a "new" C8VEC.
</li>
<li>
<b>C8VEC_NORM_L2</b> returns the L2 norm of a C8VEC.
</li>
<li>
<b>C8VEC_PRINT</b> prints a C8VEC, with an optional title.
</li>
<li>
<b>C8VEC_UNIFORM_01</b> returns a unit C8VEC.
</li>
<li>
<b>C8VEC_UNITY</b> returns the N roots of unity in a C8VEC.
</li>
<li>
<b>CARRY</b> returns the CARRY matrix.
</li>
<li>
<b>CARRY_DETERMINANT</b> returns the determinant of the CARRY matrix.
</li>
<li>
<b>CARRY_EIGENVALUES</b> returns the eigenvalues of the CARRY matrix.
</li>
<li>
<b>CARRY_INVERSE</b> returns the inverse of the CARRY matrix.
</li>
<li>
<b>CARRY_LEFT</b> returns the left eigenvectors of the CARRY matrix.
</li>
<li>
<b>CARRY_RIGHT</b> returns the right eigenvectors of the CARRY matrix.
</li>
<li>
<b>CAUCHY</b> returns the CAUCHY matrix.
</li>
<li>
<b>CAUCHY_DETERMINANT</b> returns the determinant of the CAUCHY matrix.
</li>
<li>
<b>CAUCHY_INVERSE</b> returns the inverse of the CAUCHY matrix.
</li>
<li>
<b>CHEBY_DIFF1</b> returns the CHEBY_DIFF1 matrix.
</li>
<li>
<b>CHEBY_DIFF1_NULL</b> returns a null vector of the CHEBY_DIFF1 matrix.
</li>
<li>
<b>CHEBY_T</b> returns the CHEBY_T matrix.
</li>
<li>
<b>CHEBY_T_DETERMINANT</b> returns the determinant of the CHEBY_T matrix.
</li>
<li>
<b>CHEBY_T_INVERSE</b> returns the inverse of the CHEBY_T matrix.
</li>
<li>
<b>CHEBY_U</b> returns the CHEBY_U matrix.
</li>
<li>
<b>CHEBY_U_DETERMINANT</b> returns the determinant of the CHEBY_U matrix.
</li>
<li>
<b>CHEBY_U_INVERSE</b> returns the inverse of the CHEBY_U matrix.
</li>
<li>
<b>CHEBY_U_POLYNOMIAL</b> evaluates the Chebyshev polynomials of the second kind.
</li>
<li>
<b>CHEBY_VAN1</b> returns the CHEBY_VAN1 matrix.
</li>
<li>
<b>CHEBY_VAN2</b> returns the CHEBY_VAN2 matrix.
</li>
<li>
<b>CHEBY_VAN2_DETERMINANT</b> returns the determinant of the CHEBY_VAN2 matrix.
</li>
<li>
<b>CHEBY_VAN2_INVERSE</b> returns the inverse of the CHEBY_VAN2 matrix.
</li>
<li>
<b>CHEBY_VAN3</b> returns the CHEBY_VAN3 matrix.
</li>
<li>
<b>CHEBY_VAN3_DETERMINANT</b> returns the determinant of the CHEBY_VAN3 matrix.
</li>
<li>
<b>CHEBY_VAN3_INVERSE</b> returns the inverse of the CHEBY_VAN3 matrix.
</li>
<li>
<b>CHOW</b> returns the CHOW matrix.
</li>
<li>
<b>CHOW_DETERMINANT</b> returns the determinant of the CHOW matrix.
</li>
<li>
<b>CHOW_EIGENVALUES</b> returns the eigenvalues of the CHOW matrix.
</li>
<li>
<b>CHOW_INVERSE</b> returns the inverse of the CHOW matrix.
</li>
<li>
<b>CHOW_LEFT</b> returns the left eigenvectors for the CHOW matrix.
</li>
<li>
<b>CHOW_RIGHT</b> returns the right eigenvectors for the CHOW matrix.
</li>
<li>
<b>CIRCULANT</b> returns the CIRCULANT matrix.
</li>
<li>
<b>CIRCULANT_DETERMINANT</b> returns the determinant of the CIRCULANT matrix.
</li>
<li>
<b>CIRCULANT_EIGENVALUES</b> returns the eigenvalues of the CIRCULANT matrix.
</li>
<li>
<b>CIRCULANT_INVERSE</b> returns the inverse of the CIRCULANT matrix.
</li>
<li>
<b>CIRCULANT2</b> returns the CIRCULANT2 matrix.
</li>
<li>
<b>CIRCULANT2_DETERMINANT</b> returns the determinant of the CIRCULANT2 matrix.
</li>
<li>
<b>CIRCULANT2_EIGENVALUES</b> returns the eigenvalues of the CIRCULANT2 matrix.
</li>
<li>
<b>CIRCULANT2_INVERSE</b> returns the inverse of the CIRCULANT2 matrix.
</li>
<li>
<b>CLEMENT1</b> returns the CLEMENT1 matrix.
</li>
<li>
<b>CLEMENT1_DETERMINANT</b> returns the determinant of the CLEMENT1 matrix.
</li>
<li>
<b>CLEMENT1_EIGENVALUES</b> returns the eigenvalues of the CLEMENT1 matrix.
</li>
<li>
<b>CLEMENT1_INVERSE</b> returns the inverse of the CLEMENT1 matrix.
</li>
<li>
<b>CLEMENT2</b> returns the CLEMENT2 matrix.
</li>
<li>
<b>CLEMENT2_DETERMINANT</b> returns the determinant of the CLEMENT2 matrix.
</li>
<li>
<b>CLEMENT2_EIGENVALUES</b> returns the eigenvalues of the CLEMENT2 matrix.
</li>
<li>
<b>CLEMENT2_INVERSE</b> returns the inverse of the CLEMENT2 matrix.
</li>
<li>
<b>CLEMENT3</b> returns the CLEMENT3 matrix.
</li>
<li>
<b>CLEMENT3_DETERMINANT</b> returns the determinant of the CLEMENT3 matrix.
</li>
<li>
<b>CLEMENT3_INVERSE</b> returns the inverse of the CLEMENT3 matrix.
</li>
<li>
<b>COMBIN</b> returns the COMBIN matrix.
</li>
<li>
<b>COMBIN_CONDITION</b> returns the L1 condition of the COMBIN matrix.
</li>
<li>
<b>COMBIN_DETERMINANT</b> returns the determinant of the COMBIN matrix.
</li>
<li>
<b>COMBIN_EIGENVALUES</b> returns the eigenvalues of the COMBIN matrix.
</li>
<li>
<b>COMBIN_INVERSE</b> returns the inverse of the COMBIN matrix.
</li>
<li>
<b>COMBIN_RIGHT</b> returns the right eigenvectors of the COMBIN matrix.
</li>
<li>
<b>COMPANION</b> returns the COMPANION matrix.
</li>
<li>
<b>COMPANION_DETERMINANT</b> returns the determinant of the COMPANION matrix.
</li>
<li>
<b>COMPANION_INVERSE</b> returns the inverse of the COMPANION matrix.
</li>
<li>
<b>COMPLEX3</b> returns the COMPLEX3 matrix.
</li>
<li>
<b>COMPLEX3_INVERSE</b> returns the inverse of the COMPLEX3 matrix.
</li>
<li>
<b>COMPLEX_I</b> returns the COMPLEX_I matrix.
</li>
<li>
<b>COMPLEX_I_DETERMINANT</b> returns the determinant of the COMPLEX_I matrix.
</li>
<li>
<b>COMPLEX_I_INVERSE</b> returns the inverse of the COMPLEX_I matrix.
</li>
<li>
<b>CONEX1</b> returns the CONEX1 matrix.
</li>
<li>
<b>CONEX1_DETERMINANT</b> returns the determinant of the CONEX1 matrix.
</li>
<li>
<b>CONEX1_INVERSE</b> returns the inverse of the CONEX1 matrix.
</li>
<li>
<b>CONEX2</b> returns the CONEX2 matrix.
</li>
<li>
<b>CONEX2_DETERMINANT</b> returns the determinant of the CONEX2 matrix.
</li>
<li>
<b>CONEX2_INVERSE</b> returns the inverse of the CONEX2 matrix.
</li>
<li>
<b>CONEX3</b> returns the CONEX3 matrix.
</li>
<li>
<b>CONEX3_CONDITION</b> returns the L1 condition of the CONEX3 matrix.
</li>
<li>
<b>CONEX3_DETERMINANT</b> returns the determinant of the CONEX3 matrix.
</li>
<li>
<b>CONEX3_INVERSE</b> returns the inverse of the CONEX3 matrix.
</li>
<li>
<b>CONEX4</b> returns the CONEX4 matrix.
</li>
<li>
<b>CONEX4_INVERSE</b> returns the inverse of the CONEX4 matrix.
</li>
<li>
<b>CONFERENCE</b> returns the CONFERENCE matrix.
</li>
<li>
<b>CONFERENCE_DETERMINANT</b> returns the determinant of the CONFERENCE matrix.
</li>
<li>
<b>CONFERENCE_INVERSE</b> returns the inverse of the CONFERENCE matrix.
</li>
<li>
<b>CREATION</b> returns the CREATION matrix.
</li>
<li>
<b>CREATION_DETERMINANT</b> returns the determinant of the CREATION matrix.
</li>
<li>
<b>CREATION_NULL</b> returns a null vector of the CREATION matrix.
</li>
<li>
<b>CYCOL_RANDOM</b> returns the CYCOL_RANDOM matrix.
</li>
<li>
<b>DAUB2</b> returns the DAUB2 matrix.
</li>
<li>
<b>DAUB2_DETERMINANT</b> returns the determinant of the DAUB2 matrix.
</li>
<li>
<b>DAUB2_INVERSE</b> returns the inverse of the DAUB2 matrix.
</li>
<li>
<b>DAUB4</b> returns the DAUB4 matrix.
</li>
<li>
<b>DAUB4_DETERMINANT</b> returns the determinant of the DAUB4 matrix.
</li>
<li>
<b>DAUB4_INVERSE</b> returns the inverse of the DAUB4 matrix.
</li>
<li>
<b>DAUB6</b> returns the DAUB6 matrix.
</li>
<li>
<b>DAUB6_DETERMINANT</b> returns the determinant of the DAUB6 matrix.
</li>
<li>
<b>DAUB6_INVERSE</b> returns the inverse of the DAUB6 matrix.
</li>
<li>
<b>DAUB8</b> returns the DAUB8 matrix.
</li>
<li>
<b>DAUB8_DETERMINANT</b> returns the determinant of the DAUB8 matrix.
</li>
<li>
<b>DAUB8_INVERSE</b> returns the inverse of the DAUB8 matrix.
</li>
<li>
<b>DAUB10</b> returns the DAUB10 matrix.
</li>
<li>
<b>DAUB10_DETERMINANT</b> returns the determinant of the DAUB10 matrix.
</li>
<li>
<b>DAUB10_INVERSE</b> returns the inverse of the DAUB10 matrix.
</li>
<li>
<b>DAUB12</b> returns the DAUB12 matrix.
</li>
<li>
<b>DAUB12_DETERMINANT</b> returns the determinant of the DAUB12 matrix.
</li>
<li>
<b>DAUB12_INVERSE</b> returns the inverse of the DAUB12 matrix.
</li>
<li>
<b>DIAGONAL</b> returns the DIAGONAL matrix.
</li>
<li>
<b>DIAGONAL_DETERMINANT</b> returns the determinant of the DIAGONAL matrix.
</li>
<li>
<b>DIAGONAL_EIGENVALUES</b> returns the eigenvalues of the DIAGONAL matrix.
</li>
<li>
<b>DIAGONAL_INVERSE</b> returns the inverse of the DIAGONAL matrix.
</li>
<li>
<b>DIF1</b> returns the DIF1 matrix.
</li>
<li>
<b>DIF1_DETERMINANT</b> returns the determinant of the DIF1 matrix.
</li>
<li>
<b>DIF1_EIGENVALUES</b> returns the eigenvalues of the DIF1 matrix.
</li>
<li>
<b>DIF1_NULL</b> returns a null vector of the DIF1 matrix.
</li>
<li>
<b>DIF1CYCLIC</b> returns the DIF1CYCLIC matrix.
</li>
<li>
<b>DIF1CYCLIC_DETERMINANT:</b> determinant of the DIF1CYCLIC matrix.
</li>
<li>
<b>DIF1CYCLIC_NULL</b> returns a null vector of the DIF1CYCLIC matrix.
</li>
<li>
<b>DIF2</b> returns the DIF2 matrix.
</li>
<li>
<b>DIF2_CHOLESKY</b> returns the Cholesky factor of the DIF2 matrix.
</li>
<li>
<b>DIF2_DETERMINANT</b> returns the determinant of the DIF2 matrix.
</li>
<li>
<b>DIF2_EIGENVALUES</b> returns the eigenvalues of the DIF2 matrix.
</li>
<li>
<b>DIF2_INVERSE</b> returns the inverse of the DIF2 matrix.
</li>
<li>
<b>DIF2_PLU</b> returns the PLU factors of the DIF2 matrix.
</li>
<li>
<b>DIF2_RHS</b> returns the DIF2 right hand side.
</li>
<li>
<b>DIF2_RIGHT</b> returns the right eigenvectors of the DIF2 matrix.
</li>
<li>
<b>DIF2_SOLUTION</b> returns the DIF2 solution matrix.
</li>
<li>
<b>DIF2CYCLIC</b> returns the DIF2CYCLIC matrix.
</li>
<li>
<b>DIF2CYCLIC_DETERMINANT:</b> determinant of the DIF2CYCLIC matrix.
</li>
<li>
<b>DIF2CYCLIC_NULL:</b> null vector of the DIF2CYCLIC matrix.
</li>
<li>
<b>DORR</b> returns the DORR matrix.
</li>
<li>
<b>DOWNSHIFT</b> returns the DOWNSHIFT matrix.
</li>
<li>
<b>DOWNSHIFT_DETERMINANT</b> returns the determinant of the DOWNSHIFT matrix.
</li>
<li>
<b>DOWNSHIFT_EIGENVALUES</b> returns the eigenvalues of the DOWNSHIFT matrix.
</li>
<li>
<b>DOWNSHIFT_INVERSE</b> returns the inverse of the DOWNSHIFT matrix.
</li>
<li>
<b>EBERLEIN</b> returns the EBERLEIN matrix.
</li>
<li>
<b>EBERLEIN_DETERMINANT</b> returns the determinant of the EBERLEIN matrix.
</li>
<li>
<b>EBERLEIN_EIGENVALUES</b> returns the eigenvalues of the EBERLEIN matrix.
</li>
<li>
<b>EBERLEIN_NULL</b> returns a left null vector of the EBERLEIN matrix.
</li>
<li>
<b>EULERIAN</b> returns the EULERIAN matrix.
</li>
<li>
<b>EULERIAN_DETERMINANT</b> returns the determinant of the EULERIAN matrix.
</li>
<li>
<b>EULERIAN_INVERSE</b> computes the inverse of the EULERIAN matrix.
</li>
<li>
<b>EXCHANGE</b> returns the EXCHANGE matrix.
</li>
<li>
<b>EXCHANGE_DETERMINANT</b> returns the determinant of the EXCHANGE matrix.
</li>
<li>
<b>EXCHANGE_EIGENVALUES</b> returns the eigenvalues of the EXCHANGE matrix.
</li>
<li>
<b>EXCHANGE_INVERSE</b> returns the inverse of the EXCHANGE matrix.
</li>
<li>
<b>EXCHANGE_RIGHT</b> returns the right eigenvectors of the EXCHANGE matrix.
</li>
<li>
<b>FIBONACCI1</b> returns the FIBONACCI1 matrix.
</li>
<li>
<b>FIBONACCI1_DETERMINANT</b> returns the determinant of the FIBONACCI1 matrix.
</li>
<li>
<b>FIBONACCI1_NULL</b> returns a null vector of the FIBONACCI1 matrix.
</li>
<li>
<b>FIBONACCI2</b> returns the FIBONACCI2 matrix.
</li>
<li>
<b>FIBONACCI2_DETERMINANT</b> returns the determinant of the FIBONACCI2 matrix.
</li>
<li>
<b>FIBONACCI2_EIGENVALUES</b> returns the eigenvalues of the FIBONACCI2 matrix.
</li>
<li>
<b>FIBONACCI2_INVERSE</b> returns the inverse of the FIBONACCI2 matrix.
</li>
<li>
<b>FIBONACCI3</b> returns the FIBONACCI3 matrix.
</li>
<li>
<b>FIBONACCI3_DETERMINANT</b> returns the determinant of the FIBONACCI3 matrix.
</li>
<li>
<b>FIBONACCI3_EIGENVALUES</b> returns the eigenvalues of the FIBONACCI3 matrix.
</li>
<li>
<b>FIBONACCI3_INVERSE</b> returns the inverse of the FIBONACCI3 matrix.
</li>
<li>
<b>FIEDLER</b> returns the FIEDLER matrix.
</li>
<li>
<b>FIEDLER_DETERMINANT</b> returns the determinant of the FIEDLER matrix.
</li>
<li>
<b>FIEDLER_INVERSE</b> returns the inverse of the FIEDLER matrix.
</li>
<li>
<b>FORSYTHE</b> returns the FORSYTHE matrix.
</li>
<li>
<b>FORSYTHE_DETERMINANT</b> returns the determinant of the FORSYTHE matrix.
</li>
<li>
<b>FORSYTHE_EIGENVALUES</b> returns the eigenvalues of the FORSYTHE matrix.
</li>
<li>
<b>FORSYTHE_INVERSE</b> returns the inverse of the Forsythe matrix.
</li>
<li>
<b>FOURIER</b> returns the FOURIER matrix.
</li>
<li>
<b>FOURIER_DETERMINANT</b> returns the determinant of the FOURIER matrix.
</li>
<li>
<b>FOURIER_EIGENVALUES</b> returns the eigenvalues of the FOURIER matrix.
</li>
<li>
<b>FOURIER_INVERSE</b> returns the inverse of the FOURIER matrix.
</li>
<li>
<b>FOURIER_COSINE</b> returns the FOURIER_COSINE matrix.
</li>
<li>
<b>FOURIER_COSINE_DETERMINANT:</b> determinant of the FOURIER_COSINE matrix.
</li>
<li>
<b>FOURIER_COSINE_INVERSE</b> returns the inverse of the FOURIER_COSINE matrix.
</li>
<li>
<b>FOURIER_SINE</b> returns the FOURIER_SINE matrix.
</li>
<li>
<b>FOURIER_SINE_DETERMINANT</b> returns the determinant of the FOURIER_SINE matrix.
</li>
<li>
<b>FOURIER_SINE_INVERSE</b> returns the inverse of the FOURIER_SINE matrix.
</li>
<li>
<b>FRANK</b> returns the FRANK matrix.
</li>
<li>
<b>FRANK_DETERMINANT</b> returns the determinant of the FRANK matrix.
</li>
<li>
<b>FRANK_INVERSE</b> returns the inverse of the FRANK matrix.
</li>
<li>
<b>FRANK_RHS</b> returns the FRANK right hand side.
</li>
<li>
<b>FRANK_SOLUTION</b> returns the FRANK solution matrix.
</li>
<li>
<b>GEAR</b> returns the GEAR matrix.
</li>
<li>
<b>GEAR_DETERMINANT</b> returns the determinant of the GEAR matrix.
</li>
<li>
<b>GEAR_EIGENVALUES</b> returns the eigenvalues of the GEAR matrix.
</li>
<li>
<b>GFPP</b> returns the GFPP matrix.
</li>
<li>
<b>GFPP_DETERMINANT</b> returns the determinant of the GFPP matrix.
</li>
<li>
<b>GFPP_INVERSE</b> returns the inverse of the GFPP matrix.
</li>
<li>
<b>GFPP_PLU</b> returns the PLU factorization of the GFPP matrix.
</li>
<li>
<b>GIVENS</b> returns the GIVENS matrix.
</li>
<li>
<b>GIVENS_DETERMINANT</b> returns the determinant of the GIVENS matrix.
</li>
<li>
<b>GIVENS_EIGENVALUES</b> returns the eigenvalues of the GIVENS matrix.
</li>
<li>
<b>GIVENS_INVERSE</b> returns the inverse of the GIVENS matrix.
</li>
<li>
<b>GIVENS_PLU</b> returns the PLU factors of the GIVENS matrix.
</li>
<li>
<b>GK316</b> returns the GK316 matrix.
</li>
<li>
<b>GK316_DETERMINANT</b> returns the determinant of the GK316 matrix.
</li>
<li>
<b>GK316_EIGENVALUES</b> returns the eigenvalues of the GK316 matrix.
</li>
<li>
<b>GK316_INVERSE</b> returns the inverse of the GK316 matrix.
</li>
<li>
<b>GK323</b> returns the GK323 matrix.
</li>
<li>
<b>GK323_DETERMINANT</b> returns the determinant of the GK323 matrix.
</li>
<li>
<b>GK323_INVERSE</b> returns the inverse of the GK323 matrix.
</li>
<li>
<b>GK324</b> returns the GK324 matrix.
</li>
<li>
<b>GK324_DETERMINANT</b> returns the determinant of the GK324 matrix.
</li>
<li>
<b>GK324_INVERSE</b> returns the inverse of the GK324 matrix.
</li>
<li>
<b>GRCAR</b> returns the GRCAR matrix.
</li>
<li>
<b>HADAMARD</b> returns the HADAMARD matrix.
</li>
<li>
<b>HAMMING</b> computes the HAMMING matrix.
</li>
<li>
<b>HANKEL</b> returns the HANKEL matrix.
</li>
<li>