1
./readhb_nozeros < HB/can_24.psa > tmp/A
3
./readhb_size < HB/can_24.psa > tmp/Asize
6
===========================================================
7
=== UMFPACK v5.0.1 ========================================
8
===========================================================
9
UMFPACK V5.0.1 (Aug 31, 2006), Control:
10
Matrix entry defined as: double
11
Int (generic integer) defined as: int
14
1: dense row parameter: 0.2
15
"dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
16
2: dense column parameter: 0.2
17
"dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
18
3: pivot tolerance: 0.1
19
4: block size for dense matrix kernels: 32
21
6: initial allocation ratio: 0.7
22
7: max iterative refinement steps: 2
23
12: 2-by-2 pivot tolerance: 0.01
24
13: Q fixed during numerical factorization: 0 (auto)
25
14: AMD dense row/col parameter: 10
26
"dense" rows/columns have > max (16, (10)*sqrt(n)) entries
27
Only used if the AMD ordering is used.
28
15: diagonal pivot tolerance: 0.001
29
Only used if diagonal pivoting is attempted.
30
16: scaling: 1 (divide each row by sum of abs. values in each row)
31
17: frontal matrix allocation ratio: 0.5
33
19: AMD and COLAMD aggressive absorption: 1 (yes)
35
The following options can only be changed at compile-time:
36
8: BLAS library used: Fortran BLAS. size of BLAS integer: 4
37
9: compiled for ANSI C
38
10: CPU timer is POSIX times ( ) routine.
39
11: compiled for normal operation (debugging disabled)
40
computer/operating system: Linux
41
size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes)
45
n 24 nrow 24 ncol 24 nz 160
46
triplet-form matrix, n_row = 24, n_col = 24 nz = 160. OK
48
triplet-to-col time: wall 0 cpu 0
49
column-form matrix, n_row 24 n_col 24, nz = 160. OK
51
UMFPACK V5.0.1 (Aug 31, 2006), Info:
52
matrix entry defined as: double
53
Int (generic integer) defined as: int
54
BLAS library used: Fortran BLAS. size of BLAS integer: 4
56
CPU timer: POSIX times ( ) routine.
57
number of rows in matrix A: 24
58
number of columns in matrix A: 24
59
entries in matrix A: 160
60
memory usage reported in: 8-byte Units
62
size of UF_long: 8 bytes
63
size of pointer: 8 bytes
64
size of numerical entry: 8 bytes
66
strategy used: symmetric
67
ordering used: amd on A+A'
68
modify Q during factorization: no
69
prefer diagonal pivoting: yes
70
pivots with zero Markowitz cost: 0
71
submatrix S after removing zero-cost pivots:
72
number of "dense" rows: 0
73
number of "dense" columns: 0
74
number of empty rows: 0
75
number of empty columns 0
76
submatrix S square and diagonal preserved
77
pattern of square submatrix S:
78
number rows and columns 24
79
symmetry of nonzero pattern: 1.000000
80
nz in S+S' (excl. diagonal): 136
81
nz on diagonal of matrix S: 24
82
fraction of nz on diagonal: 1.000000
83
AMD statistics, for strict diagonal pivoting:
84
est. flops for LU factorization: 1.00300e+03
85
est. nz in L+U (incl. diagonal): 218
86
est. largest front (# entries): 64
87
est. max nz in any column of L: 8
88
number of "dense" rows/columns in S+S': 0
89
symbolic factorization defragmentations: 0
90
symbolic memory usage (Units): 725
91
symbolic memory usage (MBytes): 0.0
92
Symbolic size (Units): 131
93
Symbolic size (MBytes): 0
94
symbolic factorization CPU time (sec): 0.00
95
symbolic factorization wallclock time(sec): 0.00
97
symbolic/numeric factorization: upper bound actual %
98
variable-sized part of Numeric object:
99
initial size (Units) 763 - -
100
peak size (Units) 3244 - -
101
final size (Units) 393 - -
102
Numeric final size (Units) 598 - -
103
Numeric final size (MBytes) 0.0 - -
104
peak memory usage (Units) 3840 - -
105
peak memory usage (MBytes) 0.0 - -
106
numeric factorization flops 2.37900e+03 - -
107
nz in L (incl diagonal) 149 - -
108
nz in U (incl diagonal) 208 - -
109
nz in L+U (incl diagonal) 333 - -
110
largest front (# entries) 182 - -
111
largest # rows in front 13 - -
112
largest # columns in front 14 - -
118
UMFPACK V5.0.1 (Aug 31, 2006), Info:
119
matrix entry defined as: double
120
Int (generic integer) defined as: int
121
BLAS library used: Fortran BLAS. size of BLAS integer: 4
123
CPU timer: POSIX times ( ) routine.
124
number of rows in matrix A: 24
125
number of columns in matrix A: 24
126
entries in matrix A: 160
127
memory usage reported in: 8-byte Units
129
size of UF_long: 8 bytes
130
size of pointer: 8 bytes
131
size of numerical entry: 8 bytes
133
strategy used: symmetric
134
ordering used: amd on A+A'
135
modify Q during factorization: no
136
prefer diagonal pivoting: yes
137
pivots with zero Markowitz cost: 0
138
submatrix S after removing zero-cost pivots:
139
number of "dense" rows: 0
140
number of "dense" columns: 0
141
number of empty rows: 0
142
number of empty columns 0
143
submatrix S square and diagonal preserved
144
pattern of square submatrix S:
145
number rows and columns 24
146
symmetry of nonzero pattern: 1.000000
147
nz in S+S' (excl. diagonal): 136
148
nz on diagonal of matrix S: 24
149
fraction of nz on diagonal: 1.000000
150
AMD statistics, for strict diagonal pivoting:
151
est. flops for LU factorization: 1.00300e+03
152
est. nz in L+U (incl. diagonal): 218
153
est. largest front (# entries): 64
154
est. max nz in any column of L: 8
155
number of "dense" rows/columns in S+S': 0
156
symbolic factorization defragmentations: 0
157
symbolic memory usage (Units): 725
158
symbolic memory usage (MBytes): 0.0
159
Symbolic size (Units): 131
160
Symbolic size (MBytes): 0
161
symbolic factorization CPU time (sec): 0.00
162
symbolic factorization wallclock time(sec): 0.00
164
matrix scaled: yes (divided each row by sum of abs values in each row)
165
minimum sum (abs (rows of A)): 4.00000e+00
166
maximum sum (abs (rows of A)): 9.00000e+00
168
symbolic/numeric factorization: upper bound actual %
169
variable-sized part of Numeric object:
170
initial size (Units) 763 711 93%
171
peak size (Units) 3244 2709 84%
172
final size (Units) 393 133 34%
173
Numeric final size (Units) 598 326 55%
174
Numeric final size (MBytes) 0.0 0.0 55%
175
peak memory usage (Units) 3840 3305 86%
176
peak memory usage (MBytes) 0.0 0.0 86%
177
numeric factorization flops 2.37900e+03 1.57000e+02 7%
178
nz in L (incl diagonal) 149 53 36%
179
nz in U (incl diagonal) 208 73 35%
180
nz in L+U (incl diagonal) 333 102 31%
181
largest front (# entries) 182 78 43%
182
largest # rows in front 13 7 54%
183
largest # columns in front 14 13 93%
185
initial allocation ratio used: 1.2
186
# of forced updates due to frontal growth: 0
187
number of off-diagonal pivots: 10
188
nz in L (incl diagonal), if none dropped 53
189
nz in U (incl diagonal), if none dropped 73
190
number of small entries dropped 0
191
nonzeros on diagonal of U: 24
192
min abs. value on diagonal of U: 1.11e-01
193
max abs. value on diagonal of U: 2.50e-01
194
estimate of reciprocal of condition number: 4.44e-01
195
indices in compressed pattern: 76
196
numerical values stored in Numeric object: 102
197
numeric factorization defragmentations: 0
198
numeric factorization reallocations: 0
199
costly numeric factorization reallocations: 0
200
numeric factorization CPU time (sec): 0.00
201
numeric factorization wallclock time (sec): 0.00
202
symbolic + numeric CPU time (sec): 0.00
203
symbolic + numeric wall clock time (sec): 0.00
205
solve flops: 1.06000e+03
206
iterative refinement steps taken: 0
207
iterative refinement steps attempted: 0
208
sparse backward error omega1: 7.86e-17
209
sparse backward error omega2: 0.00e+00
210
solve CPU time (sec): 0.00
211
solve wall clock time (sec): 0.00
213
total symbolic + numeric + solve flops: 1.21700e+03
214
total symbolic + numeric + solve CPU time: 0.00
215
total symbolic+numeric+solve wall clock time: 0.00
218
UMFPACK V5.0.1 (Aug 31, 2006): OK
220
dense vector, n = 24. OK
222
relative maxnorm of residual, ||Ax-b||/||b||: 2.58379e-16
223
relative maxnorm of error, ||x-xtrue||/||xtrue||: 1.92754e-15
226
Writing tmp/info.umf4
227
umf4 done, strategy: 0
230
===========================================================
231
=== AMD ===================================================
232
===========================================================
235
------- Now trying the AMD ordering. This not part of
236
the UMFPACK analysis or factorization, above, but a separate
237
test of just the AMD ordering routine.
239
amd version 2.0, May 5, 2006: approximate minimum degree ordering:
240
dense row parameter: 10
241
(rows with more than max (10 * sqrt (n), 16) entries are
242
considered "dense", and placed last in output permutation)
243
aggressive absorption: yes
245
AMD ordering time: cpu 0.00 wall 0.00
247
amd: approximate minimum degree ordering, results:
249
n, dimension of A: 24
250
nz, number of nonzeros in A: 160
251
symmetry of A: 1.0000
252
number of nonzeros on diagonal: 24
253
nonzeros in pattern of A+A' (excl. diagonal): 136
254
# dense rows/columns of A+A': 0
255
memory used, in bytes: 1516
256
# of memory compactions: 0
258
The following approximate statistics are for a subsequent
259
factorization of A(P,P) + A(P,P)'. They are slight upper
260
bounds if there are no dense rows/columns in A+A', and become
261
looser if dense rows/columns exist.
263
nonzeros in L (excluding diagonal): 97
264
nonzeros in L (including diagonal): 121
265
# divide operations for LDL' or LU: 97
266
# multiply-subtract operations for LDL': 275
267
# multiply-subtract operations for LU: 453
268
max nz. in any column of L (incl. diagonal): 8
270
chol flop count for real A, sqrt counted as 1 flop: 671
271
LDL' flop count for real A: 647
272
LDL' flop count for complex A: 3073
273
LU flop count for real A (with no pivoting): 1003
274
LU flop count for complex A (with no pivoting): 4497
277
./readhb_nozeros < HB/west0067.rua > tmp/A
279
./readhb_size < HB/west0067.rua > tmp/Asize
282
===========================================================
283
=== UMFPACK v5.0.1 ========================================
284
===========================================================
285
UMFPACK V5.0.1 (Aug 31, 2006), Control:
286
Matrix entry defined as: double
287
Int (generic integer) defined as: int
290
1: dense row parameter: 0.2
291
"dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
292
2: dense column parameter: 0.2
293
"dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
294
3: pivot tolerance: 0.1
295
4: block size for dense matrix kernels: 32
296
5: strategy: 0 (auto)
297
6: initial allocation ratio: 0.7
298
7: max iterative refinement steps: 2
299
12: 2-by-2 pivot tolerance: 0.01
300
13: Q fixed during numerical factorization: 0 (auto)
301
14: AMD dense row/col parameter: 10
302
"dense" rows/columns have > max (16, (10)*sqrt(n)) entries
303
Only used if the AMD ordering is used.
304
15: diagonal pivot tolerance: 0.001
305
Only used if diagonal pivoting is attempted.
306
16: scaling: 1 (divide each row by sum of abs. values in each row)
307
17: frontal matrix allocation ratio: 0.5
308
18: drop tolerance: 0
309
19: AMD and COLAMD aggressive absorption: 1 (yes)
311
The following options can only be changed at compile-time:
312
8: BLAS library used: Fortran BLAS. size of BLAS integer: 4
313
9: compiled for ANSI C
314
10: CPU timer is POSIX times ( ) routine.
315
11: compiled for normal operation (debugging disabled)
316
computer/operating system: Linux
317
size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes)
321
n 67 nrow 67 ncol 67 nz 294
322
triplet-form matrix, n_row = 67, n_col = 67 nz = 294. OK
324
triplet-to-col time: wall 0 cpu 0
325
column-form matrix, n_row 67 n_col 67, nz = 294. OK
327
UMFPACK V5.0.1 (Aug 31, 2006), Info:
328
matrix entry defined as: double
329
Int (generic integer) defined as: int
330
BLAS library used: Fortran BLAS. size of BLAS integer: 4
332
CPU timer: POSIX times ( ) routine.
333
number of rows in matrix A: 67
334
number of columns in matrix A: 67
335
entries in matrix A: 294
336
memory usage reported in: 8-byte Units
338
size of UF_long: 8 bytes
339
size of pointer: 8 bytes
340
size of numerical entry: 8 bytes
342
strategy used: unsymmetric
343
ordering used: colamd on A
344
modify Q during factorization: yes
345
prefer diagonal pivoting: no
346
pivots with zero Markowitz cost: 1
347
submatrix S after removing zero-cost pivots:
348
number of "dense" rows: 0
349
number of "dense" columns: 0
350
number of empty rows: 0
351
number of empty columns 0
352
submatrix S not square or diagonal not preserved
353
symbolic factorization defragmentations: 1
354
symbolic memory usage (Units): 1639
355
symbolic memory usage (MBytes): 0.0
356
Symbolic size (Units): 252
357
Symbolic size (MBytes): 0
358
symbolic factorization CPU time (sec): 0.00
359
symbolic factorization wallclock time(sec): 0.00
361
symbolic/numeric factorization: upper bound actual %
362
variable-sized part of Numeric object:
363
initial size (Units) 1711 - -
364
peak size (Units) 6115 - -
365
final size (Units) 1628 - -
366
Numeric final size (Units) 2108 - -
367
Numeric final size (MBytes) 0.0 - -
368
peak memory usage (Units) 7476 - -
369
peak memory usage (MBytes) 0.1 - -
370
numeric factorization flops 1.41920e+04 - -
371
nz in L (incl diagonal) 542 - -
372
nz in U (incl diagonal) 902 - -
373
nz in L+U (incl diagonal) 1377 - -
374
largest front (# entries) 483 - -
375
largest # rows in front 21 - -
376
largest # columns in front 23 - -
382
UMFPACK V5.0.1 (Aug 31, 2006), Info:
383
matrix entry defined as: double
384
Int (generic integer) defined as: int
385
BLAS library used: Fortran BLAS. size of BLAS integer: 4
387
CPU timer: POSIX times ( ) routine.
388
number of rows in matrix A: 67
389
number of columns in matrix A: 67
390
entries in matrix A: 294
391
memory usage reported in: 8-byte Units
393
size of UF_long: 8 bytes
394
size of pointer: 8 bytes
395
size of numerical entry: 8 bytes
397
strategy used: unsymmetric
398
ordering used: colamd on A
399
modify Q during factorization: yes
400
prefer diagonal pivoting: no
401
pivots with zero Markowitz cost: 1
402
submatrix S after removing zero-cost pivots:
403
number of "dense" rows: 0
404
number of "dense" columns: 0
405
number of empty rows: 0
406
number of empty columns 0
407
submatrix S not square or diagonal not preserved
408
symbolic factorization defragmentations: 1
409
symbolic memory usage (Units): 1639
410
symbolic memory usage (MBytes): 0.0
411
Symbolic size (Units): 252
412
Symbolic size (MBytes): 0
413
symbolic factorization CPU time (sec): 0.00
414
symbolic factorization wallclock time(sec): 0.00
416
matrix scaled: yes (divided each row by sum of abs values in each row)
417
minimum sum (abs (rows of A)): 1.00000e+00
418
maximum sum (abs (rows of A)): 6.59006e+00
420
symbolic/numeric factorization: upper bound actual %
421
variable-sized part of Numeric object:
422
initial size (Units) 1711 1577 92%
423
peak size (Units) 6115 3581 59%
424
final size (Units) 1628 681 42%
425
Numeric final size (Units) 2108 1128 54%
426
Numeric final size (MBytes) 0.0 0.0 54%
427
peak memory usage (Units) 7476 4942 66%
428
peak memory usage (MBytes) 0.1 0.0 66%
429
numeric factorization flops 1.41920e+04 2.51700e+03 18%
430
nz in L (incl diagonal) 542 325 60%
431
nz in U (incl diagonal) 902 339 38%
432
nz in L+U (incl diagonal) 1377 597 43%
433
largest front (# entries) 483 80 17%
434
largest # rows in front 21 10 48%
435
largest # columns in front 23 11 48%
437
initial allocation ratio used: 0.7
438
# of forced updates due to frontal growth: 0
439
nz in L (incl diagonal), if none dropped 325
440
nz in U (incl diagonal), if none dropped 339
441
number of small entries dropped 0
442
nonzeros on diagonal of U: 67
443
min abs. value on diagonal of U: 2.74e-02
444
max abs. value on diagonal of U: 2.28e+00
445
estimate of reciprocal of condition number: 1.20e-02
446
indices in compressed pattern: 259
447
numerical values stored in Numeric object: 600
448
numeric factorization defragmentations: 1
449
numeric factorization reallocations: 1
450
costly numeric factorization reallocations: 1
451
numeric factorization CPU time (sec): 0.00
452
numeric factorization wallclock time (sec): 0.00
453
symbolic + numeric CPU time (sec): 0.00
454
symbolic + numeric wall clock time (sec): 0.00
456
solve flops: 6.17300e+03
457
iterative refinement steps taken: 1
458
iterative refinement steps attempted: 1
459
sparse backward error omega1: 1.91e-16
460
sparse backward error omega2: 0.00e+00
461
solve CPU time (sec): 0.00
462
solve wall clock time (sec): 0.00
464
total symbolic + numeric + solve flops: 8.69000e+03
465
total symbolic + numeric + solve CPU time: 0.00
466
total symbolic+numeric+solve wall clock time: 0.00
469
UMFPACK V5.0.1 (Aug 31, 2006): OK
471
dense vector, n = 67. OK
473
relative maxnorm of residual, ||Ax-b||/||b||: 1.83101e-16
474
relative maxnorm of error, ||x-xtrue||/||xtrue||: 1.23043e-15
477
Writing tmp/info.umf4
478
umf4 done, strategy: 0
481
===========================================================
482
=== AMD ===================================================
483
===========================================================
486
------- Now trying the AMD ordering. This not part of
487
the UMFPACK analysis or factorization, above, but a separate
488
test of just the AMD ordering routine.
490
amd version 2.0, May 5, 2006: approximate minimum degree ordering:
491
dense row parameter: 10
492
(rows with more than max (10 * sqrt (n), 16) entries are
493
considered "dense", and placed last in output permutation)
494
aggressive absorption: yes
496
AMD ordering time: cpu 0.00 wall 0.00
498
amd: approximate minimum degree ordering, results:
500
n, dimension of A: 67
501
nz, number of nonzeros in A: 294
502
symmetry of A: 0.0342
503
number of nonzeros on diagonal: 2
504
nonzeros in pattern of A+A' (excl. diagonal): 574
505
# dense rows/columns of A+A': 0
506
memory used, in bytes: 5164
507
# of memory compactions: 1
509
The following approximate statistics are for a subsequent
510
factorization of A(P,P) + A(P,P)'. They are slight upper
511
bounds if there are no dense rows/columns in A+A', and become
512
looser if dense rows/columns exist.
514
nonzeros in L (excluding diagonal): 930
515
nonzeros in L (including diagonal): 997
516
# divide operations for LDL' or LU: 930
517
# multiply-subtract operations for LDL': 9170
518
# multiply-subtract operations for LU: 17410
519
max nz. in any column of L (incl. diagonal): 33
521
chol flop count for real A, sqrt counted as 1 flop: 19337
522
LDL' flop count for real A: 19270
523
LDL' flop count for complex A: 81730
524
LU flop count for real A (with no pivoting): 35750
525
LU flop count for complex A (with no pivoting): 147650
528
./readhb_nozeros < HB/fs_183_6.rua > tmp/A
530
./readhb_size < HB/fs_183_6.rua > tmp/Asize
533
===========================================================
534
=== UMFPACK v5.0.1 ========================================
535
===========================================================
536
UMFPACK V5.0.1 (Aug 31, 2006), Control:
537
Matrix entry defined as: double
538
Int (generic integer) defined as: int
541
1: dense row parameter: 0.2
542
"dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
543
2: dense column parameter: 0.2
544
"dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
545
3: pivot tolerance: 0.1
546
4: block size for dense matrix kernels: 32
547
5: strategy: 0 (auto)
548
6: initial allocation ratio: 0.7
549
7: max iterative refinement steps: 2
550
12: 2-by-2 pivot tolerance: 0.01
551
13: Q fixed during numerical factorization: 0 (auto)
552
14: AMD dense row/col parameter: 10
553
"dense" rows/columns have > max (16, (10)*sqrt(n)) entries
554
Only used if the AMD ordering is used.
555
15: diagonal pivot tolerance: 0.001
556
Only used if diagonal pivoting is attempted.
557
16: scaling: 1 (divide each row by sum of abs. values in each row)
558
17: frontal matrix allocation ratio: 0.5
559
18: drop tolerance: 0
560
19: AMD and COLAMD aggressive absorption: 1 (yes)
562
The following options can only be changed at compile-time:
563
8: BLAS library used: Fortran BLAS. size of BLAS integer: 4
564
9: compiled for ANSI C
565
10: CPU timer is POSIX times ( ) routine.
566
11: compiled for normal operation (debugging disabled)
567
computer/operating system: Linux
568
size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes)
572
n 183 nrow 183 ncol 183 nz 1000
573
triplet-form matrix, n_row = 183, n_col = 183 nz = 1000. OK
575
triplet-to-col time: wall 0 cpu 0
576
column-form matrix, n_row 183 n_col 183, nz = 1000. OK
578
UMFPACK V5.0.1 (Aug 31, 2006), Info:
579
matrix entry defined as: double
580
Int (generic integer) defined as: int
581
BLAS library used: Fortran BLAS. size of BLAS integer: 4
583
CPU timer: POSIX times ( ) routine.
584
number of rows in matrix A: 183
585
number of columns in matrix A: 183
586
entries in matrix A: 1000
587
memory usage reported in: 8-byte Units
589
size of UF_long: 8 bytes
590
size of pointer: 8 bytes
591
size of numerical entry: 8 bytes
593
strategy used: symmetric 2-by-2
594
ordering used: amd on A+A'
595
modify Q during factorization: no
596
prefer diagonal pivoting: yes
597
pivots with zero Markowitz cost: 36
598
submatrix S after removing zero-cost pivots:
599
number of "dense" rows: 4
600
number of "dense" columns: 0
601
number of empty rows: 0
602
number of empty columns 0
603
submatrix S square and diagonal preserved
604
pattern of square submatrix S:
605
number rows and columns 147
606
symmetry of nonzero pattern: 0.490515
607
nz in S+S' (excl. diagonal): 1114
608
nz on diagonal of matrix S: 147
609
fraction of nz on diagonal: 1.000000
610
2-by-2 pivoting to place large entries on diagonal:
611
# of small diagonal entries of S: 7
613
symmetry of P2*S: 0.490515
614
nz in P2*S+(P2*S)' (excl. diag.): 1114
615
nz on diagonal of P2*S: 147
616
fraction of nz on diag of P2*S: 1.000000
617
AMD statistics, for strict diagonal pivoting:
618
est. flops for LU factorization: 1.02930e+04
619
est. nz in L+U (incl. diagonal): 1625
620
est. largest front (# entries): 196
621
est. max nz in any column of L: 14
622
number of "dense" rows/columns in S+S': 0
623
symbolic factorization defragmentations: 0
624
symbolic memory usage (Units): 4846
625
symbolic memory usage (MBytes): 0.0
626
Symbolic size (Units): 763
627
Symbolic size (MBytes): 0
628
symbolic factorization CPU time (sec): 0.00
629
symbolic factorization wallclock time(sec): 0.00
631
symbolic/numeric factorization: upper bound actual %
632
variable-sized part of Numeric object:
633
initial size (Units) 4458 - -
634
peak size (Units) 26277 - -
635
final size (Units) 15717 - -
636
Numeric final size (Units) 16951 - -
637
Numeric final size (MBytes) 0.1 - -
638
peak memory usage (Units) 29687 - -
639
peak memory usage (MBytes) 0.2 - -
640
numeric factorization flops 2.67903e+05 - -
641
nz in L (incl diagonal) 2122 - -
642
nz in U (incl diagonal) 9931 - -
643
nz in L+U (incl diagonal) 11870 - -
644
largest front (# entries) 2337 - -
645
largest # rows in front 21 - -
646
largest # columns in front 136 - -
652
UMFPACK V5.0.1 (Aug 31, 2006), Info:
653
matrix entry defined as: double
654
Int (generic integer) defined as: int
655
BLAS library used: Fortran BLAS. size of BLAS integer: 4
657
CPU timer: POSIX times ( ) routine.
658
number of rows in matrix A: 183
659
number of columns in matrix A: 183
660
entries in matrix A: 1000
661
memory usage reported in: 8-byte Units
663
size of UF_long: 8 bytes
664
size of pointer: 8 bytes
665
size of numerical entry: 8 bytes
667
strategy used: symmetric 2-by-2
668
ordering used: amd on A+A'
669
modify Q during factorization: no
670
prefer diagonal pivoting: yes
671
pivots with zero Markowitz cost: 36
672
submatrix S after removing zero-cost pivots:
673
number of "dense" rows: 4
674
number of "dense" columns: 0
675
number of empty rows: 0
676
number of empty columns 0
677
submatrix S square and diagonal preserved
678
pattern of square submatrix S:
679
number rows and columns 147
680
symmetry of nonzero pattern: 0.490515
681
nz in S+S' (excl. diagonal): 1114
682
nz on diagonal of matrix S: 147
683
fraction of nz on diagonal: 1.000000
684
2-by-2 pivoting to place large entries on diagonal:
685
# of small diagonal entries of S: 7
687
symmetry of P2*S: 0.490515
688
nz in P2*S+(P2*S)' (excl. diag.): 1114
689
nz on diagonal of P2*S: 147
690
fraction of nz on diag of P2*S: 1.000000
691
AMD statistics, for strict diagonal pivoting:
692
est. flops for LU factorization: 1.02930e+04
693
est. nz in L+U (incl. diagonal): 1625
694
est. largest front (# entries): 196
695
est. max nz in any column of L: 14
696
number of "dense" rows/columns in S+S': 0
697
symbolic factorization defragmentations: 0
698
symbolic memory usage (Units): 4846
699
symbolic memory usage (MBytes): 0.0
700
Symbolic size (Units): 763
701
Symbolic size (MBytes): 0
702
symbolic factorization CPU time (sec): 0.00
703
symbolic factorization wallclock time(sec): 0.00
705
matrix scaled: yes (divided each row by sum of abs values in each row)
706
minimum sum (abs (rows of A)): 1.84689e-01
707
maximum sum (abs (rows of A)): 8.73139e+08
709
symbolic/numeric factorization: upper bound actual %
710
variable-sized part of Numeric object:
711
initial size (Units) 4458 4090 92%
712
peak size (Units) 26277 8488 32%
713
final size (Units) 15717 1658 11%
714
Numeric final size (Units) 16951 2801 17%
715
Numeric final size (MBytes) 0.1 0.0 17%
716
peak memory usage (Units) 29687 11898 40%
717
peak memory usage (MBytes) 0.2 0.1 40%
718
numeric factorization flops 2.67903e+05 7.82700e+03 3%
719
nz in L (incl diagonal) 2122 838 39%
720
nz in U (incl diagonal) 9931 804 8%
721
nz in L+U (incl diagonal) 11870 1459 12%
722
largest front (# entries) 2337 420 18%
723
largest # rows in front 21 14 67%
724
largest # columns in front 136 36 26%
726
initial allocation ratio used: 0.265
727
# of forced updates due to frontal growth: 0
728
number of off-diagonal pivots: 3
729
nz in L (incl diagonal), if none dropped 838
730
nz in U (incl diagonal), if none dropped 804
731
number of small entries dropped 0
732
nonzeros on diagonal of U: 183
733
min abs. value on diagonal of U: 2.30e-09
734
max abs. value on diagonal of U: 1.00e+00
735
estimate of reciprocal of condition number: 2.30e-09
736
indices in compressed pattern: 550
737
numerical values stored in Numeric object: 1396
738
numeric factorization defragmentations: 1
739
numeric factorization reallocations: 1
740
costly numeric factorization reallocations: 1
741
numeric factorization CPU time (sec): 0.00
742
numeric factorization wallclock time (sec): 0.00
743
symbolic + numeric CPU time (sec): 0.00
744
symbolic + numeric wall clock time (sec): 0.00
746
solve flops: 1.79470e+04
747
iterative refinement steps taken: 1
748
iterative refinement steps attempted: 1
749
sparse backward error omega1: 2.18e-16
750
sparse backward error omega2: 0.00e+00
751
solve CPU time (sec): 0.00
752
solve wall clock time (sec): 0.00
754
total symbolic + numeric + solve flops: 2.57740e+04
755
total symbolic + numeric + solve CPU time: 0.00
756
total symbolic+numeric+solve wall clock time: 0.00
759
UMFPACK V5.0.1 (Aug 31, 2006): OK
761
dense vector, n = 183. OK
763
relative maxnorm of residual, ||Ax-b||/||b||: 1.55669e-16
764
relative maxnorm of error, ||x-xtrue||/||xtrue||: 9.08801e-07
767
Writing tmp/info.umf4
768
umf4 done, strategy: 0
771
===========================================================
772
=== AMD ===================================================
773
===========================================================
776
------- Now trying the AMD ordering. This not part of
777
the UMFPACK analysis or factorization, above, but a separate
778
test of just the AMD ordering routine.
780
amd version 2.0, May 5, 2006: approximate minimum degree ordering:
781
dense row parameter: 10
782
(rows with more than max (10 * sqrt (n), 16) entries are
783
considered "dense", and placed last in output permutation)
784
aggressive absorption: yes
786
AMD ordering time: cpu 0.00 wall 0.01
788
amd: approximate minimum degree ordering, results:
790
n, dimension of A: 183
791
nz, number of nonzeros in A: 1000
792
symmetry of A: 0.4431
793
number of nonzeros on diagonal: 183
794
nonzeros in pattern of A+A' (excl. diagonal): 1272
795
# dense rows/columns of A+A': 0
796
memory used, in bytes: 12692
797
# of memory compactions: 1
799
The following approximate statistics are for a subsequent
800
factorization of A(P,P) + A(P,P)'. They are slight upper
801
bounds if there are no dense rows/columns in A+A', and become
802
looser if dense rows/columns exist.
804
nonzeros in L (excluding diagonal): 882
805
nonzeros in L (including diagonal): 1065
806
# divide operations for LDL' or LU: 882
807
# multiply-subtract operations for LDL': 3378
808
# multiply-subtract operations for LU: 5874
809
max nz. in any column of L (incl. diagonal): 15
811
chol flop count for real A, sqrt counted as 1 flop: 7821
812
LDL' flop count for real A: 7638
813
LDL' flop count for complex A: 34962
814
LU flop count for real A (with no pivoting): 12630
815
LU flop count for complex A (with no pivoting): 54930
818
./readhb < HB/fs_183_6.rua > tmp/A
820
./readhb_size < HB/fs_183_6.rua > tmp/Asize
823
===========================================================
824
=== UMFPACK v5.0.1 ========================================
825
===========================================================
826
UMFPACK V5.0.1 (Aug 31, 2006), Control:
827
Matrix entry defined as: double
828
Int (generic integer) defined as: int
831
1: dense row parameter: 0.2
832
"dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
833
2: dense column parameter: 0.2
834
"dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
835
3: pivot tolerance: 0.1
836
4: block size for dense matrix kernels: 32
837
5: strategy: 0 (auto)
838
6: initial allocation ratio: 0.7
839
7: max iterative refinement steps: 2
840
12: 2-by-2 pivot tolerance: 0.01
841
13: Q fixed during numerical factorization: 0 (auto)
842
14: AMD dense row/col parameter: 10
843
"dense" rows/columns have > max (16, (10)*sqrt(n)) entries
844
Only used if the AMD ordering is used.
845
15: diagonal pivot tolerance: 0.001
846
Only used if diagonal pivoting is attempted.
847
16: scaling: 1 (divide each row by sum of abs. values in each row)
848
17: frontal matrix allocation ratio: 0.5
849
18: drop tolerance: 0
850
19: AMD and COLAMD aggressive absorption: 1 (yes)
852
The following options can only be changed at compile-time:
853
8: BLAS library used: Fortran BLAS. size of BLAS integer: 4
854
9: compiled for ANSI C
855
10: CPU timer is POSIX times ( ) routine.
856
11: compiled for normal operation (debugging disabled)
857
computer/operating system: Linux
858
size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes)
862
n 183 nrow 183 ncol 183 nz 1069
863
triplet-form matrix, n_row = 183, n_col = 183 nz = 1069. OK
865
triplet-to-col time: wall 0 cpu 0
866
column-form matrix, n_row 183 n_col 183, nz = 1069. OK
868
UMFPACK V5.0.1 (Aug 31, 2006), Info:
869
matrix entry defined as: double
870
Int (generic integer) defined as: int
871
BLAS library used: Fortran BLAS. size of BLAS integer: 4
873
CPU timer: POSIX times ( ) routine.
874
number of rows in matrix A: 183
875
number of columns in matrix A: 183
876
entries in matrix A: 1069
877
memory usage reported in: 8-byte Units
879
size of UF_long: 8 bytes
880
size of pointer: 8 bytes
881
size of numerical entry: 8 bytes
883
strategy used: symmetric 2-by-2
884
ordering used: amd on A+A'
885
modify Q during factorization: no
886
prefer diagonal pivoting: yes
887
pivots with zero Markowitz cost: 29
888
submatrix S after removing zero-cost pivots:
889
number of "dense" rows: 4
890
number of "dense" columns: 0
891
number of empty rows: 0
892
number of empty columns 0
893
submatrix S square and diagonal preserved
894
pattern of square submatrix S:
895
number rows and columns 154
896
symmetry of nonzero pattern: 0.446860
897
nz in S+S' (excl. diagonal): 1286
898
nz on diagonal of matrix S: 154
899
fraction of nz on diagonal: 1.000000
900
2-by-2 pivoting to place large entries on diagonal:
901
# of small diagonal entries of S: 7
903
symmetry of P2*S: 0.446860
904
nz in P2*S+(P2*S)' (excl. diag.): 1286
905
nz on diagonal of P2*S: 154
906
fraction of nz on diag of P2*S: 1.000000
907
AMD statistics, for strict diagonal pivoting:
908
est. flops for LU factorization: 1.78450e+04
909
est. nz in L+U (incl. diagonal): 2080
910
est. largest front (# entries): 400
911
est. max nz in any column of L: 20
912
number of "dense" rows/columns in S+S': 0
913
symbolic factorization defragmentations: 0
914
symbolic memory usage (Units): 4966
915
symbolic memory usage (MBytes): 0.0
916
Symbolic size (Units): 773
917
Symbolic size (MBytes): 0
918
symbolic factorization CPU time (sec): 0.00
919
symbolic factorization wallclock time(sec): 0.01
921
symbolic/numeric factorization: upper bound actual %
922
variable-sized part of Numeric object:
923
initial size (Units) 4742 - -
924
peak size (Units) 26357 - -
925
final size (Units) 17822 - -
926
Numeric final size (Units) 19056 - -
927
Numeric final size (MBytes) 0.1 - -
928
peak memory usage (Units) 29809 - -
929
peak memory usage (MBytes) 0.2 - -
930
numeric factorization flops 3.51312e+05 - -
931
nz in L (incl diagonal) 2633 - -
932
nz in U (incl diagonal) 10968 - -
933
nz in L+U (incl diagonal) 13418 - -
934
largest front (# entries) 3220 - -
935
largest # rows in front 25 - -
936
largest # columns in front 140 - -
942
UMFPACK V5.0.1 (Aug 31, 2006), Info:
943
matrix entry defined as: double
944
Int (generic integer) defined as: int
945
BLAS library used: Fortran BLAS. size of BLAS integer: 4
947
CPU timer: POSIX times ( ) routine.
948
number of rows in matrix A: 183
949
number of columns in matrix A: 183
950
entries in matrix A: 1069
951
memory usage reported in: 8-byte Units
953
size of UF_long: 8 bytes
954
size of pointer: 8 bytes
955
size of numerical entry: 8 bytes
957
strategy used: symmetric 2-by-2
958
ordering used: amd on A+A'
959
modify Q during factorization: no
960
prefer diagonal pivoting: yes
961
pivots with zero Markowitz cost: 29
962
submatrix S after removing zero-cost pivots:
963
number of "dense" rows: 4
964
number of "dense" columns: 0
965
number of empty rows: 0
966
number of empty columns 0
967
submatrix S square and diagonal preserved
968
pattern of square submatrix S:
969
number rows and columns 154
970
symmetry of nonzero pattern: 0.446860
971
nz in S+S' (excl. diagonal): 1286
972
nz on diagonal of matrix S: 154
973
fraction of nz on diagonal: 1.000000
974
2-by-2 pivoting to place large entries on diagonal:
975
# of small diagonal entries of S: 7
977
symmetry of P2*S: 0.446860
978
nz in P2*S+(P2*S)' (excl. diag.): 1286
979
nz on diagonal of P2*S: 154
980
fraction of nz on diag of P2*S: 1.000000
981
AMD statistics, for strict diagonal pivoting:
982
est. flops for LU factorization: 1.78450e+04
983
est. nz in L+U (incl. diagonal): 2080
984
est. largest front (# entries): 400
985
est. max nz in any column of L: 20
986
number of "dense" rows/columns in S+S': 0
987
symbolic factorization defragmentations: 0
988
symbolic memory usage (Units): 4966
989
symbolic memory usage (MBytes): 0.0
990
Symbolic size (Units): 773
991
Symbolic size (MBytes): 0
992
symbolic factorization CPU time (sec): 0.00
993
symbolic factorization wallclock time(sec): 0.01
995
matrix scaled: yes (divided each row by sum of abs values in each row)
996
minimum sum (abs (rows of A)): 1.84689e-01
997
maximum sum (abs (rows of A)): 8.73139e+08
999
symbolic/numeric factorization: upper bound actual %
1000
variable-sized part of Numeric object:
1001
initial size (Units) 4742 4372 92%
1002
peak size (Units) 26357 11189 42%
1003
final size (Units) 17822 2107 12%
1004
Numeric final size (Units) 19056 3250 17%
1005
Numeric final size (MBytes) 0.1 0.0 17%
1006
peak memory usage (Units) 29809 14641 49%
1007
peak memory usage (MBytes) 0.2 0.1 49%
1008
numeric factorization flops 3.51312e+05 1.19670e+04 3%
1009
nz in L (incl diagonal) 2633 1136 43%
1010
nz in U (incl diagonal) 10968 870 8%
1011
nz in L+U (incl diagonal) 13418 1823 14%
1012
largest front (# entries) 3220 728 23%
1013
largest # rows in front 25 20 80%
1014
largest # columns in front 140 58 41%
1016
initial allocation ratio used: 0.282
1017
# of forced updates due to frontal growth: 1
1018
number of off-diagonal pivots: 3
1019
nz in L (incl diagonal), if none dropped 1136
1020
nz in U (incl diagonal), if none dropped 870
1021
number of small entries dropped 0
1022
nonzeros on diagonal of U: 183
1023
min abs. value on diagonal of U: 2.30e-09
1024
max abs. value on diagonal of U: 1.00e+00
1025
estimate of reciprocal of condition number: 2.30e-09
1026
indices in compressed pattern: 741
1027
numerical values stored in Numeric object: 1781
1028
numeric factorization defragmentations: 1
1029
numeric factorization reallocations: 1
1030
costly numeric factorization reallocations: 1
1031
numeric factorization CPU time (sec): 0.00
1032
numeric factorization wallclock time (sec): 0.00
1033
symbolic + numeric CPU time (sec): 0.00
1034
symbolic + numeric wall clock time (sec): 0.01
1035
symbolic + numeric mflops (wall clock): 1.20
1037
solve flops: 2.00240e+04
1038
iterative refinement steps taken: 1
1039
iterative refinement steps attempted: 1
1040
sparse backward error omega1: 2.17e-16
1041
sparse backward error omega2: 0.00e+00
1042
solve CPU time (sec): 0.00
1043
solve wall clock time (sec): 0.00
1045
total symbolic + numeric + solve flops: 3.19910e+04
1046
total symbolic + numeric + solve CPU time: 0.00
1047
total symbolic+numeric+solve wall clock time: 0.01
1048
total symbolic+numeric+solve mflops(wallclock) 3.20
1051
UMFPACK V5.0.1 (Aug 31, 2006): OK
1053
dense vector, n = 183. OK
1055
relative maxnorm of residual, ||Ax-b||/||b||: 1.55669e-16
1056
relative maxnorm of error, ||x-xtrue||/||xtrue||: 1.01861e-06
1059
Writing tmp/info.umf4
1060
umf4 done, strategy: 0
1063
===========================================================
1064
=== AMD ===================================================
1065
===========================================================
1068
------- Now trying the AMD ordering. This not part of
1069
the UMFPACK analysis or factorization, above, but a separate
1070
test of just the AMD ordering routine.
1072
amd version 2.0, May 5, 2006: approximate minimum degree ordering:
1073
dense row parameter: 10
1074
(rows with more than max (10 * sqrt (n), 16) entries are
1075
considered "dense", and placed last in output permutation)
1076
aggressive absorption: yes
1078
AMD ordering time: cpu 0.00 wall 0.00
1080
amd: approximate minimum degree ordering, results:
1082
n, dimension of A: 183
1083
nz, number of nonzeros in A: 1069
1084
symmetry of A: 0.4176
1085
number of nonzeros on diagonal: 183
1086
nonzeros in pattern of A+A' (excl. diagonal): 1402
1087
# dense rows/columns of A+A': 0
1088
memory used, in bytes: 13316
1089
# of memory compactions: 1
1091
The following approximate statistics are for a subsequent
1092
factorization of A(P,P) + A(P,P)'. They are slight upper
1093
bounds if there are no dense rows/columns in A+A', and become
1094
looser if dense rows/columns exist.
1096
nonzeros in L (excluding diagonal): 1072
1097
nonzeros in L (including diagonal): 1255
1098
# divide operations for LDL' or LU: 1072
1099
# multiply-subtract operations for LDL': 5320
1100
# multiply-subtract operations for LU: 9568
1101
max nz. in any column of L (incl. diagonal): 21
1103
chol flop count for real A, sqrt counted as 1 flop: 11895
1104
LDL' flop count for real A: 11712
1105
LDL' flop count for complex A: 52208
1106
LU flop count for real A (with no pivoting): 20208
1107
LU flop count for complex A (with no pivoting): 86192
1110
./readhb < HB/arc130.rua > tmp/A
1112
./readhb_size < HB/arc130.rua > tmp/Asize
1115
===========================================================
1116
=== UMFPACK v5.0.1 ========================================
1117
===========================================================
1118
UMFPACK V5.0.1 (Aug 31, 2006), Control:
1119
Matrix entry defined as: double
1120
Int (generic integer) defined as: int
1123
1: dense row parameter: 0.2
1124
"dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
1125
2: dense column parameter: 0.2
1126
"dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
1127
3: pivot tolerance: 0.1
1128
4: block size for dense matrix kernels: 32
1129
5: strategy: 0 (auto)
1130
6: initial allocation ratio: 0.7
1131
7: max iterative refinement steps: 2
1132
12: 2-by-2 pivot tolerance: 0.01
1133
13: Q fixed during numerical factorization: 0 (auto)
1134
14: AMD dense row/col parameter: 10
1135
"dense" rows/columns have > max (16, (10)*sqrt(n)) entries
1136
Only used if the AMD ordering is used.
1137
15: diagonal pivot tolerance: 0.001
1138
Only used if diagonal pivoting is attempted.
1139
16: scaling: 1 (divide each row by sum of abs. values in each row)
1140
17: frontal matrix allocation ratio: 0.5
1141
18: drop tolerance: 0
1142
19: AMD and COLAMD aggressive absorption: 1 (yes)
1144
The following options can only be changed at compile-time:
1145
8: BLAS library used: Fortran BLAS. size of BLAS integer: 4
1146
9: compiled for ANSI C
1147
10: CPU timer is POSIX times ( ) routine.
1148
11: compiled for normal operation (debugging disabled)
1149
computer/operating system: Linux
1150
size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes)
1154
n 130 nrow 130 ncol 130 nz 1282
1155
triplet-form matrix, n_row = 130, n_col = 130 nz = 1282. OK
1157
triplet-to-col time: wall 0 cpu 0
1158
column-form matrix, n_row 130 n_col 130, nz = 1282. OK
1160
UMFPACK V5.0.1 (Aug 31, 2006), Info:
1161
matrix entry defined as: double
1162
Int (generic integer) defined as: int
1163
BLAS library used: Fortran BLAS. size of BLAS integer: 4
1165
CPU timer: POSIX times ( ) routine.
1166
number of rows in matrix A: 130
1167
number of columns in matrix A: 130
1168
entries in matrix A: 1282
1169
memory usage reported in: 8-byte Units
1170
size of int: 4 bytes
1171
size of UF_long: 8 bytes
1172
size of pointer: 8 bytes
1173
size of numerical entry: 8 bytes
1175
strategy used: symmetric
1176
ordering used: amd on A+A'
1177
modify Q during factorization: no
1178
prefer diagonal pivoting: yes
1179
pivots with zero Markowitz cost: 6
1180
submatrix S after removing zero-cost pivots:
1181
number of "dense" rows: 7
1182
number of "dense" columns: 0
1183
number of empty rows: 0
1184
number of empty columns 0
1185
submatrix S square and diagonal preserved
1186
pattern of square submatrix S:
1187
number rows and columns 124
1188
symmetry of nonzero pattern: 0.841193
1189
nz in S+S' (excl. diagonal): 1204
1190
nz on diagonal of matrix S: 124
1191
fraction of nz on diagonal: 1.000000
1192
AMD statistics, for strict diagonal pivoting:
1193
est. flops for LU factorization: 8.27000e+03
1194
est. nz in L+U (incl. diagonal): 1336
1195
est. largest front (# entries): 324
1196
est. max nz in any column of L: 18
1197
number of "dense" rows/columns in S+S': 2
1198
symbolic factorization defragmentations: 0
1199
symbolic memory usage (Units): 4766
1200
symbolic memory usage (MBytes): 0.0
1201
Symbolic size (Units): 644
1202
Symbolic size (MBytes): 0
1203
symbolic factorization CPU time (sec): 0.00
1204
symbolic factorization wallclock time(sec): 0.00
1206
symbolic/numeric factorization: upper bound actual %
1207
variable-sized part of Numeric object:
1208
initial size (Units) 4729 - -
1209
peak size (Units) 25036 - -
1210
final size (Units) 12837 - -
1211
Numeric final size (Units) 13731 - -
1212
Numeric final size (MBytes) 0.1 - -
1213
peak memory usage (Units) 27695 - -
1214
peak memory usage (MBytes) 0.2 - -
1215
numeric factorization flops 9.41610e+04 - -
1216
nz in L (incl diagonal) 1009 - -
1217
nz in U (incl diagonal) 7849 - -
1218
nz in L+U (incl diagonal) 8728 - -
1219
largest front (# entries) 2337 - -
1220
largest # rows in front 19 - -
1221
largest # columns in front 123 - -
1227
UMFPACK V5.0.1 (Aug 31, 2006), Info:
1228
matrix entry defined as: double
1229
Int (generic integer) defined as: int
1230
BLAS library used: Fortran BLAS. size of BLAS integer: 4
1232
CPU timer: POSIX times ( ) routine.
1233
number of rows in matrix A: 130
1234
number of columns in matrix A: 130
1235
entries in matrix A: 1282
1236
memory usage reported in: 8-byte Units
1237
size of int: 4 bytes
1238
size of UF_long: 8 bytes
1239
size of pointer: 8 bytes
1240
size of numerical entry: 8 bytes
1242
strategy used: symmetric
1243
ordering used: amd on A+A'
1244
modify Q during factorization: no
1245
prefer diagonal pivoting: yes
1246
pivots with zero Markowitz cost: 6
1247
submatrix S after removing zero-cost pivots:
1248
number of "dense" rows: 7
1249
number of "dense" columns: 0
1250
number of empty rows: 0
1251
number of empty columns 0
1252
submatrix S square and diagonal preserved
1253
pattern of square submatrix S:
1254
number rows and columns 124
1255
symmetry of nonzero pattern: 0.841193
1256
nz in S+S' (excl. diagonal): 1204
1257
nz on diagonal of matrix S: 124
1258
fraction of nz on diagonal: 1.000000
1259
AMD statistics, for strict diagonal pivoting:
1260
est. flops for LU factorization: 8.27000e+03
1261
est. nz in L+U (incl. diagonal): 1336
1262
est. largest front (# entries): 324
1263
est. max nz in any column of L: 18
1264
number of "dense" rows/columns in S+S': 2
1265
symbolic factorization defragmentations: 0
1266
symbolic memory usage (Units): 4766
1267
symbolic memory usage (MBytes): 0.0
1268
Symbolic size (Units): 644
1269
Symbolic size (MBytes): 0
1270
symbolic factorization CPU time (sec): 0.00
1271
symbolic factorization wallclock time(sec): 0.00
1273
matrix scaled: yes (divided each row by sum of abs values in each row)
1274
minimum sum (abs (rows of A)): 7.94859e-01
1275
maximum sum (abs (rows of A)): 1.08460e+06
1277
symbolic/numeric factorization: upper bound actual %
1278
variable-sized part of Numeric object:
1279
initial size (Units) 4729 4451 94%
1280
peak size (Units) 25036 6477 26%
1281
final size (Units) 12837 1054 8%
1282
Numeric final size (Units) 13731 1883 14%
1283
Numeric final size (MBytes) 0.1 0.0 14%
1284
peak memory usage (Units) 27695 9136 33%
1285
peak memory usage (MBytes) 0.2 0.1 33%
1286
numeric factorization flops 9.41610e+04 4.20900e+03 4%
1287
nz in L (incl diagonal) 1009 417 41%
1288
nz in U (incl diagonal) 7849 787 10%
1289
nz in L+U (incl diagonal) 8728 1074 12%
1290
largest front (# entries) 2337 270 12%
1291
largest # rows in front 19 18 95%
1292
largest # columns in front 123 15 12%
1294
initial allocation ratio used: 0.36
1295
# of forced updates due to frontal growth: 0
1296
number of off-diagonal pivots: 0
1297
nz in L (incl diagonal), if none dropped 417
1298
nz in U (incl diagonal), if none dropped 796
1299
number of small entries dropped 9
1300
nonzeros on diagonal of U: 130
1301
min abs. value on diagonal of U: 9.22e-07
1302
max abs. value on diagonal of U: 1.00e+00
1303
estimate of reciprocal of condition number: 9.22e-07
1304
indices in compressed pattern: 79
1305
numerical values stored in Numeric object: 977
1306
numeric factorization defragmentations: 1
1307
numeric factorization reallocations: 1
1308
costly numeric factorization reallocations: 1
1309
numeric factorization CPU time (sec): 0.00
1310
numeric factorization wallclock time (sec): 0.00
1311
symbolic + numeric CPU time (sec): 0.00
1312
symbolic + numeric wall clock time (sec): 0.00
1314
solve flops: 1.80440e+04
1315
iterative refinement steps taken: 1
1316
iterative refinement steps attempted: 1
1317
sparse backward error omega1: 1.06e-16
1318
sparse backward error omega2: 0.00e+00
1319
solve CPU time (sec): 0.00
1320
solve wall clock time (sec): 0.00
1322
total symbolic + numeric + solve flops: 2.22530e+04
1323
total symbolic + numeric + solve CPU time: 0.00
1324
total symbolic+numeric+solve wall clock time: 0.00
1327
UMFPACK V5.0.1 (Aug 31, 2006): OK
1329
dense vector, n = 130. OK
1331
relative maxnorm of residual, ||Ax-b||/||b||: 4.12105e-16
1332
relative maxnorm of error, ||x-xtrue||/||xtrue||: 2.15116e-10
1335
Writing tmp/info.umf4
1336
umf4 done, strategy: 0
1339
===========================================================
1340
=== AMD ===================================================
1341
===========================================================
1344
------- Now trying the AMD ordering. This not part of
1345
the UMFPACK analysis or factorization, above, but a separate
1346
test of just the AMD ordering routine.
1348
amd version 2.0, May 5, 2006: approximate minimum degree ordering:
1349
dense row parameter: 10
1350
(rows with more than max (10 * sqrt (n), 16) entries are
1351
considered "dense", and placed last in output permutation)
1352
aggressive absorption: yes
1354
AMD ordering time: cpu 0.00 wall 0.00
1356
amd: approximate minimum degree ordering, results:
1358
n, dimension of A: 130
1359
nz, number of nonzeros in A: 1282
1360
symmetry of A: 0.7587
1361
number of nonzeros on diagonal: 130
1362
nonzeros in pattern of A+A' (excl. diagonal): 1430
1363
# dense rows/columns of A+A': 2
1364
memory used, in bytes: 11544
1365
# of memory compactions: 0
1367
The following approximate statistics are for a subsequent
1368
factorization of A(P,P) + A(P,P)'. They are slight upper
1369
bounds if there are no dense rows/columns in A+A', and become
1370
looser if dense rows/columns exist.
1372
nonzeros in L (excluding diagonal): 756
1373
nonzeros in L (including diagonal): 886
1374
# divide operations for LDL' or LU: 756
1375
# multiply-subtract operations for LDL': 2959
1376
# multiply-subtract operations for LU: 5162
1377
max nz. in any column of L (incl. diagonal): 18
1379
chol flop count for real A, sqrt counted as 1 flop: 6804
1380
LDL' flop count for real A: 6674
1381
LDL' flop count for complex A: 30476
1382
LU flop count for real A (with no pivoting): 11080
1383
LU flop count for complex A (with no pivoting): 48100
1386
./readhb_nozeros < HB/arc130.rua > tmp/A
1388
./readhb_size < HB/arc130.rua > tmp/Asize
1391
===========================================================
1392
=== UMFPACK v5.0.1 ========================================
1393
===========================================================
1394
UMFPACK V5.0.1 (Aug 31, 2006), Control:
1395
Matrix entry defined as: double
1396
Int (generic integer) defined as: int
1399
1: dense row parameter: 0.2
1400
"dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
1401
2: dense column parameter: 0.2
1402
"dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
1403
3: pivot tolerance: 0.1
1404
4: block size for dense matrix kernels: 32
1405
5: strategy: 0 (auto)
1406
6: initial allocation ratio: 0.7
1407
7: max iterative refinement steps: 2
1408
12: 2-by-2 pivot tolerance: 0.01
1409
13: Q fixed during numerical factorization: 0 (auto)
1410
14: AMD dense row/col parameter: 10
1411
"dense" rows/columns have > max (16, (10)*sqrt(n)) entries
1412
Only used if the AMD ordering is used.
1413
15: diagonal pivot tolerance: 0.001
1414
Only used if diagonal pivoting is attempted.
1415
16: scaling: 1 (divide each row by sum of abs. values in each row)
1416
17: frontal matrix allocation ratio: 0.5
1417
18: drop tolerance: 0
1418
19: AMD and COLAMD aggressive absorption: 1 (yes)
1420
The following options can only be changed at compile-time:
1421
8: BLAS library used: Fortran BLAS. size of BLAS integer: 4
1422
9: compiled for ANSI C
1423
10: CPU timer is POSIX times ( ) routine.
1424
11: compiled for normal operation (debugging disabled)
1425
computer/operating system: Linux
1426
size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes)
1430
n 130 nrow 130 ncol 130 nz 1037
1431
triplet-form matrix, n_row = 130, n_col = 130 nz = 1037. OK
1433
triplet-to-col time: wall 0 cpu 0
1434
column-form matrix, n_row 130 n_col 130, nz = 1037. OK
1436
UMFPACK V5.0.1 (Aug 31, 2006), Info:
1437
matrix entry defined as: double
1438
Int (generic integer) defined as: int
1439
BLAS library used: Fortran BLAS. size of BLAS integer: 4
1441
CPU timer: POSIX times ( ) routine.
1442
number of rows in matrix A: 130
1443
number of columns in matrix A: 130
1444
entries in matrix A: 1037
1445
memory usage reported in: 8-byte Units
1446
size of int: 4 bytes
1447
size of UF_long: 8 bytes
1448
size of pointer: 8 bytes
1449
size of numerical entry: 8 bytes
1451
strategy used: symmetric
1452
ordering used: amd on A+A'
1453
modify Q during factorization: no
1454
prefer diagonal pivoting: yes
1455
pivots with zero Markowitz cost: 54
1456
submatrix S after removing zero-cost pivots:
1457
number of "dense" rows: 5
1458
number of "dense" columns: 0
1459
number of empty rows: 0
1460
number of empty columns 0
1461
submatrix S square and diagonal preserved
1462
pattern of square submatrix S:
1463
number rows and columns 76
1464
symmetry of nonzero pattern: 0.733224
1465
nz in S+S' (excl. diagonal): 774
1466
nz on diagonal of matrix S: 76
1467
fraction of nz on diagonal: 1.000000
1468
AMD statistics, for strict diagonal pivoting:
1469
est. flops for LU factorization: 5.81700e+03
1470
est. nz in L+U (incl. diagonal): 858
1471
est. largest front (# entries): 289
1472
est. max nz in any column of L: 17
1473
number of "dense" rows/columns in S+S': 0
1474
symbolic factorization defragmentations: 0
1475
symbolic memory usage (Units): 4118
1476
symbolic memory usage (MBytes): 0.0
1477
Symbolic size (Units): 534
1478
Symbolic size (MBytes): 0
1479
symbolic factorization CPU time (sec): 0.00
1480
symbolic factorization wallclock time(sec): 0.00
1482
symbolic/numeric factorization: upper bound actual %
1483
variable-sized part of Numeric object:
1484
initial size (Units) 3326 - -
1485
peak size (Units) 9801 - -
1486
final size (Units) 4259 - -
1487
Numeric final size (Units) 5153 - -
1488
Numeric final size (MBytes) 0.0 - -
1489
peak memory usage (Units) 12149 - -
1490
peak memory usage (MBytes) 0.1 - -
1491
numeric factorization flops 2.47640e+04 - -
1492
nz in L (incl diagonal) 606 - -
1493
nz in U (incl diagonal) 2537 - -
1494
nz in L+U (incl diagonal) 3013 - -
1495
largest front (# entries) 459 - -
1496
largest # rows in front 17 - -
1497
largest # columns in front 48 - -
1503
UMFPACK V5.0.1 (Aug 31, 2006), Info:
1504
matrix entry defined as: double
1505
Int (generic integer) defined as: int
1506
BLAS library used: Fortran BLAS. size of BLAS integer: 4
1508
CPU timer: POSIX times ( ) routine.
1509
number of rows in matrix A: 130
1510
number of columns in matrix A: 130
1511
entries in matrix A: 1037
1512
memory usage reported in: 8-byte Units
1513
size of int: 4 bytes
1514
size of UF_long: 8 bytes
1515
size of pointer: 8 bytes
1516
size of numerical entry: 8 bytes
1518
strategy used: symmetric
1519
ordering used: amd on A+A'
1520
modify Q during factorization: no
1521
prefer diagonal pivoting: yes
1522
pivots with zero Markowitz cost: 54
1523
submatrix S after removing zero-cost pivots:
1524
number of "dense" rows: 5
1525
number of "dense" columns: 0
1526
number of empty rows: 0
1527
number of empty columns 0
1528
submatrix S square and diagonal preserved
1529
pattern of square submatrix S:
1530
number rows and columns 76
1531
symmetry of nonzero pattern: 0.733224
1532
nz in S+S' (excl. diagonal): 774
1533
nz on diagonal of matrix S: 76
1534
fraction of nz on diagonal: 1.000000
1535
AMD statistics, for strict diagonal pivoting:
1536
est. flops for LU factorization: 5.81700e+03
1537
est. nz in L+U (incl. diagonal): 858
1538
est. largest front (# entries): 289
1539
est. max nz in any column of L: 17
1540
number of "dense" rows/columns in S+S': 0
1541
symbolic factorization defragmentations: 0
1542
symbolic memory usage (Units): 4118
1543
symbolic memory usage (MBytes): 0.0
1544
Symbolic size (Units): 534
1545
Symbolic size (MBytes): 0
1546
symbolic factorization CPU time (sec): 0.00
1547
symbolic factorization wallclock time(sec): 0.00
1549
matrix scaled: yes (divided each row by sum of abs values in each row)
1550
minimum sum (abs (rows of A)): 7.94859e-01
1551
maximum sum (abs (rows of A)): 1.08460e+06
1553
symbolic/numeric factorization: upper bound actual %
1554
variable-sized part of Numeric object:
1555
initial size (Units) 3326 3062 92%
1556
peak size (Units) 9801 6376 65%
1557
final size (Units) 4259 1141 27%
1558
Numeric final size (Units) 5153 1970 38%
1559
Numeric final size (MBytes) 0.0 0.0 38%
1560
peak memory usage (Units) 12149 8724 72%
1561
peak memory usage (MBytes) 0.1 0.1 72%
1562
numeric factorization flops 2.47640e+04 4.10700e+03 17%
1563
nz in L (incl diagonal) 606 409 67%
1564
nz in U (incl diagonal) 2537 792 31%
1565
nz in L+U (incl diagonal) 3013 1071 36%
1566
largest front (# entries) 459 240 52%
1567
largest # rows in front 17 16 94%
1568
largest # columns in front 48 15 31%
1570
initial allocation ratio used: 0.755
1571
# of forced updates due to frontal growth: 0
1572
number of off-diagonal pivots: 0
1573
nz in L (incl diagonal), if none dropped 409
1574
nz in U (incl diagonal), if none dropped 792
1575
number of small entries dropped 0
1576
nonzeros on diagonal of U: 130
1577
min abs. value on diagonal of U: 9.22e-07
1578
max abs. value on diagonal of U: 1.00e+00
1579
estimate of reciprocal of condition number: 9.22e-07
1580
indices in compressed pattern: 70
1581
numerical values stored in Numeric object: 782
1582
numeric factorization defragmentations: 1
1583
numeric factorization reallocations: 1
1584
costly numeric factorization reallocations: 1
1585
numeric factorization CPU time (sec): 0.00
1586
numeric factorization wallclock time (sec): 0.00
1587
symbolic + numeric CPU time (sec): 0.00
1588
symbolic + numeric wall clock time (sec): 0.00
1590
solve flops: 1.58270e+04
1591
iterative refinement steps taken: 1
1592
iterative refinement steps attempted: 1
1593
sparse backward error omega1: 1.47e-16
1594
sparse backward error omega2: 0.00e+00
1595
solve CPU time (sec): 0.00
1596
solve wall clock time (sec): 0.00
1598
total symbolic + numeric + solve flops: 1.99340e+04
1599
total symbolic + numeric + solve CPU time: 0.00
1600
total symbolic+numeric+solve wall clock time: 0.00
1603
UMFPACK V5.0.1 (Aug 31, 2006): OK
1605
dense vector, n = 130. OK
1607
relative maxnorm of residual, ||Ax-b||/||b||: 2.74736e-16
1608
relative maxnorm of error, ||x-xtrue||/||xtrue||: 1.92322e-10
1611
Writing tmp/info.umf4
1612
umf4 done, strategy: 0
1615
===========================================================
1616
=== AMD ===================================================
1617
===========================================================
1620
------- Now trying the AMD ordering. This not part of
1621
the UMFPACK analysis or factorization, above, but a separate
1622
test of just the AMD ordering routine.
1624
amd version 2.0, May 5, 2006: approximate minimum degree ordering:
1625
dense row parameter: 10
1626
(rows with more than max (10 * sqrt (n), 16) entries are
1627
considered "dense", and placed last in output permutation)
1628
aggressive absorption: yes
1630
AMD ordering time: cpu 0.00 wall 0.00
1632
amd: approximate minimum degree ordering, results:
1634
n, dimension of A: 130
1635
nz, number of nonzeros in A: 1037
1636
symmetry of A: 0.4939
1637
number of nonzeros on diagonal: 130
1638
nonzeros in pattern of A+A' (excl. diagonal): 1366
1639
# dense rows/columns of A+A': 2
1640
memory used, in bytes: 11236
1641
# of memory compactions: 0
1643
The following approximate statistics are for a subsequent
1644
factorization of A(P,P) + A(P,P)'. They are slight upper
1645
bounds if there are no dense rows/columns in A+A', and become
1646
looser if dense rows/columns exist.
1648
nonzeros in L (excluding diagonal): 725
1649
nonzeros in L (including diagonal): 855
1650
# divide operations for LDL' or LU: 725
1651
# multiply-subtract operations for LDL': 2742
1652
# multiply-subtract operations for LU: 4759
1653
max nz. in any column of L (incl. diagonal): 18
1655
chol flop count for real A, sqrt counted as 1 flop: 6339
1656
LDL' flop count for real A: 6209
1657
LDL' flop count for complex A: 28461
1658
LU flop count for real A (with no pivoting): 10243
1659
LU flop count for complex A (with no pivoting): 44597
1662
./readhb_nozeros < HB/arc130.rua > tmp/A
1664
./readhb_size < HB/arc130.rua > tmp/Asize
1667
===========================================================
1668
=== UMFPACK v5.0.1 ========================================
1669
===========================================================
1671
UMFPACK V5.0.1 (Aug 31, 2006), Control:
1672
Matrix entry defined as: double
1673
Int (generic integer) defined as: int
1676
1: dense row parameter: 0.2
1677
"dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
1678
2: dense column parameter: 0.2
1679
"dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
1680
3: pivot tolerance: 0.1
1681
4: block size for dense matrix kernels: 32
1682
5: strategy: 0 (auto)
1683
6: initial allocation ratio: 0.7
1684
7: max iterative refinement steps: 2
1685
12: 2-by-2 pivot tolerance: 0.01
1686
13: Q fixed during numerical factorization: 0 (auto)
1687
14: AMD dense row/col parameter: 10
1688
"dense" rows/columns have > max (16, (10)*sqrt(n)) entries
1689
Only used if the AMD ordering is used.
1690
15: diagonal pivot tolerance: 0.001
1691
Only used if diagonal pivoting is attempted.
1692
16: scaling: 1 (divide each row by sum of abs. values in each row)
1693
17: frontal matrix allocation ratio: 0.5
1694
18: drop tolerance: 1e-06
1695
19: AMD and COLAMD aggressive absorption: 1 (yes)
1697
The following options can only be changed at compile-time:
1698
8: BLAS library used: Fortran BLAS. size of BLAS integer: 4
1699
9: compiled for ANSI C
1700
10: CPU timer is POSIX times ( ) routine.
1701
11: compiled for normal operation (debugging disabled)
1702
computer/operating system: Linux
1703
size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes)
1707
n 130 nrow 130 ncol 130 nz 1037
1708
triplet-form matrix, n_row = 130, n_col = 130 nz = 1037. OK
1710
triplet-to-col time: wall 0 cpu 0
1711
column-form matrix, n_row 130 n_col 130, nz = 1037. OK
1713
UMFPACK V5.0.1 (Aug 31, 2006), Info:
1714
matrix entry defined as: double
1715
Int (generic integer) defined as: int
1716
BLAS library used: Fortran BLAS. size of BLAS integer: 4
1718
CPU timer: POSIX times ( ) routine.
1719
number of rows in matrix A: 130
1720
number of columns in matrix A: 130
1721
entries in matrix A: 1037
1722
memory usage reported in: 8-byte Units
1723
size of int: 4 bytes
1724
size of UF_long: 8 bytes
1725
size of pointer: 8 bytes
1726
size of numerical entry: 8 bytes
1728
strategy used: symmetric
1729
ordering used: amd on A+A'
1730
modify Q during factorization: no
1731
prefer diagonal pivoting: yes
1732
pivots with zero Markowitz cost: 54
1733
submatrix S after removing zero-cost pivots:
1734
number of "dense" rows: 5
1735
number of "dense" columns: 0
1736
number of empty rows: 0
1737
number of empty columns 0
1738
submatrix S square and diagonal preserved
1739
pattern of square submatrix S:
1740
number rows and columns 76
1741
symmetry of nonzero pattern: 0.733224
1742
nz in S+S' (excl. diagonal): 774
1743
nz on diagonal of matrix S: 76
1744
fraction of nz on diagonal: 1.000000
1745
AMD statistics, for strict diagonal pivoting:
1746
est. flops for LU factorization: 5.81700e+03
1747
est. nz in L+U (incl. diagonal): 858
1748
est. largest front (# entries): 289
1749
est. max nz in any column of L: 17
1750
number of "dense" rows/columns in S+S': 0
1751
symbolic factorization defragmentations: 0
1752
symbolic memory usage (Units): 4118
1753
symbolic memory usage (MBytes): 0.0
1754
Symbolic size (Units): 534
1755
Symbolic size (MBytes): 0
1756
symbolic factorization CPU time (sec): 0.00
1757
symbolic factorization wallclock time(sec): 0.00
1759
symbolic/numeric factorization: upper bound actual %
1760
variable-sized part of Numeric object:
1761
initial size (Units) 3326 - -
1762
peak size (Units) 9801 - -
1763
final size (Units) 4259 - -
1764
Numeric final size (Units) 5153 - -
1765
Numeric final size (MBytes) 0.0 - -
1766
peak memory usage (Units) 12149 - -
1767
peak memory usage (MBytes) 0.1 - -
1768
numeric factorization flops 2.47640e+04 - -
1769
nz in L (incl diagonal) 606 - -
1770
nz in U (incl diagonal) 2537 - -
1771
nz in L+U (incl diagonal) 3013 - -
1772
largest front (# entries) 459 - -
1773
largest # rows in front 17 - -
1774
largest # columns in front 48 - -
1780
UMFPACK V5.0.1 (Aug 31, 2006), Info:
1781
matrix entry defined as: double
1782
Int (generic integer) defined as: int
1783
BLAS library used: Fortran BLAS. size of BLAS integer: 4
1785
CPU timer: POSIX times ( ) routine.
1786
number of rows in matrix A: 130
1787
number of columns in matrix A: 130
1788
entries in matrix A: 1037
1789
memory usage reported in: 8-byte Units
1790
size of int: 4 bytes
1791
size of UF_long: 8 bytes
1792
size of pointer: 8 bytes
1793
size of numerical entry: 8 bytes
1795
strategy used: symmetric
1796
ordering used: amd on A+A'
1797
modify Q during factorization: no
1798
prefer diagonal pivoting: yes
1799
pivots with zero Markowitz cost: 54
1800
submatrix S after removing zero-cost pivots:
1801
number of "dense" rows: 5
1802
number of "dense" columns: 0
1803
number of empty rows: 0
1804
number of empty columns 0
1805
submatrix S square and diagonal preserved
1806
pattern of square submatrix S:
1807
number rows and columns 76
1808
symmetry of nonzero pattern: 0.733224
1809
nz in S+S' (excl. diagonal): 774
1810
nz on diagonal of matrix S: 76
1811
fraction of nz on diagonal: 1.000000
1812
AMD statistics, for strict diagonal pivoting:
1813
est. flops for LU factorization: 5.81700e+03
1814
est. nz in L+U (incl. diagonal): 858
1815
est. largest front (# entries): 289
1816
est. max nz in any column of L: 17
1817
number of "dense" rows/columns in S+S': 0
1818
symbolic factorization defragmentations: 0
1819
symbolic memory usage (Units): 4118
1820
symbolic memory usage (MBytes): 0.0
1821
Symbolic size (Units): 534
1822
Symbolic size (MBytes): 0
1823
symbolic factorization CPU time (sec): 0.00
1824
symbolic factorization wallclock time(sec): 0.00
1826
matrix scaled: yes (divided each row by sum of abs values in each row)
1827
minimum sum (abs (rows of A)): 7.94859e-01
1828
maximum sum (abs (rows of A)): 1.08460e+06
1830
symbolic/numeric factorization: upper bound actual %
1831
variable-sized part of Numeric object:
1832
initial size (Units) 3326 2762 83%
1833
peak size (Units) 9801 5323 54%
1834
final size (Units) 4259 457 11%
1835
Numeric final size (Units) 5153 1286 25%
1836
Numeric final size (MBytes) 0.0 0.0 25%
1837
peak memory usage (Units) 12149 7671 63%
1838
peak memory usage (MBytes) 0.1 0.1 63%
1839
numeric factorization flops 2.47640e+04 4.10700e+03 17%
1840
nz in L (incl diagonal) 606 318 52%
1841
nz in U (incl diagonal) 2537 285 11%
1842
nz in L+U (incl diagonal) 3013 473 16%
1843
largest front (# entries) 459 240 52%
1844
largest # rows in front 17 16 94%
1845
largest # columns in front 48 15 31%
1847
initial allocation ratio used: 0.755
1848
# of forced updates due to frontal growth: 0
1849
number of off-diagonal pivots: 0
1850
nz in L (incl diagonal), if none dropped 409
1851
nz in U (incl diagonal), if none dropped 792
1852
number of small entries dropped 598
1853
nonzeros on diagonal of U: 130
1854
min abs. value on diagonal of U: 9.22e-07
1855
max abs. value on diagonal of U: 1.00e+00
1856
estimate of reciprocal of condition number: 9.22e-07
1857
indices in compressed pattern: 82
1858
numerical values stored in Numeric object: 386
1859
numeric factorization defragmentations: 1
1860
numeric factorization reallocations: 1
1861
costly numeric factorization reallocations: 1
1862
numeric factorization CPU time (sec): 0.00
1863
numeric factorization wallclock time (sec): 0.00
1864
symbolic + numeric CPU time (sec): 0.00
1865
symbolic + numeric wall clock time (sec): 0.00
1867
solve flops: 2.06060e+04
1868
iterative refinement steps taken: 2
1869
iterative refinement steps attempted: 2
1870
sparse backward error omega1: 1.00e-16
1871
sparse backward error omega2: 0.00e+00
1872
solve CPU time (sec): 0.00
1873
solve wall clock time (sec): 0.00
1875
total symbolic + numeric + solve flops: 2.47130e+04
1876
total symbolic + numeric + solve CPU time: 0.00
1877
total symbolic+numeric+solve wall clock time: 0.00
1880
UMFPACK V5.0.1 (Aug 31, 2006): OK
1882
dense vector, n = 130. OK
1884
relative maxnorm of residual, ||Ax-b||/||b||: 2.74736e-16
1885
relative maxnorm of error, ||x-xtrue||/||xtrue||: 1.92269e-10
1888
Writing tmp/info.umf4
1889
umf4 done, strategy: 0
1892
===========================================================
1893
=== AMD ===================================================
1894
===========================================================
1897
------- Now trying the AMD ordering. This not part of
1898
the UMFPACK analysis or factorization, above, but a separate
1899
test of just the AMD ordering routine.
1901
amd version 2.0, May 5, 2006: approximate minimum degree ordering:
1902
dense row parameter: 10
1903
(rows with more than max (10 * sqrt (n), 16) entries are
1904
considered "dense", and placed last in output permutation)
1905
aggressive absorption: yes
1907
AMD ordering time: cpu 0.00 wall 0.00
1909
amd: approximate minimum degree ordering, results:
1911
n, dimension of A: 130
1912
nz, number of nonzeros in A: 1037
1913
symmetry of A: 0.4939
1914
number of nonzeros on diagonal: 130
1915
nonzeros in pattern of A+A' (excl. diagonal): 1366
1916
# dense rows/columns of A+A': 2
1917
memory used, in bytes: 11236
1918
# of memory compactions: 0
1920
The following approximate statistics are for a subsequent
1921
factorization of A(P,P) + A(P,P)'. They are slight upper
1922
bounds if there are no dense rows/columns in A+A', and become
1923
looser if dense rows/columns exist.
1925
nonzeros in L (excluding diagonal): 725
1926
nonzeros in L (including diagonal): 855
1927
# divide operations for LDL' or LU: 725
1928
# multiply-subtract operations for LDL': 2742
1929
# multiply-subtract operations for LU: 4759
1930
max nz. in any column of L (incl. diagonal): 18
1932
chol flop count for real A, sqrt counted as 1 flop: 6339
1933
LDL' flop count for real A: 6209
1934
LDL' flop count for complex A: 28461
1935
LU flop count for real A (with no pivoting): 10243
1936
LU flop count for complex A (with no pivoting): 44597
added
removed
UMFPACK/Demo/Opteron64/umf4.out
