1
2
3--------------------------------------------------------
4Input file: ../Matrix/A01
5name: Dense/0  n: 0 entries: 0
6--------------------------------------------------------
7
8
9AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
10    dense row parameter: 10
11    (rows with more than max (10 * sqrt (n), 16) entries are
12    considered "dense", and placed last in output permutation)
13    aggressive absorption:  yes
14    size of AMD integer: 8
15
16
17AMD version 2.4.6, May 4, 2016, results:
18    status: OK
19    n, dimension of A:                                  0
20
21    The following approximate statistics are for a subsequent
22    factorization of A(P,P) + A(P,P)'.  They are slight upper
23    bounds if there are no dense rows/columns in A+A', and become
24    looser if dense rows/columns exist.
25
26Factorize PAP'=LDL' and solve Ax=b
27Nz in L: 0  Flop count: 0
28relative maxnorm of residual: 0
29Factorize A=LDL' and solve Ax=b
30Nz in L: 0  Flop count: 0
31relative maxnorm of residual: 0
32
33
34--------------------------------------------------------
35Input file: ../Matrix/A02
36name: Dense/0  n: 0 entries: 0  (jumbled version)
37--------------------------------------------------------
38
39
40AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
41    dense row parameter: 10
42    (rows with more than max (10 * sqrt (n), 16) entries are
43    considered "dense", and placed last in output permutation)
44    aggressive absorption:  yes
45    size of AMD integer: 8
46
47
48AMD version 2.4.6, May 4, 2016, results:
49    status: OK
50    n, dimension of A:                                  0
51
52    The following approximate statistics are for a subsequent
53    factorization of A(P,P) + A(P,P)'.  They are slight upper
54    bounds if there are no dense rows/columns in A+A', and become
55    looser if dense rows/columns exist.
56
57Factorize PAP'=LDL' and solve Ax=b
58Nz in L: 0  Flop count: 0
59relative maxnorm of residual: 0
60Factorize A=LDL' and solve Ax=b
61Nz in L: 0  Flop count: 0
62relative maxnorm of residual: 0
63
64
65--------------------------------------------------------
66Input file: ../Matrix/A03
67name: Dense/1  n: 1 entries: 1
68--------------------------------------------------------
69
70
71AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
72    dense row parameter: 10
73    (rows with more than max (10 * sqrt (n), 16) entries are
74    considered "dense", and placed last in output permutation)
75    aggressive absorption:  yes
76    size of AMD integer: 8
77
78
79AMD version 2.4.6, May 4, 2016, results:
80    status: OK
81    n, dimension of A:                                  1
82    nz, number of nonzeros in A:                        1
83    symmetry of A:                                      1.0000
84    number of nonzeros on diagonal:                     1
85    nonzeros in pattern of A+A' (excl. diagonal):       0
86    # dense rows/columns of A+A':                       0
87    memory used, in bytes:                              72
88    # of memory compactions:                            0
89
90    The following approximate statistics are for a subsequent
91    factorization of A(P,P) + A(P,P)'.  They are slight upper
92    bounds if there are no dense rows/columns in A+A', and become
93    looser if dense rows/columns exist.
94
95    nonzeros in L (excluding diagonal):                 0
96    nonzeros in L (including diagonal):                 1
97    # divide operations for LDL' or LU:                 0
98    # multiply-subtract operations for LDL':            0
99    # multiply-subtract operations for LU:              0
100    max nz. in any column of L (incl. diagonal):        1
101
102    chol flop count for real A, sqrt counted as 1 flop: 1
103    LDL' flop count for real A:                         0
104    LDL' flop count for complex A:                      0
105    LU flop count for real A (with no pivoting):        0
106    LU flop count for complex A (with no pivoting):     0
107
108Factorize PAP'=LDL' and solve Ax=b
109Nz in L: 0  Flop count: 0
110relative maxnorm of residual: 0
111Factorize A=LDL' and solve Ax=b
112Nz in L: 0  Flop count: 0
113relative maxnorm of residual: 0
114
115
116--------------------------------------------------------
117Input file: ../Matrix/A04
118name: Dense/1  n: 1 entries: 2  (jumbled version)
119--------------------------------------------------------
120
121
122AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
123    dense row parameter: 10
124    (rows with more than max (10 * sqrt (n), 16) entries are
125    considered "dense", and placed last in output permutation)
126    aggressive absorption:  yes
127    size of AMD integer: 8
128
129
130AMD version 2.4.6, May 4, 2016, results:
131    status: OK, but jumbled
132    n, dimension of A:                                  1
133    nz, number of nonzeros in A:                        1
134    symmetry of A:                                      1.0000
135    number of nonzeros on diagonal:                     1
136    nonzeros in pattern of A+A' (excl. diagonal):       0
137    # dense rows/columns of A+A':                       0
138    memory used, in bytes:                              104
139    # of memory compactions:                            0
140
141    The following approximate statistics are for a subsequent
142    factorization of A(P,P) + A(P,P)'.  They are slight upper
143    bounds if there are no dense rows/columns in A+A', and become
144    looser if dense rows/columns exist.
145
146    nonzeros in L (excluding diagonal):                 0
147    nonzeros in L (including diagonal):                 1
148    # divide operations for LDL' or LU:                 0
149    # multiply-subtract operations for LDL':            0
150    # multiply-subtract operations for LU:              0
151    max nz. in any column of L (incl. diagonal):        1
152
153    chol flop count for real A, sqrt counted as 1 flop: 1
154    LDL' flop count for real A:                         0
155    LDL' flop count for complex A:                      0
156    LU flop count for real A (with no pivoting):        0
157    LU flop count for complex A (with no pivoting):     0
158
159Factorize PAP'=LDL' and solve Ax=b
160Nz in L: 0  Flop count: 0
161relative maxnorm of residual: 8.32667e-17
162Factorize A=LDL' and solve Ax=b
163Nz in L: 0  Flop count: 0
164relative maxnorm of residual: 8.32667e-17
165
166
167--------------------------------------------------------
168Input file: ../Matrix/A05
169name: Dense/2  n: 2 entries: 4
170--------------------------------------------------------
171
172
173AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
174    dense row parameter: 10
175    (rows with more than max (10 * sqrt (n), 16) entries are
176    considered "dense", and placed last in output permutation)
177    aggressive absorption:  yes
178    size of AMD integer: 8
179
180
181AMD version 2.4.6, May 4, 2016, results:
182    status: OK
183    n, dimension of A:                                  2
184    nz, number of nonzeros in A:                        4
185    symmetry of A:                                      1.0000
186    number of nonzeros on diagonal:                     2
187    nonzeros in pattern of A+A' (excl. diagonal):       2
188    # dense rows/columns of A+A':                       0
189    memory used, in bytes:                              160
190    # of memory compactions:                            0
191
192    The following approximate statistics are for a subsequent
193    factorization of A(P,P) + A(P,P)'.  They are slight upper
194    bounds if there are no dense rows/columns in A+A', and become
195    looser if dense rows/columns exist.
196
197    nonzeros in L (excluding diagonal):                 1
198    nonzeros in L (including diagonal):                 3
199    # divide operations for LDL' or LU:                 1
200    # multiply-subtract operations for LDL':            1
201    # multiply-subtract operations for LU:              1
202    max nz. in any column of L (incl. diagonal):        2
203
204    chol flop count for real A, sqrt counted as 1 flop: 5
205    LDL' flop count for real A:                         3
206    LDL' flop count for complex A:                      17
207    LU flop count for real A (with no pivoting):        3
208    LU flop count for complex A (with no pivoting):     17
209
210Factorize PAP'=LDL' and solve Ax=b
211Nz in L: 1  Flop count: 3
212relative maxnorm of residual: 5.55112e-17
213Factorize A=LDL' and solve Ax=b
214Nz in L: 1  Flop count: 3
215relative maxnorm of residual: 5.55112e-17
216
217
218--------------------------------------------------------
219Input file: ../Matrix/A06
220name: Dense/2  n: 2 entries: 5  (jumbled version)
221--------------------------------------------------------
222
223
224AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
225    dense row parameter: 10
226    (rows with more than max (10 * sqrt (n), 16) entries are
227    considered "dense", and placed last in output permutation)
228    aggressive absorption:  yes
229    size of AMD integer: 8
230
231
232AMD version 2.4.6, May 4, 2016, results:
233    status: OK, but jumbled
234    n, dimension of A:                                  2
235    nz, number of nonzeros in A:                        4
236    symmetry of A:                                      1.0000
237    number of nonzeros on diagonal:                     2
238    nonzeros in pattern of A+A' (excl. diagonal):       2
239    # dense rows/columns of A+A':                       0
240    memory used, in bytes:                              224
241    # of memory compactions:                            0
242
243    The following approximate statistics are for a subsequent
244    factorization of A(P,P) + A(P,P)'.  They are slight upper
245    bounds if there are no dense rows/columns in A+A', and become
246    looser if dense rows/columns exist.
247
248    nonzeros in L (excluding diagonal):                 1
249    nonzeros in L (including diagonal):                 3
250    # divide operations for LDL' or LU:                 1
251    # multiply-subtract operations for LDL':            1
252    # multiply-subtract operations for LU:              1
253    max nz. in any column of L (incl. diagonal):        2
254
255    chol flop count for real A, sqrt counted as 1 flop: 5
256    LDL' flop count for real A:                         3
257    LDL' flop count for complex A:                      17
258    LU flop count for real A (with no pivoting):        3
259    LU flop count for complex A (with no pivoting):     17
260
261Factorize PAP'=LDL' and solve Ax=b
262Nz in L: 1  Flop count: 3
263relative maxnorm of residual: 1.11022e-16
264Factorize A=LDL' and solve Ax=b
265Nz in L: 1  Flop count: 3
266relative maxnorm of residual: 1.11022e-16
267
268
269--------------------------------------------------------
270Input file: ../Matrix/A07
271name: Dense/3  n: 3 entries: 9
272--------------------------------------------------------
273
274
275AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
276    dense row parameter: 10
277    (rows with more than max (10 * sqrt (n), 16) entries are
278    considered "dense", and placed last in output permutation)
279    aggressive absorption:  yes
280    size of AMD integer: 8
281
282
283AMD version 2.4.6, May 4, 2016, results:
284    status: OK
285    n, dimension of A:                                  3
286    nz, number of nonzeros in A:                        9
287    symmetry of A:                                      1.0000
288    number of nonzeros on diagonal:                     3
289    nonzeros in pattern of A+A' (excl. diagonal):       6
290    # dense rows/columns of A+A':                       0
291    memory used, in bytes:                              272
292    # of memory compactions:                            0
293
294    The following approximate statistics are for a subsequent
295    factorization of A(P,P) + A(P,P)'.  They are slight upper
296    bounds if there are no dense rows/columns in A+A', and become
297    looser if dense rows/columns exist.
298
299    nonzeros in L (excluding diagonal):                 3
300    nonzeros in L (including diagonal):                 6
301    # divide operations for LDL' or LU:                 3
302    # multiply-subtract operations for LDL':            4
303    # multiply-subtract operations for LU:              5
304    max nz. in any column of L (incl. diagonal):        3
305
306    chol flop count for real A, sqrt counted as 1 flop: 14
307    LDL' flop count for real A:                         11
308    LDL' flop count for complex A:                      59
309    LU flop count for real A (with no pivoting):        13
310    LU flop count for complex A (with no pivoting):     67
311
312Factorize PAP'=LDL' and solve Ax=b
313Nz in L: 3  Flop count: 11
314relative maxnorm of residual: 1.11022e-16
315Factorize A=LDL' and solve Ax=b
316Nz in L: 3  Flop count: 11
317relative maxnorm of residual: 1.11022e-16
318
319
320--------------------------------------------------------
321Input file: ../Matrix/A08
322name: Dense/3  n: 3 entries: 11  (jumbled version)
323--------------------------------------------------------
324
325
326AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
327    dense row parameter: 10
328    (rows with more than max (10 * sqrt (n), 16) entries are
329    considered "dense", and placed last in output permutation)
330    aggressive absorption:  yes
331    size of AMD integer: 8
332
333
334AMD version 2.4.6, May 4, 2016, results:
335    status: OK, but jumbled
336    n, dimension of A:                                  3
337    nz, number of nonzeros in A:                        9
338    symmetry of A:                                      1.0000
339    number of nonzeros on diagonal:                     3
340    nonzeros in pattern of A+A' (excl. diagonal):       6
341    # dense rows/columns of A+A':                       0
342    memory used, in bytes:                              392
343    # of memory compactions:                            0
344
345    The following approximate statistics are for a subsequent
346    factorization of A(P,P) + A(P,P)'.  They are slight upper
347    bounds if there are no dense rows/columns in A+A', and become
348    looser if dense rows/columns exist.
349
350    nonzeros in L (excluding diagonal):                 3
351    nonzeros in L (including diagonal):                 6
352    # divide operations for LDL' or LU:                 3
353    # multiply-subtract operations for LDL':            4
354    # multiply-subtract operations for LU:              5
355    max nz. in any column of L (incl. diagonal):        3
356
357    chol flop count for real A, sqrt counted as 1 flop: 14
358    LDL' flop count for real A:                         11
359    LDL' flop count for complex A:                      59
360    LU flop count for real A (with no pivoting):        13
361    LU flop count for complex A (with no pivoting):     67
362
363Factorize PAP'=LDL' and solve Ax=b
364Nz in L: 3  Flop count: 11
365relative maxnorm of residual: 1.38778e-16
366Factorize A=LDL' and solve Ax=b
367Nz in L: 3  Flop count: 11
368relative maxnorm of residual: 1.38778e-16
369
370
371--------------------------------------------------------
372Input file: ../Matrix/A09
373name: HB/can_24  n: 24 entries: 160
374--------------------------------------------------------
375
376
377AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
378    dense row parameter: 10
379    (rows with more than max (10 * sqrt (n), 16) entries are
380    considered "dense", and placed last in output permutation)
381    aggressive absorption:  yes
382    size of AMD integer: 8
383
384
385AMD version 2.4.6, May 4, 2016, results:
386    status: OK
387    n, dimension of A:                                  24
388    nz, number of nonzeros in A:                        160
389    symmetry of A:                                      1.0000
390    number of nonzeros on diagonal:                     24
391    nonzeros in pattern of A+A' (excl. diagonal):       136
392    # dense rows/columns of A+A':                       0
393    memory used, in bytes:                              3032
394    # of memory compactions:                            0
395
396    The following approximate statistics are for a subsequent
397    factorization of A(P,P) + A(P,P)'.  They are slight upper
398    bounds if there are no dense rows/columns in A+A', and become
399    looser if dense rows/columns exist.
400
401    nonzeros in L (excluding diagonal):                 97
402    nonzeros in L (including diagonal):                 121
403    # divide operations for LDL' or LU:                 97
404    # multiply-subtract operations for LDL':            275
405    # multiply-subtract operations for LU:              453
406    max nz. in any column of L (incl. diagonal):        8
407
408    chol flop count for real A, sqrt counted as 1 flop: 671
409    LDL' flop count for real A:                         647
410    LDL' flop count for complex A:                      3073
411    LU flop count for real A (with no pivoting):        1003
412    LU flop count for complex A (with no pivoting):     4497
413
414Factorize PAP'=LDL' and solve Ax=b
415Nz in L: 96  Flop count: 632
416Ax=b not solved since D(1,1) is zero.
417Factorize A=LDL' and solve Ax=b
418Nz in L: 146  Flop count: 1360
419Ax=b not solved since D(5,5) is zero.
420
421
422--------------------------------------------------------
423Input file: ../Matrix/A10
424name: HB/can_24  n: 24 entries: 188  (jumbled version)
425--------------------------------------------------------
426
427
428AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
429    dense row parameter: 10
430    (rows with more than max (10 * sqrt (n), 16) entries are
431    considered "dense", and placed last in output permutation)
432    aggressive absorption:  yes
433    size of AMD integer: 8
434
435
436AMD version 2.4.6, May 4, 2016, results:
437    status: OK, but jumbled
438    n, dimension of A:                                  24
439    nz, number of nonzeros in A:                        160
440    symmetry of A:                                      1.0000
441    number of nonzeros on diagonal:                     24
442    nonzeros in pattern of A+A' (excl. diagonal):       136
443    # dense rows/columns of A+A':                       0
444    memory used, in bytes:                              4736
445    # of memory compactions:                            0
446
447    The following approximate statistics are for a subsequent
448    factorization of A(P,P) + A(P,P)'.  They are slight upper
449    bounds if there are no dense rows/columns in A+A', and become
450    looser if dense rows/columns exist.
451
452    nonzeros in L (excluding diagonal):                 97
453    nonzeros in L (including diagonal):                 121
454    # divide operations for LDL' or LU:                 97
455    # multiply-subtract operations for LDL':            275
456    # multiply-subtract operations for LU:              453
457    max nz. in any column of L (incl. diagonal):        8
458
459    chol flop count for real A, sqrt counted as 1 flop: 671
460    LDL' flop count for real A:                         647
461    LDL' flop count for complex A:                      3073
462    LU flop count for real A (with no pivoting):        1003
463    LU flop count for complex A (with no pivoting):     4497
464
465Factorize PAP'=LDL' and solve Ax=b
466Nz in L: 96  Flop count: 632
467Ax=b not solved since D(1,1) is zero.
468Factorize A=LDL' and solve Ax=b
469Nz in L: 146  Flop count: 1360
470Ax=b not solved since D(5,5) is zero.
471
472
473--------------------------------------------------------
474Input file: ../Matrix/A11
475name: FIDAP/ex5  n: 27 entries: 279
476--------------------------------------------------------
477
478
479AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
480    dense row parameter: 10
481    (rows with more than max (10 * sqrt (n), 16) entries are
482    considered "dense", and placed last in output permutation)
483    aggressive absorption:  yes
484    size of AMD integer: 8
485
486
487AMD version 2.4.6, May 4, 2016, results:
488    status: OK
489    n, dimension of A:                                  27
490    nz, number of nonzeros in A:                        279
491    symmetry of A:                                      1.0000
492    number of nonzeros on diagonal:                     27
493    nonzeros in pattern of A+A' (excl. diagonal):       252
494    # dense rows/columns of A+A':                       0
495    memory used, in bytes:                              4360
496    # of memory compactions:                            0
497
498    The following approximate statistics are for a subsequent
499    factorization of A(P,P) + A(P,P)'.  They are slight upper
500    bounds if there are no dense rows/columns in A+A', and become
501    looser if dense rows/columns exist.
502
503    nonzeros in L (excluding diagonal):                 126
504    nonzeros in L (including diagonal):                 153
505    # divide operations for LDL' or LU:                 126
506    # multiply-subtract operations for LDL':            414
507    # multiply-subtract operations for LU:              702
508    max nz. in any column of L (incl. diagonal):        9
509
510    chol flop count for real A, sqrt counted as 1 flop: 981
511    LDL' flop count for real A:                         954
512    LDL' flop count for complex A:                      4446
513    LU flop count for real A (with no pivoting):        1530
514    LU flop count for complex A (with no pivoting):     6750
515
516Factorize PAP'=LDL' and solve Ax=b
517Nz in L: 126  Flop count: 954
518relative maxnorm of residual: 2.59625e-10
519Factorize A=LDL' and solve Ax=b
520Nz in L: 276  Flop count: 4206
521relative maxnorm of residual: 2.72848e-10
522
523
524--------------------------------------------------------
525Input file: ../Matrix/A12
526name: FIDAP/ex5  n: 27 entries: 325  (jumbled version)
527--------------------------------------------------------
528
529
530AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
531    dense row parameter: 10
532    (rows with more than max (10 * sqrt (n), 16) entries are
533    considered "dense", and placed last in output permutation)
534    aggressive absorption:  yes
535    size of AMD integer: 8
536
537
538AMD version 2.4.6, May 4, 2016, results:
539    status: OK, but jumbled
540    n, dimension of A:                                  27
541    nz, number of nonzeros in A:                        279
542    symmetry of A:                                      1.0000
543    number of nonzeros on diagonal:                     27
544    nonzeros in pattern of A+A' (excl. diagonal):       252
545    # dense rows/columns of A+A':                       0
546    memory used, in bytes:                              7184
547    # of memory compactions:                            0
548
549    The following approximate statistics are for a subsequent
550    factorization of A(P,P) + A(P,P)'.  They are slight upper
551    bounds if there are no dense rows/columns in A+A', and become
552    looser if dense rows/columns exist.
553
554    nonzeros in L (excluding diagonal):                 126
555    nonzeros in L (including diagonal):                 153
556    # divide operations for LDL' or LU:                 126
557    # multiply-subtract operations for LDL':            414
558    # multiply-subtract operations for LU:              702
559    max nz. in any column of L (incl. diagonal):        9
560
561    chol flop count for real A, sqrt counted as 1 flop: 981
562    LDL' flop count for real A:                         954
563    LDL' flop count for complex A:                      4446
564    LU flop count for real A (with no pivoting):        1530
565    LU flop count for complex A (with no pivoting):     6750
566
567Factorize PAP'=LDL' and solve Ax=b
568Nz in L: 126  Flop count: 954
569relative maxnorm of residual: 3.27418e-10
570Factorize A=LDL' and solve Ax=b
571Nz in L: 276  Flop count: 4206
572relative maxnorm of residual: 2.32376e-10
573
574
575--------------------------------------------------------
576Input file: ../Matrix/A13
577name: HB/bcsstk01  n: 48 entries: 400
578--------------------------------------------------------
579
580
581AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
582    dense row parameter: 10
583    (rows with more than max (10 * sqrt (n), 16) entries are
584    considered "dense", and placed last in output permutation)
585    aggressive absorption:  yes
586    size of AMD integer: 8
587
588
589AMD version 2.4.6, May 4, 2016, results:
590    status: OK
591    n, dimension of A:                                  48
592    nz, number of nonzeros in A:                        400
593    symmetry of A:                                      1.0000
594    number of nonzeros on diagonal:                     48
595    nonzeros in pattern of A+A' (excl. diagonal):       352
596    # dense rows/columns of A+A':                       0
597    memory used, in bytes:                              6832
598    # of memory compactions:                            0
599
600    The following approximate statistics are for a subsequent
601    factorization of A(P,P) + A(P,P)'.  They are slight upper
602    bounds if there are no dense rows/columns in A+A', and become
603    looser if dense rows/columns exist.
604
605    nonzeros in L (excluding diagonal):                 441
606    nonzeros in L (including diagonal):                 489
607    # divide operations for LDL' or LU:                 441
608    # multiply-subtract operations for LDL':            2760
609    # multiply-subtract operations for LU:              5079
610    max nz. in any column of L (incl. diagonal):        20
611
612    chol flop count for real A, sqrt counted as 1 flop: 6009
613    LDL' flop count for real A:                         5961
614    LDL' flop count for complex A:                      26049
615    LU flop count for real A (with no pivoting):        10599
616    LU flop count for complex A (with no pivoting):     44601
617
618Factorize PAP'=LDL' and solve Ax=b
619Nz in L: 441  Flop count: 5961
620relative maxnorm of residual: 2.38712e-13
621Factorize A=LDL' and solve Ax=b
622Nz in L: 829  Flop count: 20103
623relative maxnorm of residual: 2.27374e-13
624
625
626--------------------------------------------------------
627Input file: ../Matrix/A14
628name: HB/bcsstk01  n: 48 entries: 472  (jumbled version)
629--------------------------------------------------------
630
631
632AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
633    dense row parameter: 10
634    (rows with more than max (10 * sqrt (n), 16) entries are
635    considered "dense", and placed last in output permutation)
636    aggressive absorption:  yes
637    size of AMD integer: 8
638
639
640AMD version 2.4.6, May 4, 2016, results:
641    status: OK, but jumbled
642    n, dimension of A:                                  48
643    nz, number of nonzeros in A:                        400
644    symmetry of A:                                      1.0000
645    number of nonzeros on diagonal:                     48
646    nonzeros in pattern of A+A' (excl. diagonal):       352
647    # dense rows/columns of A+A':                       0
648    memory used, in bytes:                              11000
649    # of memory compactions:                            0
650
651    The following approximate statistics are for a subsequent
652    factorization of A(P,P) + A(P,P)'.  They are slight upper
653    bounds if there are no dense rows/columns in A+A', and become
654    looser if dense rows/columns exist.
655
656    nonzeros in L (excluding diagonal):                 441
657    nonzeros in L (including diagonal):                 489
658    # divide operations for LDL' or LU:                 441
659    # multiply-subtract operations for LDL':            2760
660    # multiply-subtract operations for LU:              5079
661    max nz. in any column of L (incl. diagonal):        20
662
663    chol flop count for real A, sqrt counted as 1 flop: 6009
664    LDL' flop count for real A:                         5961
665    LDL' flop count for complex A:                      26049
666    LU flop count for real A (with no pivoting):        10599
667    LU flop count for complex A (with no pivoting):     44601
668
669Factorize PAP'=LDL' and solve Ax=b
670Nz in L: 441  Flop count: 5961
671relative maxnorm of residual: 2.27374e-13
672Factorize A=LDL' and solve Ax=b
673Nz in L: 829  Flop count: 20103
674relative maxnorm of residual: 3.83693e-13
675
676
677--------------------------------------------------------
678Input file: ../Matrix/A15
679name: HB/bcsstm01  n: 48 entries: 24
680--------------------------------------------------------
681
682
683AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
684    dense row parameter: 10
685    (rows with more than max (10 * sqrt (n), 16) entries are
686    considered "dense", and placed last in output permutation)
687    aggressive absorption:  yes
688    size of AMD integer: 8
689
690
691AMD version 2.4.6, May 4, 2016, results:
692    status: OK
693    n, dimension of A:                                  48
694    nz, number of nonzeros in A:                        24
695    symmetry of A:                                      1.0000
696    number of nonzeros on diagonal:                     24
697    nonzeros in pattern of A+A' (excl. diagonal):       0
698    # dense rows/columns of A+A':                       0
699    memory used, in bytes:                              3456
700    # of memory compactions:                            0
701
702    The following approximate statistics are for a subsequent
703    factorization of A(P,P) + A(P,P)'.  They are slight upper
704    bounds if there are no dense rows/columns in A+A', and become
705    looser if dense rows/columns exist.
706
707    nonzeros in L (excluding diagonal):                 0
708    nonzeros in L (including diagonal):                 48
709    # divide operations for LDL' or LU:                 0
710    # multiply-subtract operations for LDL':            0
711    # multiply-subtract operations for LU:              0
712    max nz. in any column of L (incl. diagonal):        1
713
714    chol flop count for real A, sqrt counted as 1 flop: 48
715    LDL' flop count for real A:                         0
716    LDL' flop count for complex A:                      0
717    LU flop count for real A (with no pivoting):        0
718    LU flop count for complex A (with no pivoting):     0
719
720Factorize PAP'=LDL' and solve Ax=b
721Nz in L: 0  Flop count: 0
722Ax=b not solved since D(3,3) is zero.
723Factorize A=LDL' and solve Ax=b
724Nz in L: 0  Flop count: 0
725Ax=b not solved since D(3,3) is zero.
726
727
728--------------------------------------------------------
729Input file: ../Matrix/A16
730name: HB/bcsstm01  n: 48 entries: 26  (jumbled version)
731--------------------------------------------------------
732
733
734AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
735    dense row parameter: 10
736    (rows with more than max (10 * sqrt (n), 16) entries are
737    considered "dense", and placed last in output permutation)
738    aggressive absorption:  yes
739    size of AMD integer: 8
740
741
742AMD version 2.4.6, May 4, 2016, results:
743    status: OK, but jumbled
744    n, dimension of A:                                  48
745    nz, number of nonzeros in A:                        24
746    symmetry of A:                                      1.0000
747    number of nonzeros on diagonal:                     24
748    nonzeros in pattern of A+A' (excl. diagonal):       0
749    # dense rows/columns of A+A':                       0
750    memory used, in bytes:                              4056
751    # of memory compactions:                            0
752
753    The following approximate statistics are for a subsequent
754    factorization of A(P,P) + A(P,P)'.  They are slight upper
755    bounds if there are no dense rows/columns in A+A', and become
756    looser if dense rows/columns exist.
757
758    nonzeros in L (excluding diagonal):                 0
759    nonzeros in L (including diagonal):                 48
760    # divide operations for LDL' or LU:                 0
761    # multiply-subtract operations for LDL':            0
762    # multiply-subtract operations for LU:              0
763    max nz. in any column of L (incl. diagonal):        1
764
765    chol flop count for real A, sqrt counted as 1 flop: 48
766    LDL' flop count for real A:                         0
767    LDL' flop count for complex A:                      0
768    LU flop count for real A (with no pivoting):        0
769    LU flop count for complex A (with no pivoting):     0
770
771Factorize PAP'=LDL' and solve Ax=b
772Nz in L: 0  Flop count: 0
773Ax=b not solved since D(3,3) is zero.
774Factorize A=LDL' and solve Ax=b
775Nz in L: 0  Flop count: 0
776Ax=b not solved since D(3,3) is zero.
777
778
779--------------------------------------------------------
780Input file: ../Matrix/A17
781name: Pothen/mesh1e1  n: 48 entries: 306
782--------------------------------------------------------
783
784
785AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
786    dense row parameter: 10
787    (rows with more than max (10 * sqrt (n), 16) entries are
788    considered "dense", and placed last in output permutation)
789    aggressive absorption:  yes
790    size of AMD integer: 8
791
792
793AMD version 2.4.6, May 4, 2016, results:
794    status: OK
795    n, dimension of A:                                  48
796    nz, number of nonzeros in A:                        306
797    symmetry of A:                                      1.0000
798    number of nonzeros on diagonal:                     48
799    nonzeros in pattern of A+A' (excl. diagonal):       258
800    # dense rows/columns of A+A':                       0
801    memory used, in bytes:                              5928
802    # of memory compactions:                            1
803
804    The following approximate statistics are for a subsequent
805    factorization of A(P,P) + A(P,P)'.  They are slight upper
806    bounds if there are no dense rows/columns in A+A', and become
807    looser if dense rows/columns exist.
808
809    nonzeros in L (excluding diagonal):                 288
810    nonzeros in L (including diagonal):                 336
811    # divide operations for LDL' or LU:                 288
812    # multiply-subtract operations for LDL':            1171
813    # multiply-subtract operations for LU:              2054
814    max nz. in any column of L (incl. diagonal):        13
815
816    chol flop count for real A, sqrt counted as 1 flop: 2678
817    LDL' flop count for real A:                         2630
818    LDL' flop count for complex A:                      11960
819    LU flop count for real A (with no pivoting):        4396
820    LU flop count for complex A (with no pivoting):     19024
821
822Factorize PAP'=LDL' and solve Ax=b
823Nz in L: 288  Flop count: 2630
824relative maxnorm of residual: 5.96745e-16
825Factorize A=LDL' and solve Ax=b
826Nz in L: 511  Flop count: 7383
827relative maxnorm of residual: 6.93889e-16
828
829
830--------------------------------------------------------
831Input file: ../Matrix/A18
832name: Pothen/mesh1e1  n: 48 entries: 359  (jumbled version)
833--------------------------------------------------------
834
835
836AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
837    dense row parameter: 10
838    (rows with more than max (10 * sqrt (n), 16) entries are
839    considered "dense", and placed last in output permutation)
840    aggressive absorption:  yes
841    size of AMD integer: 8
842
843
844AMD version 2.4.6, May 4, 2016, results:
845    status: OK, but jumbled
846    n, dimension of A:                                  48
847    nz, number of nonzeros in A:                        306
848    symmetry of A:                                      1.0000
849    number of nonzeros on diagonal:                     48
850    nonzeros in pattern of A+A' (excl. diagonal):       258
851    # dense rows/columns of A+A':                       0
852    memory used, in bytes:                              9192
853    # of memory compactions:                            1
854
855    The following approximate statistics are for a subsequent
856    factorization of A(P,P) + A(P,P)'.  They are slight upper
857    bounds if there are no dense rows/columns in A+A', and become
858    looser if dense rows/columns exist.
859
860    nonzeros in L (excluding diagonal):                 288
861    nonzeros in L (including diagonal):                 336
862    # divide operations for LDL' or LU:                 288
863    # multiply-subtract operations for LDL':            1171
864    # multiply-subtract operations for LU:              2054
865    max nz. in any column of L (incl. diagonal):        13
866
867    chol flop count for real A, sqrt counted as 1 flop: 2678
868    LDL' flop count for real A:                         2630
869    LDL' flop count for complex A:                      11960
870    LU flop count for real A (with no pivoting):        4396
871    LU flop count for complex A (with no pivoting):     19024
872
873Factorize PAP'=LDL' and solve Ax=b
874Nz in L: 288  Flop count: 2630
875relative maxnorm of residual: 5.55112e-16
876Factorize A=LDL' and solve Ax=b
877Nz in L: 511  Flop count: 7383
878relative maxnorm of residual: 5.55112e-16
879
880
881--------------------------------------------------------
882Input file: ../Matrix/A19
883name: Bai/bfwb62  n: 62 entries: 342
884--------------------------------------------------------
885
886
887AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
888    dense row parameter: 10
889    (rows with more than max (10 * sqrt (n), 16) entries are
890    considered "dense", and placed last in output permutation)
891    aggressive absorption:  yes
892    size of AMD integer: 8
893
894
895AMD version 2.4.6, May 4, 2016, results:
896    status: OK
897    n, dimension of A:                                  62
898    nz, number of nonzeros in A:                        342
899    symmetry of A:                                      1.0000
900    number of nonzeros on diagonal:                     62
901    nonzeros in pattern of A+A' (excl. diagonal):       280
902    # dense rows/columns of A+A':                       0
903    memory used, in bytes:                              7152
904    # of memory compactions:                            0
905
906    The following approximate statistics are for a subsequent
907    factorization of A(P,P) + A(P,P)'.  They are slight upper
908    bounds if there are no dense rows/columns in A+A', and become
909    looser if dense rows/columns exist.
910
911    nonzeros in L (excluding diagonal):                 226
912    nonzeros in L (including diagonal):                 288
913    # divide operations for LDL' or LU:                 226
914    # multiply-subtract operations for LDL':            623
915    # multiply-subtract operations for LU:              1020
916    max nz. in any column of L (incl. diagonal):        9
917
918    chol flop count for real A, sqrt counted as 1 flop: 1534
919    LDL' flop count for real A:                         1472
920    LDL' flop count for complex A:                      7018
921    LU flop count for real A (with no pivoting):        2266
922    LU flop count for complex A (with no pivoting):     10194
923
924Factorize PAP'=LDL' and solve Ax=b
925Nz in L: 226  Flop count: 1472
926relative maxnorm of residual: 5.55112e-16
927Factorize A=LDL' and solve Ax=b
928Nz in L: 662  Flop count: 11350
929relative maxnorm of residual: 1.11022e-15
930
931
932--------------------------------------------------------
933Input file: ../Matrix/A20
934name: Bai/bfwb62  n: 62 entries: 407  (jumbled version)
935--------------------------------------------------------
936
937
938AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
939    dense row parameter: 10
940    (rows with more than max (10 * sqrt (n), 16) entries are
941    considered "dense", and placed last in output permutation)
942    aggressive absorption:  yes
943    size of AMD integer: 8
944
945
946AMD version 2.4.6, May 4, 2016, results:
947    status: OK, but jumbled
948    n, dimension of A:                                  62
949    nz, number of nonzeros in A:                        342
950    symmetry of A:                                      1.0000
951    number of nonzeros on diagonal:                     62
952    nonzeros in pattern of A+A' (excl. diagonal):       280
953    # dense rows/columns of A+A':                       0
954    memory used, in bytes:                              10912
955    # of memory compactions:                            0
956
957    The following approximate statistics are for a subsequent
958    factorization of A(P,P) + A(P,P)'.  They are slight upper
959    bounds if there are no dense rows/columns in A+A', and become
960    looser if dense rows/columns exist.
961
962    nonzeros in L (excluding diagonal):                 226
963    nonzeros in L (including diagonal):                 288
964    # divide operations for LDL' or LU:                 226
965    # multiply-subtract operations for LDL':            623
966    # multiply-subtract operations for LU:              1020
967    max nz. in any column of L (incl. diagonal):        9
968
969    chol flop count for real A, sqrt counted as 1 flop: 1534
970    LDL' flop count for real A:                         1472
971    LDL' flop count for complex A:                      7018
972    LU flop count for real A (with no pivoting):        2266
973    LU flop count for complex A (with no pivoting):     10194
974
975Factorize PAP'=LDL' and solve Ax=b
976Nz in L: 226  Flop count: 1472
977relative maxnorm of residual: 5.68434e-14
978Factorize A=LDL' and solve Ax=b
979Nz in L: 662  Flop count: 11350
980relative maxnorm of residual: 2.15827e-12
981
982
983--------------------------------------------------------
984Input file: ../Matrix/A21
985name: HB/bcsstk02  n: 66 entries: 4356
986--------------------------------------------------------
987
988
989AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
990    dense row parameter: 10
991    (rows with more than max (10 * sqrt (n), 16) entries are
992    considered "dense", and placed last in output permutation)
993    aggressive absorption:  yes
994    size of AMD integer: 8
995
996
997AMD version 2.4.6, May 4, 2016, results:
998    status: OK
999    n, dimension of A:                                  66
1000    nz, number of nonzeros in A:                        4356
1001    symmetry of A:                                      1.0000
1002    number of nonzeros on diagonal:                     66
1003    nonzeros in pattern of A+A' (excl. diagonal):       4290
1004    # dense rows/columns of A+A':                       0
1005    memory used, in bytes:                              45936
1006    # of memory compactions:                            0
1007
1008    The following approximate statistics are for a subsequent
1009    factorization of A(P,P) + A(P,P)'.  They are slight upper
1010    bounds if there are no dense rows/columns in A+A', and become
1011    looser if dense rows/columns exist.
1012
1013    nonzeros in L (excluding diagonal):                 2145
1014    nonzeros in L (including diagonal):                 2211
1015    # divide operations for LDL' or LU:                 2145
1016    # multiply-subtract operations for LDL':            47905
1017    # multiply-subtract operations for LU:              93665
1018    max nz. in any column of L (incl. diagonal):        66
1019
1020    chol flop count for real A, sqrt counted as 1 flop: 98021
1021    LDL' flop count for real A:                         97955
1022    LDL' flop count for complex A:                      402545
1023    LU flop count for real A (with no pivoting):        189475
1024    LU flop count for complex A (with no pivoting):     768625
1025
1026Factorize PAP'=LDL' and solve Ax=b
1027Nz in L: 2145  Flop count: 97955
1028relative maxnorm of residual: 7.50219e-13
1029Factorize A=LDL' and solve Ax=b
1030Nz in L: 2145  Flop count: 97955
1031relative maxnorm of residual: 7.50219e-13
1032
1033
1034--------------------------------------------------------
1035Input file: ../Matrix/A22
1036name: HB/bcsstk02  n: 66 entries: 5175  (jumbled version)
1037--------------------------------------------------------
1038
1039
1040AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
1041    dense row parameter: 10
1042    (rows with more than max (10 * sqrt (n), 16) entries are
1043    considered "dense", and placed last in output permutation)
1044    aggressive absorption:  yes
1045    size of AMD integer: 8
1046
1047
1048AMD version 2.4.6, May 4, 2016, results:
1049    status: OK, but jumbled
1050    n, dimension of A:                                  66
1051    nz, number of nonzeros in A:                        4356
1052    symmetry of A:                                      1.0000
1053    number of nonzeros on diagonal:                     66
1054    nonzeros in pattern of A+A' (excl. diagonal):       4290
1055    # dense rows/columns of A+A':                       0
1056    memory used, in bytes:                              87872
1057    # of memory compactions:                            0
1058
1059    The following approximate statistics are for a subsequent
1060    factorization of A(P,P) + A(P,P)'.  They are slight upper
1061    bounds if there are no dense rows/columns in A+A', and become
1062    looser if dense rows/columns exist.
1063
1064    nonzeros in L (excluding diagonal):                 2145
1065    nonzeros in L (including diagonal):                 2211
1066    # divide operations for LDL' or LU:                 2145
1067    # multiply-subtract operations for LDL':            47905
1068    # multiply-subtract operations for LU:              93665
1069    max nz. in any column of L (incl. diagonal):        66
1070
1071    chol flop count for real A, sqrt counted as 1 flop: 98021
1072    LDL' flop count for real A:                         97955
1073    LDL' flop count for complex A:                      402545
1074    LU flop count for real A (with no pivoting):        189475
1075    LU flop count for complex A (with no pivoting):     768625
1076
1077Factorize PAP'=LDL' and solve Ax=b
1078Nz in L: 2145  Flop count: 97955
1079relative maxnorm of residual: 8.59759e-13
1080Factorize A=LDL' and solve Ax=b
1081Nz in L: 2145  Flop count: 97955
1082relative maxnorm of residual: 8.59759e-13
1083
1084
1085--------------------------------------------------------
1086Input file: ../Matrix/A23
1087name: HB/bcsstm02  n: 66 entries: 66
1088--------------------------------------------------------
1089
1090
1091AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
1092    dense row parameter: 10
1093    (rows with more than max (10 * sqrt (n), 16) entries are
1094    considered "dense", and placed last in output permutation)
1095    aggressive absorption:  yes
1096    size of AMD integer: 8
1097
1098
1099AMD version 2.4.6, May 4, 2016, results:
1100    status: OK
1101    n, dimension of A:                                  66
1102    nz, number of nonzeros in A:                        66
1103    symmetry of A:                                      1.0000
1104    number of nonzeros on diagonal:                     66
1105    nonzeros in pattern of A+A' (excl. diagonal):       0
1106    # dense rows/columns of A+A':                       0
1107    memory used, in bytes:                              4752
1108    # of memory compactions:                            0
1109
1110    The following approximate statistics are for a subsequent
1111    factorization of A(P,P) + A(P,P)'.  They are slight upper
1112    bounds if there are no dense rows/columns in A+A', and become
1113    looser if dense rows/columns exist.
1114
1115    nonzeros in L (excluding diagonal):                 0
1116    nonzeros in L (including diagonal):                 66
1117    # divide operations for LDL' or LU:                 0
1118    # multiply-subtract operations for LDL':            0
1119    # multiply-subtract operations for LU:              0
1120    max nz. in any column of L (incl. diagonal):        1
1121
1122    chol flop count for real A, sqrt counted as 1 flop: 66
1123    LDL' flop count for real A:                         0
1124    LDL' flop count for complex A:                      0
1125    LU flop count for real A (with no pivoting):        0
1126    LU flop count for complex A (with no pivoting):     0
1127
1128Factorize PAP'=LDL' and solve Ax=b
1129Nz in L: 0  Flop count: 0
1130relative maxnorm of residual: 2.22045e-16
1131Factorize A=LDL' and solve Ax=b
1132Nz in L: 0  Flop count: 0
1133relative maxnorm of residual: 2.22045e-16
1134
1135
1136--------------------------------------------------------
1137Input file: ../Matrix/A24
1138name: HB/bcsstm02  n: 66 entries: 72  (jumbled version)
1139--------------------------------------------------------
1140
1141
1142AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering
1143    dense row parameter: 10
1144    (rows with more than max (10 * sqrt (n), 16) entries are
1145    considered "dense", and placed last in output permutation)
1146    aggressive absorption:  yes
1147    size of AMD integer: 8
1148
1149
1150AMD version 2.4.6, May 4, 2016, results:
1151    status: OK, but jumbled
1152    n, dimension of A:                                  66
1153    nz, number of nonzeros in A:                        66
1154    symmetry of A:                                      1.0000
1155    number of nonzeros on diagonal:                     66
1156    nonzeros in pattern of A+A' (excl. diagonal):       0
1157    # dense rows/columns of A+A':                       0
1158    memory used, in bytes:                              5864
1159    # of memory compactions:                            0
1160
1161    The following approximate statistics are for a subsequent
1162    factorization of A(P,P) + A(P,P)'.  They are slight upper
1163    bounds if there are no dense rows/columns in A+A', and become
1164    looser if dense rows/columns exist.
1165
1166    nonzeros in L (excluding diagonal):                 0
1167    nonzeros in L (including diagonal):                 66
1168    # divide operations for LDL' or LU:                 0
1169    # multiply-subtract operations for LDL':            0
1170    # multiply-subtract operations for LU:              0
1171    max nz. in any column of L (incl. diagonal):        1
1172
1173    chol flop count for real A, sqrt counted as 1 flop: 66
1174    LDL' flop count for real A:                         0
1175    LDL' flop count for complex A:                      0
1176    LU flop count for real A (with no pivoting):        0
1177    LU flop count for complex A (with no pivoting):     0
1178
1179Factorize PAP'=LDL' and solve Ax=b
1180Nz in L: 0  Flop count: 0
1181relative maxnorm of residual: 2.22045e-16
1182Factorize A=LDL' and solve Ax=b
1183Nz in L: 0  Flop count: 0
1184relative maxnorm of residual: 2.22045e-16
1185
1186
1187--------------------------------------------------------
1188Input file: ../Matrix/A25
1189name: Dense/0  n: 0 entries: 0 (invalid matrix, Ap [0] = 1)
1190--------------------------------------------------------
1191
1192ldlamd: invalid matrix and/or permutation
1193
1194
1195--------------------------------------------------------
1196Input file: ../Matrix/A26
1197name: Dense/2  n: 2 entries: 4 (invalid perm, P[1]=99)
1198--------------------------------------------------------
1199
1200ldlamd: invalid matrix and/or permutation
1201
1202
1203--------------------------------------------------------
1204Input file: ../Matrix/A27
1205name: Dense/3  n: 3 entries: 9 (invalid perm)
1206--------------------------------------------------------
1207
1208ldlamd: invalid matrix and/or permutation
1209
1210
1211--------------------------------------------------------
1212Input file: ../Matrix/A28
1213name: Dense/3  n: 3 entries: 9 (invalid Ap)
1214--------------------------------------------------------
1215
1216ldlamd: invalid matrix and/or permutation
1217
1218
1219--------------------------------------------------------
1220Input file: ../Matrix/A29
1221name: Dense/3  n: 3 entries: 9 (invalid Ai)
1222--------------------------------------------------------
1223
1224ldlamd: invalid matrix and/or permutation
1225
1226
1227--------------------------------------------------------
1228Input file: ../Matrix/A30
1229name: Dense/3  n: 3 entries: 9 (invalid Ai)
1230--------------------------------------------------------
1231
1232ldlamd: invalid matrix and/or permutation
1233
1234Largest residual during all tests: 3.27418e-10
1235
1236ldlamd: all tests passed
1237