2
UMFPACK V5.0 (Aug 31, 2006) demo: _dl_ version
4
UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved.
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UMFPACK is available under alternate licenses,
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contact T. Davis for details.
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Your use or distribution of UMFPACK or any modified version of
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UMFPACK implies that you agree to this License.
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This library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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This library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with this library; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
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Permission is hereby granted to use or copy this program under the
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terms of the GNU LGPL, provided that the Copyright, this License,
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and the Availability of the original version is retained on all copies.
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User documentation of any code that uses this code or any modified
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version of this code must cite the Copyright, this License, the
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Availability note, and "Used by permission." Permission to modify
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the code and to distribute modified code is granted, provided the
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Copyright, this License, and the Availability note are retained,
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and a notice that the code was modified is included.
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Availability: http://www.cise.ufl.edu/research/sparse/umfpack
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UMFPACK V5.0.1 (Aug 31, 2006): OK
44
UMFPACK V5.0.1 (Aug 31, 2006), Control:
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Matrix entry defined as: double
46
Int (generic integer) defined as: UF_long
49
1: dense row parameter: 0.2
50
"dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
51
2: dense column parameter: 0.2
52
"dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
53
3: pivot tolerance: 0.1
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4: block size for dense matrix kernels: 32
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6: initial allocation ratio: 0.7
57
7: max iterative refinement steps: 2
58
12: 2-by-2 pivot tolerance: 0.01
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13: Q fixed during numerical factorization: 0 (auto)
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14: AMD dense row/col parameter: 10
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"dense" rows/columns have > max (16, (10)*sqrt(n)) entries
62
Only used if the AMD ordering is used.
63
15: diagonal pivot tolerance: 0.001
64
Only used if diagonal pivoting is attempted.
65
16: scaling: 1 (divide each row by sum of abs. values in each row)
66
17: frontal matrix allocation ratio: 0.5
68
19: AMD and COLAMD aggressive absorption: 1 (yes)
70
The following options can only be changed at compile-time:
71
8: BLAS library used: Fortran BLAS. size of BLAS integer: 4
72
9: compiled for ANSI C
73
10: CPU timer is POSIX times ( ) routine.
74
11: compiled for normal operation (debugging disabled)
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computer/operating system: Linux
76
size of int: 4 UF_long: 8 Int: 8 pointer: 8 double: 8 Entry: 8 (in bytes)
79
b: dense vector, n = 5.
88
A: triplet-form matrix, n_row = 5, n_col = 5 nz = 12.
101
triplet-form matrix OK
104
A: column-form matrix, n_row 5 n_col 5, nz = 12.
106
column 0: start: 0 end: 1 entries: 2
110
column 1: start: 2 end: 4 entries: 3
115
column 2: start: 5 end: 8 entries: 4
121
column 3: start: 9 end: 9 entries: 1
124
column 4: start: 10 end: 11 entries: 2
127
column-form matrix OK
130
Symbolic factorization of A: Symbolic object:
131
matrix to be factorized:
133
number of entries: 12
134
block size used for dense matrix kernels: 32
135
strategy used: unsymmetric
136
ordering used: colamd on A
138
performn column etree postorder: yes
139
prefer diagonal pivoting (attempt P=Q): no
140
variable-size part of Numeric object:
141
minimum initial size (Units): 69 (MBytes): 0.0
142
estimated peak size (Units): 681 (MBytes): 0.0
143
estimated final size (Units): 10 (MBytes): 0.0
144
symbolic factorization memory usage (Units): 138 (MBytes): 0.0
145
frontal matrices / supercolumns:
146
number of frontal chains: 1
147
number of frontal matrices: 1
148
largest frontal matrix row dimension: 3
149
largest frontal matrix column dimension: 3
151
Frontal chain: 0. Frontal matrices 0 to 0
152
Largest frontal matrix in Frontal chain: 3-by-3
153
Front: 0 pivot cols: 3 (pivot columns 0 to 2)
154
pivot row candidates: 2 to 4
155
leftmost descendant: 0
156
1st new candidate row : 2
159
Initial column permutation, Q1: permutation vector, n = 5.
165
permutation vector OK
168
Initial row permutation, P1: permutation vector, n = 5.
174
permutation vector OK
179
Numeric factorization of A: Numeric object:
181
relative pivot tolerance used: 0.1
182
relative symmetric pivot tolerance used: 0.001
183
matrix scaled: yes (divided each row by sum abs value in each row)
184
minimum sum (abs (rows of A)): 1.00000e+00
185
maximum sum (abs (rows of A)): 1.30000e+01
186
initial allocation parameter used: 0.7
187
frontal matrix allocation parameter used: 0.5
188
final total size of Numeric object (Units): 67
189
final total size of Numeric object (MBytes): 0.0
190
peak size of variable-size part (Units): 675
191
peak size of variable-size part (MBytes): 0.0
192
largest actual frontal matrix size: 4
193
memory defragmentations: 1
194
memory reallocations: 1
195
costly memory reallocations: 0
196
entries in compressed pattern (L and U): 2
197
number of nonzeros in L (excl diag): 4
198
number of entries stored in L (excl diag): 2
199
number of nonzeros in U (excl diag): 4
200
number of entries stored in U (excl diag): 2
201
factorization floating-point operations: 6
202
number of nonzeros on diagonal of U: 5
203
min abs. value on diagonal of U: 1.42857e-01
204
max abs. value on diagonal of U: 2.19231e+00
205
reciprocal condition number estimate: 6.52e-02
207
Scale factors applied via multiplication
208
Scale factors, Rs: dense vector, n = 5.
217
P: row permutation vector, n = 5.
223
permutation vector OK
226
Q: column permutation vector, n = 5.
232
permutation vector OK
235
L in Numeric object, in column-oriented compressed-pattern form:
236
Diagonal entries are all equal to 1.0 (not stored)
244
column 2: add 1 entries. length 1. Start of Lchain.
250
column 4: length 0. Start of Lchain.
253
U in Numeric object, in row-oriented compressed-pattern form:
254
Diagonal is stored separately.
256
row 4: length 0. End of Uchain.
258
row 3: length 1. End of Uchain.
264
row 1: length 0. End of Uchain.
273
diagonal of U: dense vector, n = 5.
283
UMFPACK V5.0.1 (Aug 31, 2006), Info:
284
matrix entry defined as: double
285
Int (generic integer) defined as: UF_long
286
BLAS library used: Fortran BLAS. size of BLAS integer: 4
288
CPU timer: POSIX times ( ) routine.
289
number of rows in matrix A: 5
290
number of columns in matrix A: 5
291
entries in matrix A: 12
292
memory usage reported in: 16-byte Units
294
size of UF_long: 8 bytes
295
size of pointer: 8 bytes
296
size of numerical entry: 8 bytes
298
strategy used: unsymmetric
299
ordering used: colamd on A
300
modify Q during factorization: yes
301
prefer diagonal pivoting: no
302
pivots with zero Markowitz cost: 2
303
submatrix S after removing zero-cost pivots:
304
number of "dense" rows: 0
305
number of "dense" columns: 0
306
number of empty rows: 0
307
number of empty columns 0
308
submatrix S square and diagonal preserved
309
pattern of square submatrix S:
310
number rows and columns 3
311
symmetry of nonzero pattern: 1.000000
312
nz in S+S' (excl. diagonal): 4
313
nz on diagonal of matrix S: 2
314
fraction of nz on diagonal: 0.666667
315
2-by-2 pivoting to place large entries on diagonal:
316
# of small diagonal entries of S: 1
318
symmetry of P2*S: 0.000000
319
nz in P2*S+(P2*S)' (excl. diag.): 6
320
nz on diagonal of P2*S: 3
321
fraction of nz on diag of P2*S: 1.000000
322
symbolic factorization defragmentations: 0
323
symbolic memory usage (Units): 138
324
symbolic memory usage (MBytes): 0.0
325
Symbolic size (Units): 41
326
Symbolic size (MBytes): 0
327
symbolic factorization CPU time (sec): 0.00
328
symbolic factorization wallclock time(sec): 0.00
330
matrix scaled: yes (divided each row by sum of abs values in each row)
331
minimum sum (abs (rows of A)): 1.00000e+00
332
maximum sum (abs (rows of A)): 1.30000e+01
334
symbolic/numeric factorization: upper bound actual %
335
variable-sized part of Numeric object:
336
initial size (Units) 69 64 93%
337
peak size (Units) 681 675 99%
338
final size (Units) 10 11 110%
339
Numeric final size (Units) 69 68 99%
340
Numeric final size (MBytes) 0.0 0.0 99%
341
peak memory usage (Units) 832 826 99%
342
peak memory usage (MBytes) 0.0 0.0 99%
343
numeric factorization flops 1.30000e+01 6.00000e+00 46%
344
nz in L (incl diagonal) 10 9 90%
345
nz in U (incl diagonal) 10 9 90%
346
nz in L+U (incl diagonal) 15 13 87%
347
largest front (# entries) 9 4 44%
348
largest # rows in front 3 2 67%
349
largest # columns in front 3 2 67%
351
initial allocation ratio used: 0.7
352
# of forced updates due to frontal growth: 0
353
nz in L (incl diagonal), if none dropped 9
354
nz in U (incl diagonal), if none dropped 9
355
number of small entries dropped 0
356
nonzeros on diagonal of U: 5
357
min abs. value on diagonal of U: 1.43e-01
358
max abs. value on diagonal of U: 2.19e+00
359
estimate of reciprocal of condition number: 6.52e-02
360
indices in compressed pattern: 2
361
numerical values stored in Numeric object: 9
362
numeric factorization defragmentations: 1
363
numeric factorization reallocations: 1
364
costly numeric factorization reallocations: 0
365
numeric factorization CPU time (sec): 0.00
366
numeric factorization wallclock time (sec): 0.00
367
symbolic + numeric CPU time (sec): 0.00
368
symbolic + numeric wall clock time (sec): 0.00
370
solve flops: 1.19000e+02
371
iterative refinement steps taken: 0
372
iterative refinement steps attempted: 0
373
sparse backward error omega1: 1.11e-16
374
sparse backward error omega2: 0.00e+00
375
solve CPU time (sec): 0.00
376
solve wall clock time (sec): 0.00
378
total symbolic + numeric + solve flops: 1.25000e+02
379
total symbolic + numeric + solve CPU time: 0.00
380
total symbolic+numeric+solve wall clock time: 0.00
383
UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved.
385
UMFPACK V5.0.1 (Aug 31, 2006): OK
388
x (solution of Ax=b): dense vector, n = 5.
396
maxnorm of residual: 1.77636e-15
399
UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved.
401
UMFPACK V5.0.1 (Aug 31, 2006): OK
403
determinant: (1.14) * 10^(2)
405
x (solution of Ax=b, solve is split into 3 steps): dense vector, n = 5.
413
maxnorm of residual: 1.77636e-15
415
UMFPACK V5.0.1 (Aug 31, 2006), Info:
416
matrix entry defined as: double
417
Int (generic integer) defined as: UF_long
418
BLAS library used: Fortran BLAS. size of BLAS integer: 4
420
CPU timer: POSIX times ( ) routine.
421
number of rows in matrix A: 5
422
number of columns in matrix A: 5
423
entries in matrix A: 12
424
memory usage reported in: 16-byte Units
426
size of UF_long: 8 bytes
427
size of pointer: 8 bytes
428
size of numerical entry: 8 bytes
430
strategy used: unsymmetric
431
ordering used: colamd on A
432
modify Q during factorization: yes
433
prefer diagonal pivoting: no
434
pivots with zero Markowitz cost: 2
435
submatrix S after removing zero-cost pivots:
436
number of "dense" rows: 0
437
number of "dense" columns: 0
438
number of empty rows: 0
439
number of empty columns 0
440
submatrix S square and diagonal preserved
441
pattern of square submatrix S:
442
number rows and columns 3
443
symmetry of nonzero pattern: 1.000000
444
nz in S+S' (excl. diagonal): 4
445
nz on diagonal of matrix S: 2
446
fraction of nz on diagonal: 0.666667
447
2-by-2 pivoting to place large entries on diagonal:
448
# of small diagonal entries of S: 1
450
symmetry of P2*S: 0.000000
451
nz in P2*S+(P2*S)' (excl. diag.): 6
452
nz on diagonal of P2*S: 3
453
fraction of nz on diag of P2*S: 1.000000
454
symbolic factorization defragmentations: 0
455
symbolic memory usage (Units): 138
456
symbolic memory usage (MBytes): 0.0
457
Symbolic size (Units): 41
458
Symbolic size (MBytes): 0
459
symbolic factorization CPU time (sec): 0.00
460
symbolic factorization wallclock time(sec): 0.00
462
matrix scaled: yes (divided each row by sum of abs values in each row)
463
minimum sum (abs (rows of A)): 1.00000e+00
464
maximum sum (abs (rows of A)): 1.30000e+01
466
symbolic/numeric factorization: upper bound actual %
467
variable-sized part of Numeric object:
468
initial size (Units) 69 64 93%
469
peak size (Units) 681 675 99%
470
final size (Units) 10 11 110%
471
Numeric final size (Units) 69 68 99%
472
Numeric final size (MBytes) 0.0 0.0 99%
473
peak memory usage (Units) 832 826 99%
474
peak memory usage (MBytes) 0.0 0.0 99%
475
numeric factorization flops 1.30000e+01 6.00000e+00 46%
476
nz in L (incl diagonal) 10 9 90%
477
nz in U (incl diagonal) 10 9 90%
478
nz in L+U (incl diagonal) 15 13 87%
479
largest front (# entries) 9 4 44%
480
largest # rows in front 3 2 67%
481
largest # columns in front 3 2 67%
483
initial allocation ratio used: 0.7
484
# of forced updates due to frontal growth: 0
485
nz in L (incl diagonal), if none dropped 9
486
nz in U (incl diagonal), if none dropped 9
487
number of small entries dropped 0
488
nonzeros on diagonal of U: 5
489
min abs. value on diagonal of U: 1.43e-01
490
max abs. value on diagonal of U: 2.19e+00
491
estimate of reciprocal of condition number: 6.52e-02
492
indices in compressed pattern: 2
493
numerical values stored in Numeric object: 9
494
numeric factorization defragmentations: 1
495
numeric factorization reallocations: 1
496
costly numeric factorization reallocations: 0
497
numeric factorization CPU time (sec): 0.00
498
numeric factorization wallclock time (sec): 0.00
499
symbolic + numeric CPU time (sec): 0.00
500
symbolic + numeric wall clock time (sec): 0.00
502
solve flops: 1.11000e+02
503
iterative refinement steps taken: 0
504
iterative refinement steps attempted: 0
505
sparse backward error omega1: 7.64e-17
506
sparse backward error omega2: 0.00e+00
507
solve CPU time (sec): 0.00
508
solve wall clock time (sec): 0.00
510
total symbolic + numeric + solve flops: 1.17000e+02
511
total symbolic + numeric + solve CPU time: 0.00
512
total symbolic+numeric+solve wall clock time: 0.00
515
x (solution of A'x=b): dense vector, n = 5.
523
maxnorm of residual: 7.10543e-15
526
changing A (1,4) to zero
528
modified A: column-form matrix, n_row 5 n_col 5, nz = 12.
530
column 0: start: 0 end: 1 entries: 2
534
column 1: start: 2 end: 4 entries: 3
539
column 2: start: 5 end: 8 entries: 4
545
column 3: start: 9 end: 9 entries: 1
548
column 4: start: 10 end: 11 entries: 2
551
column-form matrix OK
554
Numeric factorization of modified A: Numeric object:
556
relative pivot tolerance used: 0.1
557
relative symmetric pivot tolerance used: 0.001
558
matrix scaled: yes (divided each row by sum abs value in each row)
559
minimum sum (abs (rows of A)): 1.00000e+00
560
maximum sum (abs (rows of A)): 7.00000e+00
561
initial allocation parameter used: 0.7
562
frontal matrix allocation parameter used: 0.5
563
final total size of Numeric object (Units): 66
564
final total size of Numeric object (MBytes): 0.0
565
peak size of variable-size part (Units): 675
566
peak size of variable-size part (MBytes): 0.0
567
largest actual frontal matrix size: 4
568
memory defragmentations: 1
569
memory reallocations: 1
570
costly memory reallocations: 0
571
entries in compressed pattern (L and U): 2
572
number of nonzeros in L (excl diag): 4
573
number of entries stored in L (excl diag): 2
574
number of nonzeros in U (excl diag): 3
575
number of entries stored in U (excl diag): 1
576
factorization floating-point operations: 4
577
number of nonzeros on diagonal of U: 5
578
min abs. value on diagonal of U: 1.50000e-01
579
max abs. value on diagonal of U: 1.00000e+00
580
reciprocal condition number estimate: 1.50e-01
582
Scale factors applied via multiplication
583
Scale factors, Rs: dense vector, n = 5.
592
P: row permutation vector, n = 5.
598
permutation vector OK
601
Q: column permutation vector, n = 5.
607
permutation vector OK
610
L in Numeric object, in column-oriented compressed-pattern form:
611
Diagonal entries are all equal to 1.0 (not stored)
619
column 2: add 1 entries. length 1. Start of Lchain.
625
column 4: length 0. Start of Lchain.
628
U in Numeric object, in row-oriented compressed-pattern form:
629
Diagonal is stored separately.
631
row 4: length 0. End of Uchain.
633
row 3: length 1. End of Uchain.
636
row 2: length 0. End of Uchain.
638
row 1: length 0. End of Uchain.
647
diagonal of U: dense vector, n = 5.
657
UMFPACK V5.0.1 (Aug 31, 2006), Info:
658
matrix entry defined as: double
659
Int (generic integer) defined as: UF_long
660
BLAS library used: Fortran BLAS. size of BLAS integer: 4
662
CPU timer: POSIX times ( ) routine.
663
number of rows in matrix A: 5
664
number of columns in matrix A: 5
665
entries in matrix A: 12
666
memory usage reported in: 16-byte Units
668
size of UF_long: 8 bytes
669
size of pointer: 8 bytes
670
size of numerical entry: 8 bytes
672
strategy used: unsymmetric
673
ordering used: colamd on A
674
modify Q during factorization: yes
675
prefer diagonal pivoting: no
676
pivots with zero Markowitz cost: 2
677
submatrix S after removing zero-cost pivots:
678
number of "dense" rows: 0
679
number of "dense" columns: 0
680
number of empty rows: 0
681
number of empty columns 0
682
submatrix S square and diagonal preserved
683
pattern of square submatrix S:
684
number rows and columns 3
685
symmetry of nonzero pattern: 1.000000
686
nz in S+S' (excl. diagonal): 4
687
nz on diagonal of matrix S: 2
688
fraction of nz on diagonal: 0.666667
689
2-by-2 pivoting to place large entries on diagonal:
690
# of small diagonal entries of S: 1
692
symmetry of P2*S: 0.000000
693
nz in P2*S+(P2*S)' (excl. diag.): 6
694
nz on diagonal of P2*S: 3
695
fraction of nz on diag of P2*S: 1.000000
696
symbolic factorization defragmentations: 0
697
symbolic memory usage (Units): 138
698
symbolic memory usage (MBytes): 0.0
699
Symbolic size (Units): 41
700
Symbolic size (MBytes): 0
701
symbolic factorization CPU time (sec): 0.00
702
symbolic factorization wallclock time(sec): 0.00
704
matrix scaled: yes (divided each row by sum of abs values in each row)
705
minimum sum (abs (rows of A)): 1.00000e+00
706
maximum sum (abs (rows of A)): 7.00000e+00
708
symbolic/numeric factorization: upper bound actual %
709
variable-sized part of Numeric object:
710
initial size (Units) 69 64 93%
711
peak size (Units) 681 675 99%
712
final size (Units) 10 10 100%
713
Numeric final size (Units) 69 67 97%
714
Numeric final size (MBytes) 0.0 0.0 97%
715
peak memory usage (Units) 832 826 99%
716
peak memory usage (MBytes) 0.0 0.0 99%
717
numeric factorization flops 1.30000e+01 4.00000e+00 31%
718
nz in L (incl diagonal) 10 9 90%
719
nz in U (incl diagonal) 10 8 80%
720
nz in L+U (incl diagonal) 15 12 80%
721
largest front (# entries) 9 4 44%
722
largest # rows in front 3 2 67%
723
largest # columns in front 3 2 67%
725
initial allocation ratio used: 0.7
726
# of forced updates due to frontal growth: 0
727
nz in L (incl diagonal), if none dropped 9
728
nz in U (incl diagonal), if none dropped 8
729
number of small entries dropped 0
730
nonzeros on diagonal of U: 5
731
min abs. value on diagonal of U: 1.50e-01
732
max abs. value on diagonal of U: 1.00e+00
733
estimate of reciprocal of condition number: 1.50e-01
734
indices in compressed pattern: 2
735
numerical values stored in Numeric object: 8
736
numeric factorization defragmentations: 1
737
numeric factorization reallocations: 1
738
costly numeric factorization reallocations: 0
739
numeric factorization CPU time (sec): 0.00
740
numeric factorization wallclock time (sec): 0.00
741
symbolic + numeric CPU time (sec): 0.00
742
symbolic + numeric wall clock time (sec): 0.00
744
solve flops: 1.17000e+02
745
iterative refinement steps taken: 0
746
iterative refinement steps attempted: 0
747
sparse backward error omega1: 7.89e-17
748
sparse backward error omega2: 0.00e+00
749
solve CPU time (sec): 0.00
750
solve wall clock time (sec): 0.00
752
total symbolic + numeric + solve flops: 1.21000e+02
753
total symbolic + numeric + solve CPU time: 0.00
754
total symbolic+numeric+solve wall clock time: 0.00
757
x (with modified A): dense vector, n = 5.
765
maxnorm of residual: 7.10543e-15
767
changing A (0,0) from 2 to 2
768
changing A (1,0) from 3 to 2
769
changing A (0,1) from 3 to 13
770
changing A (2,1) from -1 to 7
771
changing A (4,1) from 4 to 10
772
changing A (1,2) from 4 to 23
773
changing A (2,2) from -3 to 15
774
changing A (3,2) from 1 to 18
775
changing A (4,2) from 2 to 18
776
changing A (2,3) from 2 to 30
777
changing A (1,4) from 0 to 39
778
changing A (4,4) from 1 to 37
780
completely modified A (same pattern): column-form matrix, n_row 5 n_col 5, nz = 12.
782
column 0: start: 0 end: 1 entries: 2
786
column 1: start: 2 end: 4 entries: 3
791
column 2: start: 5 end: 8 entries: 4
797
column 3: start: 9 end: 9 entries: 1
800
column 4: start: 10 end: 11 entries: 2
803
column-form matrix OK
806
Saving symbolic object:
808
Freeing symbolic object:
810
Loading symbolic object:
812
Done loading symbolic object
814
Numeric factorization of completely modified A: Numeric object:
816
relative pivot tolerance used: 0.1
817
relative symmetric pivot tolerance used: 0.001
818
matrix scaled: yes (divided each row by sum abs value in each row)
819
minimum sum (abs (rows of A)): 1.50000e+01
820
maximum sum (abs (rows of A)): 6.50000e+01
821
initial allocation parameter used: 0.7
822
frontal matrix allocation parameter used: 0.5
823
final total size of Numeric object (Units): 67
824
final total size of Numeric object (MBytes): 0.0
825
peak size of variable-size part (Units): 675
826
peak size of variable-size part (MBytes): 0.0
827
largest actual frontal matrix size: 4
828
memory defragmentations: 1
829
memory reallocations: 1
830
costly memory reallocations: 0
831
entries in compressed pattern (L and U): 2
832
number of nonzeros in L (excl diag): 4
833
number of entries stored in L (excl diag): 2
834
number of nonzeros in U (excl diag): 4
835
number of entries stored in U (excl diag): 2
836
factorization floating-point operations: 6
837
number of nonzeros on diagonal of U: 5
838
min abs. value on diagonal of U: 1.33333e-01
839
max abs. value on diagonal of U: 1.00000e+00
840
reciprocal condition number estimate: 1.33e-01
842
Scale factors applied via multiplication
843
Scale factors, Rs: dense vector, n = 5.
852
P: row permutation vector, n = 5.
858
permutation vector OK
861
Q: column permutation vector, n = 5.
867
permutation vector OK
870
L in Numeric object, in column-oriented compressed-pattern form:
871
Diagonal entries are all equal to 1.0 (not stored)
879
column 2: add 1 entries. length 1. Start of Lchain.
885
column 4: length 0. Start of Lchain.
888
U in Numeric object, in row-oriented compressed-pattern form:
889
Diagonal is stored separately.
891
row 4: length 0. End of Uchain.
893
row 3: length 1. End of Uchain.
899
row 1: length 0. End of Uchain.
908
diagonal of U: dense vector, n = 5.
918
UMFPACK V5.0.1 (Aug 31, 2006), Info:
919
matrix entry defined as: double
920
Int (generic integer) defined as: UF_long
921
BLAS library used: Fortran BLAS. size of BLAS integer: 4
923
CPU timer: POSIX times ( ) routine.
924
number of rows in matrix A: 5
925
number of columns in matrix A: 5
926
entries in matrix A: 12
927
memory usage reported in: 16-byte Units
929
size of UF_long: 8 bytes
930
size of pointer: 8 bytes
931
size of numerical entry: 8 bytes
933
strategy used: unsymmetric
934
ordering used: colamd on A
935
modify Q during factorization: yes
936
prefer diagonal pivoting: no
937
pivots with zero Markowitz cost: 2
938
submatrix S after removing zero-cost pivots:
939
number of "dense" rows: 0
940
number of "dense" columns: 0
941
number of empty rows: 0
942
number of empty columns 0
943
submatrix S square and diagonal preserved
944
pattern of square submatrix S:
945
number rows and columns 3
946
symmetry of nonzero pattern: 1.000000
947
nz in S+S' (excl. diagonal): 4
948
nz on diagonal of matrix S: 2
949
fraction of nz on diagonal: 0.666667
950
2-by-2 pivoting to place large entries on diagonal:
951
# of small diagonal entries of S: 1
953
symmetry of P2*S: 0.000000
954
nz in P2*S+(P2*S)' (excl. diag.): 6
955
nz on diagonal of P2*S: 3
956
fraction of nz on diag of P2*S: 1.000000
957
symbolic factorization defragmentations: 0
958
symbolic memory usage (Units): 138
959
symbolic memory usage (MBytes): 0.0
960
Symbolic size (Units): 41
961
Symbolic size (MBytes): 0
962
symbolic factorization CPU time (sec): 0.00
963
symbolic factorization wallclock time(sec): 0.00
965
matrix scaled: yes (divided each row by sum of abs values in each row)
966
minimum sum (abs (rows of A)): 1.50000e+01
967
maximum sum (abs (rows of A)): 6.50000e+01
969
symbolic/numeric factorization: upper bound actual %
970
variable-sized part of Numeric object:
971
initial size (Units) 69 64 93%
972
peak size (Units) 681 675 99%
973
final size (Units) 10 11 110%
974
Numeric final size (Units) 69 68 99%
975
Numeric final size (MBytes) 0.0 0.0 99%
976
peak memory usage (Units) 832 826 99%
977
peak memory usage (MBytes) 0.0 0.0 99%
978
numeric factorization flops 1.30000e+01 6.00000e+00 46%
979
nz in L (incl diagonal) 10 9 90%
980
nz in U (incl diagonal) 10 9 90%
981
nz in L+U (incl diagonal) 15 13 87%
982
largest front (# entries) 9 4 44%
983
largest # rows in front 3 2 67%
984
largest # columns in front 3 2 67%
986
initial allocation ratio used: 0.7
987
# of forced updates due to frontal growth: 0
988
nz in L (incl diagonal), if none dropped 9
989
nz in U (incl diagonal), if none dropped 9
990
number of small entries dropped 0
991
nonzeros on diagonal of U: 5
992
min abs. value on diagonal of U: 1.33e-01
993
max abs. value on diagonal of U: 1.00e+00
994
estimate of reciprocal of condition number: 1.33e-01
995
indices in compressed pattern: 2
996
numerical values stored in Numeric object: 9
997
numeric factorization defragmentations: 1
998
numeric factorization reallocations: 1
999
costly numeric factorization reallocations: 0
1000
numeric factorization CPU time (sec): 0.00
1001
numeric factorization wallclock time (sec): 0.00
1002
symbolic + numeric CPU time (sec): 0.00
1003
symbolic + numeric wall clock time (sec): 0.00
1005
solve flops: 1.19000e+02
1006
iterative refinement steps taken: 0
1007
iterative refinement steps attempted: 0
1008
sparse backward error omega1: 1.04e-16
1009
sparse backward error omega2: 0.00e+00
1010
solve CPU time (sec): 0.00
1011
solve wall clock time (sec): 0.00
1013
total symbolic + numeric + solve flops: 1.25000e+02
1014
total symbolic + numeric + solve CPU time: 0.00
1015
total symbolic+numeric+solve wall clock time: 0.00
1018
x (with completely modified A): dense vector, n = 5.
1026
maxnorm of residual: 3.55271e-15
1029
C (transpose of A): column-form matrix, n_row 5 n_col 5, nz = 12.
1031
column 0: start: 0 end: 1 entries: 2
1035
column 1: start: 2 end: 4 entries: 3
1040
column 2: start: 5 end: 7 entries: 3
1045
column 3: start: 8 end: 8 entries: 1
1048
column 4: start: 9 end: 11 entries: 3
1052
column-form matrix OK
1055
Symbolic factorization of C: Symbolic object:
1056
matrix to be factorized:
1058
number of entries: 12
1059
block size used for dense matrix kernels: 32
1060
strategy used: unsymmetric
1061
ordering used: colamd on A
1063
performn column etree postorder: yes
1064
prefer diagonal pivoting (attempt P=Q): no
1065
variable-size part of Numeric object:
1066
minimum initial size (Units): 71 (MBytes): 0.0
1067
estimated peak size (Units): 683 (MBytes): 0.0
1068
estimated final size (Units): 12 (MBytes): 0.0
1069
symbolic factorization memory usage (Units): 138 (MBytes): 0.0
1070
frontal matrices / supercolumns:
1071
number of frontal chains: 1
1072
number of frontal matrices: 1
1073
largest frontal matrix row dimension: 3
1074
largest frontal matrix column dimension: 3
1076
Frontal chain: 0. Frontal matrices 0 to 0
1077
Largest frontal matrix in Frontal chain: 3-by-3
1078
Front: 0 pivot cols: 3 (pivot columns 0 to 2)
1079
pivot row candidates: 2 to 4
1080
leftmost descendant: 0
1081
1st new candidate row : 2
1084
Initial column permutation, Q1: permutation vector, n = 5.
1090
permutation vector OK
1093
Initial row permutation, P1: permutation vector, n = 5.
1099
permutation vector OK
1104
Get the contents of the Symbolic object for C:
1105
(compare with umfpack_dl_report_symbolic output, above)
1106
From the Symbolic object, C is of dimension 5-by-5
1107
with nz = 12, number of fronts = 1,
1108
number of frontal matrix chains = 1
1110
Pivot columns in each front, and parent of each front:
1111
Front 0: parent front: -1 number of pivot cols: 3
1112
0-th pivot column is column 3 in original matrix
1113
1-th pivot column is column 2 in original matrix
1114
2-th pivot column is column 0 in original matrix
1116
Note that the column ordering, above, will be refined
1117
in the numeric factorization below. The assignment of pivot
1118
columns to frontal matrices will always remain unchanged.
1120
Total number of pivot columns in frontal matrices: 3
1122
Frontal matrix chains:
1123
Frontal matrices 0 to 0 are factorized in a single
1124
working array of size 3-by-3
1126
Numeric factorization of C: Numeric object:
1128
relative pivot tolerance used: 0.1
1129
relative symmetric pivot tolerance used: 0.001
1130
matrix scaled: yes (divided each row by sum abs value in each row)
1131
minimum sum (abs (rows of A)): 4.00000e+00
1132
maximum sum (abs (rows of A)): 7.60000e+01
1133
initial allocation parameter used: 0.7
1134
frontal matrix allocation parameter used: 0.5
1135
final total size of Numeric object (Units): 69
1136
final total size of Numeric object (MBytes): 0.0
1137
peak size of variable-size part (Units): 677
1138
peak size of variable-size part (MBytes): 0.0
1139
largest actual frontal matrix size: 4
1140
memory defragmentations: 1
1141
memory reallocations: 1
1142
costly memory reallocations: 1
1143
entries in compressed pattern (L and U): 2
1144
number of nonzeros in L (excl diag): 3
1145
number of entries stored in L (excl diag): 2
1146
number of nonzeros in U (excl diag): 5
1147
number of entries stored in U (excl diag): 2
1148
factorization floating-point operations: 6
1149
number of nonzeros on diagonal of U: 5
1150
min abs. value on diagonal of U: 2.43243e-01
1151
max abs. value on diagonal of U: 1.00000e+00
1152
reciprocal condition number estimate: 2.43e-01
1154
Scale factors applied via multiplication
1155
Scale factors, Rs: dense vector, n = 5.
1164
P: row permutation vector, n = 5.
1170
permutation vector OK
1173
Q: column permutation vector, n = 5.
1179
permutation vector OK
1182
L in Numeric object, in column-oriented compressed-pattern form:
1183
Diagonal entries are all equal to 1.0 (not stored)
1190
column 2: add 1 entries. length 1. Start of Lchain.
1196
column 4: length 0. Start of Lchain.
1199
U in Numeric object, in row-oriented compressed-pattern form:
1200
Diagonal is stored separately.
1202
row 4: length 0. End of Uchain.
1204
row 3: length 1. End of Uchain.
1210
row 1: length 0. End of Uchain.
1220
diagonal of U: dense vector, n = 5.
1231
L (lower triangular factor of C): row-form matrix, n_row 5 n_col 5, nz = 8.
1233
row 0: start: 0 end: 0 entries: 1
1236
row 1: start: 1 end: 1 entries: 1
1239
row 2: start: 2 end: 2 entries: 1
1242
row 3: start: 3 end: 3 entries: 1
1245
row 4: start: 4 end: 7 entries: 4
1246
column 1 : (0.233333)
1247
column 2 : (0.866667)
1248
column 3 : (0.684685)
1253
U (upper triangular factor of C): column-form matrix, n_row 5 n_col 5, nz = 10.
1255
column 0: start: 0 end: 0 entries: 1
1258
column 1: start: 1 end: 2 entries: 2
1262
column 2: start: 3 end: 3 entries: 1
1265
column 3: start: 4 end: 5 entries: 2
1269
column 4: start: 6 end: 9 entries: 4
1274
column-form matrix OK
1277
P: permutation vector, n = 5.
1283
permutation vector OK
1286
Q: permutation vector, n = 5.
1292
permutation vector OK
1295
Scale factors: row i of A is to be multiplied by the ith scale factor
1302
Converting L to triplet form, and printing it:
1304
L, in triplet form: triplet-form matrix, n_row = 5, n_col = 5 nz = 8.
1313
triplet-form matrix OK
1316
Saving numeric object:
1318
Freeing numeric object:
1320
Loading numeric object:
1322
Done loading numeric object
1323
UMFPACK V5.0.1 (Aug 31, 2006), Info:
1324
matrix entry defined as: double
1325
Int (generic integer) defined as: UF_long
1326
BLAS library used: Fortran BLAS. size of BLAS integer: 4
1328
CPU timer: POSIX times ( ) routine.
1329
number of rows in matrix A: 5
1330
number of columns in matrix A: 5
1331
entries in matrix A: 12
1332
memory usage reported in: 16-byte Units
1333
size of int: 4 bytes
1334
size of UF_long: 8 bytes
1335
size of pointer: 8 bytes
1336
size of numerical entry: 8 bytes
1338
strategy used: unsymmetric
1339
ordering used: colamd on A
1340
modify Q during factorization: yes
1341
prefer diagonal pivoting: no
1342
pivots with zero Markowitz cost: 2
1343
submatrix S after removing zero-cost pivots:
1344
number of "dense" rows: 0
1345
number of "dense" columns: 0
1346
number of empty rows: 0
1347
number of empty columns 0
1348
submatrix S square and diagonal preserved
1349
pattern of square submatrix S:
1350
number rows and columns 3
1351
symmetry of nonzero pattern: 1.000000
1352
nz in S+S' (excl. diagonal): 4
1353
nz on diagonal of matrix S: 2
1354
fraction of nz on diagonal: 0.666667
1355
2-by-2 pivoting to place large entries on diagonal:
1356
# of small diagonal entries of S: 1
1358
symmetry of P2*S: 0.000000
1359
nz in P2*S+(P2*S)' (excl. diag.): 6
1360
nz on diagonal of P2*S: 3
1361
fraction of nz on diag of P2*S: 1.000000
1362
symbolic factorization defragmentations: 0
1363
symbolic memory usage (Units): 138
1364
symbolic memory usage (MBytes): 0.0
1365
Symbolic size (Units): 41
1366
Symbolic size (MBytes): 0
1367
symbolic factorization CPU time (sec): 0.00
1368
symbolic factorization wallclock time(sec): 0.00
1370
matrix scaled: yes (divided each row by sum of abs values in each row)
1371
minimum sum (abs (rows of A)): 4.00000e+00
1372
maximum sum (abs (rows of A)): 7.60000e+01
1374
symbolic/numeric factorization: upper bound actual %
1375
variable-sized part of Numeric object:
1376
initial size (Units) 71 66 93%
1377
peak size (Units) 683 677 99%
1378
final size (Units) 12 13 108%
1379
Numeric final size (Units) 71 70 99%
1380
Numeric final size (MBytes) 0.0 0.0 99%
1381
peak memory usage (Units) 834 828 99%
1382
peak memory usage (MBytes) 0.0 0.0 99%
1383
numeric factorization flops 1.30000e+01 6.00000e+00 46%
1384
nz in L (incl diagonal) 9 8 89%
1385
nz in U (incl diagonal) 11 10 91%
1386
nz in L+U (incl diagonal) 15 13 87%
1387
largest front (# entries) 9 4 44%
1388
largest # rows in front 3 2 67%
1389
largest # columns in front 3 2 67%
1391
initial allocation ratio used: 0.7
1392
# of forced updates due to frontal growth: 0
1393
nz in L (incl diagonal), if none dropped 8
1394
nz in U (incl diagonal), if none dropped 10
1395
number of small entries dropped 0
1396
nonzeros on diagonal of U: 5
1397
min abs. value on diagonal of U: 2.43e-01
1398
max abs. value on diagonal of U: 1.00e+00
1399
estimate of reciprocal of condition number: 2.43e-01
1400
indices in compressed pattern: 2
1401
numerical values stored in Numeric object: 9
1402
numeric factorization defragmentations: 1
1403
numeric factorization reallocations: 1
1404
costly numeric factorization reallocations: 1
1405
numeric factorization CPU time (sec): 0.00
1406
numeric factorization wallclock time (sec): 0.00
1407
symbolic + numeric CPU time (sec): 0.00
1408
symbolic + numeric wall clock time (sec): 0.00
1410
solve flops: 1.11000e+02
1411
iterative refinement steps taken: 0
1412
iterative refinement steps attempted: 0
1413
sparse backward error omega1: 8.07e-17
1414
sparse backward error omega2: 0.00e+00
1415
solve CPU time (sec): 0.00
1416
solve wall clock time (sec): 0.00
1418
total symbolic + numeric + solve flops: 1.17000e+02
1419
total symbolic + numeric + solve CPU time: 0.00
1420
total symbolic+numeric+solve wall clock time: 0.00
1423
x (solution of C'x=b): dense vector, n = 5.
1431
maxnorm of residual: 3.55271e-15
1434
Solving C'x=b again, using umfpack_dl_wsolve instead:
1435
UMFPACK V5.0.1 (Aug 31, 2006), Info:
1436
matrix entry defined as: double
1437
Int (generic integer) defined as: UF_long
1438
BLAS library used: Fortran BLAS. size of BLAS integer: 4
1440
CPU timer: POSIX times ( ) routine.
1441
number of rows in matrix A: 5
1442
number of columns in matrix A: 5
1443
entries in matrix A: 12
1444
memory usage reported in: 16-byte Units
1445
size of int: 4 bytes
1446
size of UF_long: 8 bytes
1447
size of pointer: 8 bytes
1448
size of numerical entry: 8 bytes
1450
strategy used: unsymmetric
1451
ordering used: colamd on A
1452
modify Q during factorization: yes
1453
prefer diagonal pivoting: no
1454
pivots with zero Markowitz cost: 2
1455
submatrix S after removing zero-cost pivots:
1456
number of "dense" rows: 0
1457
number of "dense" columns: 0
1458
number of empty rows: 0
1459
number of empty columns 0
1460
submatrix S square and diagonal preserved
1461
pattern of square submatrix S:
1462
number rows and columns 3
1463
symmetry of nonzero pattern: 1.000000
1464
nz in S+S' (excl. diagonal): 4
1465
nz on diagonal of matrix S: 2
1466
fraction of nz on diagonal: 0.666667
1467
2-by-2 pivoting to place large entries on diagonal:
1468
# of small diagonal entries of S: 1
1470
symmetry of P2*S: 0.000000
1471
nz in P2*S+(P2*S)' (excl. diag.): 6
1472
nz on diagonal of P2*S: 3
1473
fraction of nz on diag of P2*S: 1.000000
1474
symbolic factorization defragmentations: 0
1475
symbolic memory usage (Units): 138
1476
symbolic memory usage (MBytes): 0.0
1477
Symbolic size (Units): 41
1478
Symbolic size (MBytes): 0
1479
symbolic factorization CPU time (sec): 0.00
1480
symbolic factorization wallclock time(sec): 0.00
1482
matrix scaled: yes (divided each row by sum of abs values in each row)
1483
minimum sum (abs (rows of A)): 4.00000e+00
1484
maximum sum (abs (rows of A)): 7.60000e+01
1486
symbolic/numeric factorization: upper bound actual %
1487
variable-sized part of Numeric object:
1488
initial size (Units) 71 66 93%
1489
peak size (Units) 683 677 99%
1490
final size (Units) 12 13 108%
1491
Numeric final size (Units) 71 70 99%
1492
Numeric final size (MBytes) 0.0 0.0 99%
1493
peak memory usage (Units) 834 828 99%
1494
peak memory usage (MBytes) 0.0 0.0 99%
1495
numeric factorization flops 1.30000e+01 6.00000e+00 46%
1496
nz in L (incl diagonal) 9 8 89%
1497
nz in U (incl diagonal) 11 10 91%
1498
nz in L+U (incl diagonal) 15 13 87%
1499
largest front (# entries) 9 4 44%
1500
largest # rows in front 3 2 67%
1501
largest # columns in front 3 2 67%
1503
initial allocation ratio used: 0.7
1504
# of forced updates due to frontal growth: 0
1505
nz in L (incl diagonal), if none dropped 8
1506
nz in U (incl diagonal), if none dropped 10
1507
number of small entries dropped 0
1508
nonzeros on diagonal of U: 5
1509
min abs. value on diagonal of U: 2.43e-01
1510
max abs. value on diagonal of U: 1.00e+00
1511
estimate of reciprocal of condition number: 2.43e-01
1512
indices in compressed pattern: 2
1513
numerical values stored in Numeric object: 9
1514
numeric factorization defragmentations: 1
1515
numeric factorization reallocations: 1
1516
costly numeric factorization reallocations: 1
1517
numeric factorization CPU time (sec): 0.00
1518
numeric factorization wallclock time (sec): 0.00
1519
symbolic + numeric CPU time (sec): 0.00
1520
symbolic + numeric wall clock time (sec): 0.00
1522
solve flops: 1.11000e+02
1523
iterative refinement steps taken: 0
1524
iterative refinement steps attempted: 0
1525
sparse backward error omega1: 8.07e-17
1526
sparse backward error omega2: 0.00e+00
1527
solve CPU time (sec): 0.00
1528
solve wall clock time (sec): 0.00
1530
total symbolic + numeric + solve flops: 1.17000e+02
1531
total symbolic + numeric + solve CPU time: 0.00
1532
total symbolic+numeric+solve wall clock time: 0.00
1535
x (solution of C'x=b): dense vector, n = 5.
1543
maxnorm of residual: 3.55271e-15
1546
umfpack_dl_demo complete.
1547
Total time: 0.00 seconds (CPU time), 0.01 seconds (wallclock time)
added
removed
UMFPACK/Demo/Opteron64/umfpack_dl_demo.out
