Mercurial > octave-nkf

comparison liboctave/UMFPACK/UMFPACK/Demo/umfpack_di_demo.out @ 5164:57077d0ddc8e

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
[project @ 2005-02-25 19:55:24 by jwe]
author jwe
date Fri, 25 Feb 2005 19:55:28 +0000
parents
children
comparison
equal deleted inserted replaced
5163:9f3299378193 5164:57077d0ddc8e
1
2 UMFPACK V4.4 (Jan. 28, 2005) demo: _di_ version
3
4 UMFPACK: Copyright (c) 2005 by Timothy A. Davis. All Rights Reserved.
5
6
7 UMFPACK License:
8
9 Your use or distribution of UMFPACK or any modified version of
10 UMFPACK implies that you agree to this License.
11
12 THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
13 EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
14
15 Permission is hereby granted to use or copy this program, provided
16 that the Copyright, this License, and the Availability of the original
17 version is retained on all copies. User documentation of any code that
18 uses UMFPACK or any modified version of UMFPACK code must cite the
19 Copyright, this License, the Availability note, and "Used by permission."
20 Permission to modify the code and to distribute modified code is granted,
21 provided the Copyright, this License, and the Availability note are
22 retained, and a notice that the code was modified is included. This
23 software was developed with support from the National Science Foundation,
24 and is provided to you free of charge.
25
26 Availability: http://www.cise.ufl.edu/research/sparse/umfpack
27
28 UMFPACK V4.4 (Jan. 28, 2005): OK
29
30
31 UMFPACK V4.4 (Jan. 28, 2005), Control:
32
33 Matrix entry defined as: double
34 Int (generic integer) defined as: int
35
36 0: print level: 5
37 1: dense row parameter: 0.2
38 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries)
39 2: dense column parameter: 0.2
40 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
41 3: pivot tolerance: 0.1
42 4: block size for dense matrix kernels: 32
43 5: strategy: 0 (auto)
44 6: initial allocation ratio: 0.7
45 7: max iterative refinement steps: 2
46 12: 2-by-2 pivot tolerance: 0.01
47 13: Q fixed during numerical factorization: 0 (auto)
48 14: AMD dense row/col parameter: 10
49 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries
50 Only used if the AMD ordering is used.
51 15: diagonal pivot tolerance: 0.001
52 Only used if diagonal pivoting is attempted.
53 16: scaling: 1 (divide each row by sum of abs. values in each row)
54 17: frontal matrix allocation ratio: 0.5
55 18: drop tolerance: 0
56 19: AMD and COLAMD aggressive absorption: 1 (yes)
57
58 The following options can only be changed at compile-time:
59 8: BLAS library used: none. UMFPACK will be slow.
60 9: compiled for ANSI C (uses malloc, free, realloc, and printf)
61 10: CPU timer is POSIX times ( ) routine.
62 11: compiled for normal operation (debugging disabled)
63 computer/operating system: Linux
64 size of int: 4 long: 4 Int: 4 pointer: 4 double: 8 Entry: 8 (in bytes)
65
66
67 b: dense vector, n = 5.
68 0 : (8)
69 1 : (45)
70 2 : (-3)
71 3 : (3)
72 4 : (19)
73 dense vector OK
74
75
76 A: triplet-form matrix, n_row = 5, n_col = 5 nz = 12.
77 0 : 0 0 (2)
78 1 : 4 4 (1)
79 2 : 1 0 (3)
80 3 : 1 2 (4)
81 4 : 2 1 (-1)
82 5 : 2 2 (-3)
83 6 : 0 1 (3)
84 7 : 1 4 (6)
85 8 : 2 3 (2)
86 9 : 3 2 (1)
87 10 : 4 1 (4)
88 11 : 4 2 (2)
89 triplet-form matrix OK
90
91
92 A: column-form matrix, n_row 5 n_col 5, nz = 12.
93
94 column 0: start: 0 end: 1 entries: 2
95 row 0 : (2)
96 row 1 : (3)
97
98 column 1: start: 2 end: 4 entries: 3
99 row 0 : (3)
100 row 2 : (-1)
101 row 4 : (4)
102
103 column 2: start: 5 end: 8 entries: 4
104 row 1 : (4)
105 row 2 : (-3)
106 row 3 : (1)
107 row 4 : (2)
108
109 column 3: start: 9 end: 9 entries: 1
110 row 2 : (2)
111
112 column 4: start: 10 end: 11 entries: 2
113 row 1 : (6)
114 row 4 : (1)
115 column-form matrix OK
116
117
118 Symbolic factorization of A: Symbolic object:
119 matrix to be factorized:
120 n_row: 5 n_col: 5
121 number of entries: 12
122 block size used for dense matrix kernels: 32
123 strategy used: unsymmetric
124 ordering used: colamd on A
125
126 performn column etree postorder: yes
127 prefer diagonal pivoting (attempt P=Q): no
128 variable-size part of Numeric object:
129 minimum initial size (Units): 74 (MBytes): 0.0
130 estimated peak size (Units): 1301 (MBytes): 0.0
131 estimated final size (Units): 15 (MBytes): 0.0
132 symbolic factorization memory usage (Units): 144 (MBytes): 0.0
133 frontal matrices / supercolumns:
134 number of frontal chains: 1
135 number of frontal matrices: 1
136 largest frontal matrix row dimension: 3
137 largest frontal matrix column dimension: 3
138
139 Frontal chain: 0. Frontal matrices 0 to 0
140 Largest frontal matrix in Frontal chain: 3-by-3
141 Front: 0 pivot cols: 3 (pivot columns 0 to 2)
142 pivot row candidates: 2 to 4
143 leftmost descendant: 0
144 1st new candidate row : 2
145 parent: (none)
146
147 Initial column permutation, Q1: permutation vector, n = 5.
148 0 : 3
149 1 : 2
150 2 : 0
151 3 : 4
152 4 : 1
153 permutation vector OK
154
155
156 Initial row permutation, P1: permutation vector, n = 5.
157 0 : 2
158 1 : 3
159 2 : 0
160 3 : 1
161 4 : 4
162 permutation vector OK
163
164 Symbolic object: OK
165
166
167 Numeric factorization of A: Numeric object:
168 n_row: 5 n_col: 5
169 relative pivot tolerance used: 0.1
170 relative symmetric pivot tolerance used: 0.001
171 matrix scaled: yes (divided each row by sum abs value in each row)
172 minimum sum (abs (rows of A)): 1.00000e+00
173 maximum sum (abs (rows of A)): 1.30000e+01
174 initial allocation parameter used: 0.7
175 frontal matrix allocation parameter used: 0.5
176 final total size of Numeric object (Units): 80
177 final total size of Numeric object (MBytes): 0.0
178 peak size of variable-size part (Units): 1292
179 peak size of variable-size part (MBytes): 0.0
180 largest actual frontal matrix size: 4
181 memory defragmentations: 1
182 memory reallocations: 1
183 costly memory reallocations: 0
184 entries in compressed pattern (L and U): 2
185 number of nonzeros in L (excl diag): 4
186 number of entries stored in L (excl diag): 2
187 number of nonzeros in U (excl diag): 4
188 number of entries stored in U (excl diag): 2
189 factorization floating-point operations: 6
190 number of nonzeros on diagonal of U: 5
191 min abs. value on diagonal of U: 1.42857e-01
192 max abs. value on diagonal of U: 2.19231e+00
193 reciprocal condition number estimate: 6.52e-02
194
195 Scale factors applied via multiplication
196 Scale factors, Rs: dense vector, n = 5.
197 0 : (0.2)
198 1 : (0.0769231)
199 2 : (0.166667)
200 3 : (1)
201 4 : (0.142857)
202 dense vector OK
203
204
205 P: row permutation vector, n = 5.
206 0 : 2
207 1 : 3
208 2 : 0
209 3 : 4
210 4 : 1
211 permutation vector OK
212
213
214 Q: column permutation vector, n = 5.
215 0 : 3
216 1 : 2
217 2 : 0
218 3 : 4
219 4 : 1
220 permutation vector OK
221
222
223 L in Numeric object, in column-oriented compressed-pattern form:
224 Diagonal entries are all equal to 1.0 (not stored)
225
226 column 0: length 0.
227
228 column 1: length 2.
229 row 4 : (0.307692)
230 row 3 : (0.285714)
231
232 column 2: add 1 entries. length 1. Start of Lchain.
233 row 4 : (0.576923)
234
235 column 3: length 1.
236 row 4 : (3.23077)
237
238 column 4: length 0. Start of Lchain.
239
240
241 U in Numeric object, in row-oriented compressed-pattern form:
242 Diagonal is stored separately.
243
244 row 4: length 0. End of Uchain.
245
246 row 3: length 1. End of Uchain.
247 col 4 : (0.571429)
248
249 row 2: length 1.
250 col 4 : (0.6)
251
252 row 1: length 0. End of Uchain.
253
254 row 1: length 0.
255
256 row 0: length 2.
257 col 1 : (-0.5)
258 col 4 : (-0.166667)
259
260
261 diagonal of U: dense vector, n = 5.
262 0 : (0.333333)
263 1 : (1)
264 2 : (0.4)
265 3 : (0.142857)
266 4 : (-2.19231)
267 dense vector OK
268
269 Numeric object: OK
270
271
272 UMFPACK V4.4 (Jan. 28, 2005), Info:
273 matrix entry defined as: double
274 Int (generic integer) defined as: int
275 BLAS library used: none. UMFPACK will be slow.
276 MATLAB: no.
277 CPU timer: POSIX times ( ) routine.
278 number of rows in matrix A: 5
279 number of columns in matrix A: 5
280 entries in matrix A: 12
281 memory usage reported in: 8-byte Units
282 size of int: 4 bytes
283 size of long: 4 bytes
284 size of pointer: 4 bytes
285 size of numerical entry: 8 bytes
286
287 strategy used: unsymmetric
288 ordering used: colamd on A
289 modify Q during factorization: yes
290 prefer diagonal pivoting: no
291 pivots with zero Markowitz cost: 2
292 submatrix S after removing zero-cost pivots:
293 number of "dense" rows: 0
294 number of "dense" columns: 0
295 number of empty rows: 0
296 number of empty columns 0
297 submatrix S square and diagonal preserved
298 pattern of square submatrix S:
299 number rows and columns 3
300 symmetry of nonzero pattern: 1.000000
301 nz in S+S' (excl. diagonal): 4
302 nz on diagonal of matrix S: 2
303 fraction of nz on diagonal: 0.666667
304 2-by-2 pivoting to place large entries on diagonal:
305 # of small diagonal entries of S: 1
306 # unmatched: 0
307 symmetry of P2*S: 0.000000
308 nz in P2*S+(P2*S)' (excl. diag.): 6
309 nz on diagonal of P2*S: 3
310 fraction of nz on diag of P2*S: 1.000000
311 symbolic factorization defragmentations: 0
312 symbolic memory usage (Units): 144
313 symbolic memory usage (MBytes): 0.0
314 Symbolic size (Units): 45
315 Symbolic size (MBytes): 0
316 symbolic factorization CPU time (sec): 0.00
317 symbolic factorization wallclock time(sec): 0.00
318
319 matrix scaled: yes (divided each row by sum of abs values in each row)
320 minimum sum (abs (rows of A)): 1.00000e+00
321 maximum sum (abs (rows of A)): 1.30000e+01
322
323 symbolic/numeric factorization: upper bound actual %
324 variable-sized part of Numeric object:
325 initial size (Units) 74 69 93%
326 peak size (Units) 1301 1292 99%
327 final size (Units) 15 13 87%
328 Numeric final size (Units) 85 81 95%
329 Numeric final size (MBytes) 0.0 0.0 95%
330 peak memory usage (Units) 1473 1464 99%
331 peak memory usage (MBytes) 0.0 0.0 99%
332 numeric factorization flops 1.30000e+01 6.00000e+00 46%
333 nz in L (incl diagonal) 10 9 90%
334 nz in U (incl diagonal) 10 9 90%
335 nz in L+U (incl diagonal) 15 13 87%
336 largest front (# entries) 9 4 44%
337 largest # rows in front 3 2 67%
338 largest # columns in front 3 2 67%
339
340 initial allocation ratio used: 0.7
341 # of forced updates due to frontal growth: 0
342 nz in L (incl diagonal), if none dropped 9
343 nz in U (incl diagonal), if none dropped 9
344 number of small entries dropped 0
345 nonzeros on diagonal of U: 5
346 min abs. value on diagonal of U: 1.43e-01
347 max abs. value on diagonal of U: 2.19e+00
348 estimate of reciprocal of condition number: 6.52e-02
349 indices in compressed pattern: 2
350 numerical values stored in Numeric object: 9
351 numeric factorization defragmentations: 1
352 numeric factorization reallocations: 1
353 costly numeric factorization reallocations: 0
354 numeric factorization CPU time (sec): 0.00
355 numeric factorization wallclock time (sec): 0.00
356 symbolic + numeric CPU time (sec): 0.00
357 symbolic + numeric wall clock time (sec): 0.00
358
359 solve flops: 1.19000e+02
360 iterative refinement steps taken: 0
361 iterative refinement steps attempted: 0
362 sparse backward error omega1: 4.67e-17
363 sparse backward error omega2: 0.00e+00
364 solve CPU time (sec): 0.00
365 solve wall clock time (sec): 0.00
366
367 total symbolic + numeric + solve flops: 1.25000e+02
368 total symbolic + numeric + solve CPU time: 0.00
369 total symbolic+numeric+solve wall clock time: 0.00
370
371
372 UMFPACK: Copyright (c) 2005 by Timothy A. Davis. All Rights Reserved.
373
374 UMFPACK V4.4 (Jan. 28, 2005): OK
375
376
377 x (solution of Ax=b): dense vector, n = 5.
378 0 : (1)
379 1 : (2)
380 2 : (3)
381 3 : (4)
382 4 : (5)
383 dense vector OK
384
385 maxnorm of residual: 1.77636e-15
386
387
388 UMFPACK: Copyright (c) 2005 by Timothy A. Davis. All Rights Reserved.
389
390 UMFPACK V4.4 (Jan. 28, 2005): OK
391
392 determinant: (1.14) * 10^(2)
393
394 x (solution of Ax=b, solve is split into 3 steps): dense vector, n = 5.
395 0 : (1)
396 1 : (2)
397 2 : (3)
398 3 : (4)
399 4 : (5)
400 dense vector OK
401
402 maxnorm of residual: 1.77636e-15
403
404
405 UMFPACK V4.4 (Jan. 28, 2005), Info:
406 matrix entry defined as: double
407 Int (generic integer) defined as: int
408 BLAS library used: none. UMFPACK will be slow.
409 MATLAB: no.
410 CPU timer: POSIX times ( ) routine.
411 number of rows in matrix A: 5
412 number of columns in matrix A: 5
413 entries in matrix A: 12
414 memory usage reported in: 8-byte Units
415 size of int: 4 bytes
416 size of long: 4 bytes
417 size of pointer: 4 bytes
418 size of numerical entry: 8 bytes
419
420 strategy used: unsymmetric
421 ordering used: colamd on A
422 modify Q during factorization: yes
423 prefer diagonal pivoting: no
424 pivots with zero Markowitz cost: 2
425 submatrix S after removing zero-cost pivots:
426 number of "dense" rows: 0
427 number of "dense" columns: 0
428 number of empty rows: 0
429 number of empty columns 0
430 submatrix S square and diagonal preserved
431 pattern of square submatrix S:
432 number rows and columns 3
433 symmetry of nonzero pattern: 1.000000
434 nz in S+S' (excl. diagonal): 4
435 nz on diagonal of matrix S: 2
436 fraction of nz on diagonal: 0.666667
437 2-by-2 pivoting to place large entries on diagonal:
438 # of small diagonal entries of S: 1
439 # unmatched: 0
440 symmetry of P2*S: 0.000000
441 nz in P2*S+(P2*S)' (excl. diag.): 6
442 nz on diagonal of P2*S: 3
443 fraction of nz on diag of P2*S: 1.000000
444 symbolic factorization defragmentations: 0
445 symbolic memory usage (Units): 144
446 symbolic memory usage (MBytes): 0.0
447 Symbolic size (Units): 45
448 Symbolic size (MBytes): 0
449 symbolic factorization CPU time (sec): 0.00
450 symbolic factorization wallclock time(sec): 0.00
451
452 matrix scaled: yes (divided each row by sum of abs values in each row)
453 minimum sum (abs (rows of A)): 1.00000e+00
454 maximum sum (abs (rows of A)): 1.30000e+01
455
456 symbolic/numeric factorization: upper bound actual %
457 variable-sized part of Numeric object:
458 initial size (Units) 74 69 93%
459 peak size (Units) 1301 1292 99%
460 final size (Units) 15 13 87%
461 Numeric final size (Units) 85 81 95%
462 Numeric final size (MBytes) 0.0 0.0 95%
463 peak memory usage (Units) 1473 1464 99%
464 peak memory usage (MBytes) 0.0 0.0 99%
465 numeric factorization flops 1.30000e+01 6.00000e+00 46%
466 nz in L (incl diagonal) 10 9 90%
467 nz in U (incl diagonal) 10 9 90%
468 nz in L+U (incl diagonal) 15 13 87%
469 largest front (# entries) 9 4 44%
470 largest # rows in front 3 2 67%
471 largest # columns in front 3 2 67%
472
473 initial allocation ratio used: 0.7
474 # of forced updates due to frontal growth: 0
475 nz in L (incl diagonal), if none dropped 9
476 nz in U (incl diagonal), if none dropped 9
477 number of small entries dropped 0
478 nonzeros on diagonal of U: 5
479 min abs. value on diagonal of U: 1.43e-01
480 max abs. value on diagonal of U: 2.19e+00
481 estimate of reciprocal of condition number: 6.52e-02
482 indices in compressed pattern: 2
483 numerical values stored in Numeric object: 9
484 numeric factorization defragmentations: 1
485 numeric factorization reallocations: 1
486 costly numeric factorization reallocations: 0
487 numeric factorization CPU time (sec): 0.00
488 numeric factorization wallclock time (sec): 0.00
489 symbolic + numeric CPU time (sec): 0.00
490 symbolic + numeric wall clock time (sec): 0.00
491
492 solve flops: 1.11000e+02
493 iterative refinement steps taken: 0
494 iterative refinement steps attempted: 0
495 sparse backward error omega1: 5.84e-17
496 sparse backward error omega2: 0.00e+00
497 solve CPU time (sec): 0.00
498 solve wall clock time (sec): 0.00
499
500 total symbolic + numeric + solve flops: 1.17000e+02
501 total symbolic + numeric + solve CPU time: 0.00
502 total symbolic+numeric+solve wall clock time: 0.00
503
504
505 x (solution of A'x=b): dense vector, n = 5.
506 0 : (1.81579)
507 1 : (1.45614)
508 2 : (1.5)
509 3 : (-24.8509)
510 4 : (10.2632)
511 dense vector OK
512
513 maxnorm of residual: 7.10543e-15
514
515
516 changing A (1,4) to zero
517
518 modified A: column-form matrix, n_row 5 n_col 5, nz = 12.
519
520 column 0: start: 0 end: 1 entries: 2
521 row 0 : (2)
522 row 1 : (3)
523
524 column 1: start: 2 end: 4 entries: 3
525 row 0 : (3)
526 row 2 : (-1)
527 row 4 : (4)
528
529 column 2: start: 5 end: 8 entries: 4
530 row 1 : (4)
531 row 2 : (-3)
532 row 3 : (1)
533 row 4 : (2)
534
535 column 3: start: 9 end: 9 entries: 1
536 row 2 : (2)
537
538 column 4: start: 10 end: 11 entries: 2
539 row 1 : (0)
540 row 4 : (1)
541 column-form matrix OK
542
543
544 Numeric factorization of modified A: Numeric object:
545 n_row: 5 n_col: 5
546 relative pivot tolerance used: 0.1
547 relative symmetric pivot tolerance used: 0.001
548 matrix scaled: yes (divided each row by sum abs value in each row)
549 minimum sum (abs (rows of A)): 1.00000e+00
550 maximum sum (abs (rows of A)): 7.00000e+00
551 initial allocation parameter used: 0.7
552 frontal matrix allocation parameter used: 0.5
553 final total size of Numeric object (Units): 79
554 final total size of Numeric object (MBytes): 0.0
555 peak size of variable-size part (Units): 1292
556 peak size of variable-size part (MBytes): 0.0
557 largest actual frontal matrix size: 4
558 memory defragmentations: 1
559 memory reallocations: 1
560 costly memory reallocations: 0
561 entries in compressed pattern (L and U): 2
562 number of nonzeros in L (excl diag): 4
563 number of entries stored in L (excl diag): 2
564 number of nonzeros in U (excl diag): 3
565 number of entries stored in U (excl diag): 1
566 factorization floating-point operations: 4
567 number of nonzeros on diagonal of U: 5
568 min abs. value on diagonal of U: 1.50000e-01
569 max abs. value on diagonal of U: 1.00000e+00
570 reciprocal condition number estimate: 1.50e-01
571
572 Scale factors applied via multiplication
573 Scale factors, Rs: dense vector, n = 5.
574 0 : (0.2)
575 1 : (0.142857)
576 2 : (0.166667)
577 3 : (1)
578 4 : (0.142857)
579 dense vector OK
580
581
582 P: row permutation vector, n = 5.
583 0 : 2
584 1 : 3
585 2 : 1
586 3 : 4
587 4 : 0
588 permutation vector OK
589
590
591 Q: column permutation vector, n = 5.
592 0 : 3
593 1 : 2
594 2 : 0
595 3 : 1
596 4 : 4
597 permutation vector OK
598
599
600 L in Numeric object, in column-oriented compressed-pattern form:
601 Diagonal entries are all equal to 1.0 (not stored)
602
603 column 0: length 0.
604
605 column 1: length 2.
606 row 2 : (0.571429)
607 row 3 : (0.285714)
608
609 column 2: add 1 entries. length 1. Start of Lchain.
610 row 4 : (0.933333)
611
612 column 3: length 1.
613 row 4 : (1.05)
614
615 column 4: length 0. Start of Lchain.
616
617
618 U in Numeric object, in row-oriented compressed-pattern form:
619 Diagonal is stored separately.
620
621 row 4: length 0. End of Uchain.
622
623 row 3: length 1. End of Uchain.
624 col 4 : (0.142857)
625
626 row 2: length 0. End of Uchain.
627
628 row 1: length 0. End of Uchain.
629
630 row 1: length 0.
631
632 row 0: length 2.
633 col 1 : (-0.5)
634 col 3 : (-0.166667)
635
636
637 diagonal of U: dense vector, n = 5.
638 0 : (0.333333)
639 1 : (1)
640 2 : (0.428571)
641 3 : (0.571429)
642 4 : (-0.15)
643 dense vector OK
644
645 Numeric object: OK
646
647
648 UMFPACK V4.4 (Jan. 28, 2005), Info:
649 matrix entry defined as: double
650 Int (generic integer) defined as: int
651 BLAS library used: none. UMFPACK will be slow.
652 MATLAB: no.
653 CPU timer: POSIX times ( ) routine.
654 number of rows in matrix A: 5
655 number of columns in matrix A: 5
656 entries in matrix A: 12
657 memory usage reported in: 8-byte Units
658 size of int: 4 bytes
659 size of long: 4 bytes
660 size of pointer: 4 bytes
661 size of numerical entry: 8 bytes
662
663 strategy used: unsymmetric
664 ordering used: colamd on A
665 modify Q during factorization: yes
666 prefer diagonal pivoting: no
667 pivots with zero Markowitz cost: 2
668 submatrix S after removing zero-cost pivots:
669 number of "dense" rows: 0
670 number of "dense" columns: 0
671 number of empty rows: 0
672 number of empty columns 0
673 submatrix S square and diagonal preserved
674 pattern of square submatrix S:
675 number rows and columns 3
676 symmetry of nonzero pattern: 1.000000
677 nz in S+S' (excl. diagonal): 4
678 nz on diagonal of matrix S: 2
679 fraction of nz on diagonal: 0.666667
680 2-by-2 pivoting to place large entries on diagonal:
681 # of small diagonal entries of S: 1
682 # unmatched: 0
683 symmetry of P2*S: 0.000000
684 nz in P2*S+(P2*S)' (excl. diag.): 6
685 nz on diagonal of P2*S: 3
686 fraction of nz on diag of P2*S: 1.000000
687 symbolic factorization defragmentations: 0
688 symbolic memory usage (Units): 144
689 symbolic memory usage (MBytes): 0.0
690 Symbolic size (Units): 45
691 Symbolic size (MBytes): 0
692 symbolic factorization CPU time (sec): 0.00
693 symbolic factorization wallclock time(sec): 0.00
694
695 matrix scaled: yes (divided each row by sum of abs values in each row)
696 minimum sum (abs (rows of A)): 1.00000e+00
697 maximum sum (abs (rows of A)): 7.00000e+00
698
699 symbolic/numeric factorization: upper bound actual %
700 variable-sized part of Numeric object:
701 initial size (Units) 74 69 93%
702 peak size (Units) 1301 1292 99%
703 final size (Units) 15 12 80%
704 Numeric final size (Units) 85 80 94%
705 Numeric final size (MBytes) 0.0 0.0 94%
706 peak memory usage (Units) 1473 1464 99%
707 peak memory usage (MBytes) 0.0 0.0 99%
708 numeric factorization flops 1.30000e+01 4.00000e+00 31%
709 nz in L (incl diagonal) 10 9 90%
710 nz in U (incl diagonal) 10 8 80%
711 nz in L+U (incl diagonal) 15 12 80%
712 largest front (# entries) 9 4 44%
713 largest # rows in front 3 2 67%
714 largest # columns in front 3 2 67%
715
716 initial allocation ratio used: 0.7
717 # of forced updates due to frontal growth: 0
718 nz in L (incl diagonal), if none dropped 9
719 nz in U (incl diagonal), if none dropped 8
720 number of small entries dropped 0
721 nonzeros on diagonal of U: 5
722 min abs. value on diagonal of U: 1.50e-01
723 max abs. value on diagonal of U: 1.00e+00
724 estimate of reciprocal of condition number: 1.50e-01
725 indices in compressed pattern: 2
726 numerical values stored in Numeric object: 8
727 numeric factorization defragmentations: 1
728 numeric factorization reallocations: 1
729 costly numeric factorization reallocations: 0
730 numeric factorization CPU time (sec): 0.00
731 numeric factorization wallclock time (sec): 0.00
732 symbolic + numeric CPU time (sec): 0.00
733 symbolic + numeric wall clock time (sec): 0.00
734
735 solve flops: 1.17000e+02
736 iterative refinement steps taken: 0
737 iterative refinement steps attempted: 0
738 sparse backward error omega1: 5.92e-17
739 sparse backward error omega2: 0.00e+00
740 solve CPU time (sec): 0.00
741 solve wall clock time (sec): 0.00
742
743 total symbolic + numeric + solve flops: 1.21000e+02
744 total symbolic + numeric + solve CPU time: 0.00
745 total symbolic+numeric+solve wall clock time: 0.00
746
747
748 x (with modified A): dense vector, n = 5.
749 0 : (11)
750 1 : (-4.66667)
751 2 : (3)
752 3 : (0.666667)
753 4 : (31.6667)
754 dense vector OK
755
756 maxnorm of residual: 5.32907e-15
757
758 changing A (0,0) from 2 to 2
759 changing A (1,0) from 3 to 2
760 changing A (0,1) from 3 to 13
761 changing A (2,1) from -1 to 7
762 changing A (4,1) from 4 to 10
763 changing A (1,2) from 4 to 23
764 changing A (2,2) from -3 to 15
765 changing A (3,2) from 1 to 18
766 changing A (4,2) from 2 to 18
767 changing A (2,3) from 2 to 30
768 changing A (1,4) from 0 to 39
769 changing A (4,4) from 1 to 37
770
771 completely modified A (same pattern): column-form matrix, n_row 5 n_col 5, nz = 12.
772
773 column 0: start: 0 end: 1 entries: 2
774 row 0 : (2)
775 row 1 : (2)
776
777 column 1: start: 2 end: 4 entries: 3
778 row 0 : (13)
779 row 2 : (7)
780 row 4 : (10)
781
782 column 2: start: 5 end: 8 entries: 4
783 row 1 : (23)
784 row 2 : (15)
785 row 3 : (18)
786 row 4 : (18)
787
788 column 3: start: 9 end: 9 entries: 1
789 row 2 : (30)
790
791 column 4: start: 10 end: 11 entries: 2
792 row 1 : (39)
793 row 4 : (37)
794 column-form matrix OK
795
796
797 Saving symbolic object:
798
799 Freeing symbolic object:
800
801 Loading symbolic object:
802
803 Done loading symbolic object
804
805 Numeric factorization of completely modified A: Numeric object:
806 n_row: 5 n_col: 5
807 relative pivot tolerance used: 0.1
808 relative symmetric pivot tolerance used: 0.001
809 matrix scaled: yes (divided each row by sum abs value in each row)
810 minimum sum (abs (rows of A)): 1.50000e+01
811 maximum sum (abs (rows of A)): 6.50000e+01
812 initial allocation parameter used: 0.7
813 frontal matrix allocation parameter used: 0.5
814 final total size of Numeric object (Units): 80
815 final total size of Numeric object (MBytes): 0.0
816 peak size of variable-size part (Units): 1292
817 peak size of variable-size part (MBytes): 0.0
818 largest actual frontal matrix size: 4
819 memory defragmentations: 1
820 memory reallocations: 1
821 costly memory reallocations: 0
822 entries in compressed pattern (L and U): 2
823 number of nonzeros in L (excl diag): 4
824 number of entries stored in L (excl diag): 2
825 number of nonzeros in U (excl diag): 4
826 number of entries stored in U (excl diag): 2
827 factorization floating-point operations: 6
828 number of nonzeros on diagonal of U: 5
829 min abs. value on diagonal of U: 1.33333e-01
830 max abs. value on diagonal of U: 1.00000e+00
831 reciprocal condition number estimate: 1.33e-01
832
833 Scale factors applied via multiplication
834 Scale factors, Rs: dense vector, n = 5.
835 0 : (0.0666667)
836 1 : (0.015625)
837 2 : (0.0192308)
838 3 : (0.0555556)
839 4 : (0.0153846)
840 dense vector OK
841
842
843 P: row permutation vector, n = 5.
844 0 : 2
845 1 : 3
846 2 : 0
847 3 : 4
848 4 : 1
849 permutation vector OK
850
851
852 Q: column permutation vector, n = 5.
853 0 : 3
854 1 : 2
855 2 : 0
856 3 : 4
857 4 : 1
858 permutation vector OK
859
860
861 L in Numeric object, in column-oriented compressed-pattern form:
862 Diagonal entries are all equal to 1.0 (not stored)
863
864 column 0: length 0.
865
866 column 1: length 2.
867 row 4 : (0.359375)
868 row 3 : (0.276923)
869
870 column 2: add 1 entries. length 1. Start of Lchain.
871 row 4 : (0.234375)
872
873 column 3: length 1.
874 row 4 : (1.07052)
875
876 column 4: length 0. Start of Lchain.
877
878
879 U in Numeric object, in row-oriented compressed-pattern form:
880 Diagonal is stored separately.
881
882 row 4: length 0. End of Uchain.
883
884 row 3: length 1. End of Uchain.
885 col 4 : (0.153846)
886
887 row 2: length 1.
888 col 4 : (0.866667)
889
890 row 1: length 0. End of Uchain.
891
892 row 1: length 0.
893
894 row 0: length 2.
895 col 1 : (0.288462)
896 col 4 : (0.134615)
897
898
899 diagonal of U: dense vector, n = 5.
900 0 : (0.576923)
901 1 : (1)
902 2 : (0.133333)
903 3 : (0.569231)
904 4 : (-0.367821)
905 dense vector OK
906
907 Numeric object: OK
908
909
910 UMFPACK V4.4 (Jan. 28, 2005), Info:
911 matrix entry defined as: double
912 Int (generic integer) defined as: int
913 BLAS library used: none. UMFPACK will be slow.
914 MATLAB: no.
915 CPU timer: POSIX times ( ) routine.
916 number of rows in matrix A: 5
917 number of columns in matrix A: 5
918 entries in matrix A: 12
919 memory usage reported in: 8-byte Units
920 size of int: 4 bytes
921 size of long: 4 bytes
922 size of pointer: 4 bytes
923 size of numerical entry: 8 bytes
924
925 strategy used: unsymmetric
926 ordering used: colamd on A
927 modify Q during factorization: yes
928 prefer diagonal pivoting: no
929 pivots with zero Markowitz cost: 2
930 submatrix S after removing zero-cost pivots:
931 number of "dense" rows: 0
932 number of "dense" columns: 0
933 number of empty rows: 0
934 number of empty columns 0
935 submatrix S square and diagonal preserved
936 pattern of square submatrix S:
937 number rows and columns 3
938 symmetry of nonzero pattern: 1.000000
939 nz in S+S' (excl. diagonal): 4
940 nz on diagonal of matrix S: 2
941 fraction of nz on diagonal: 0.666667
942 2-by-2 pivoting to place large entries on diagonal:
943 # of small diagonal entries of S: 1
944 # unmatched: 0
945 symmetry of P2*S: 0.000000
946 nz in P2*S+(P2*S)' (excl. diag.): 6
947 nz on diagonal of P2*S: 3
948 fraction of nz on diag of P2*S: 1.000000
949 symbolic factorization defragmentations: 0
950 symbolic memory usage (Units): 144
951 symbolic memory usage (MBytes): 0.0
952 Symbolic size (Units): 45
953 Symbolic size (MBytes): 0
954 symbolic factorization CPU time (sec): 0.00
955 symbolic factorization wallclock time(sec): 0.00
956
957 matrix scaled: yes (divided each row by sum of abs values in each row)
958 minimum sum (abs (rows of A)): 1.50000e+01
959 maximum sum (abs (rows of A)): 6.50000e+01
960
961 symbolic/numeric factorization: upper bound actual %
962 variable-sized part of Numeric object:
963 initial size (Units) 74 69 93%
964 peak size (Units) 1301 1292 99%
965 final size (Units) 15 13 87%
966 Numeric final size (Units) 85 81 95%
967 Numeric final size (MBytes) 0.0 0.0 95%
968 peak memory usage (Units) 1473 1464 99%
969 peak memory usage (MBytes) 0.0 0.0 99%
970 numeric factorization flops 1.30000e+01 6.00000e+00 46%
971 nz in L (incl diagonal) 10 9 90%
972 nz in U (incl diagonal) 10 9 90%
973 nz in L+U (incl diagonal) 15 13 87%
974 largest front (# entries) 9 4 44%
975 largest # rows in front 3 2 67%
976 largest # columns in front 3 2 67%
977
978 initial allocation ratio used: 0.7
979 # of forced updates due to frontal growth: 0
980 nz in L (incl diagonal), if none dropped 9
981 nz in U (incl diagonal), if none dropped 9
982 number of small entries dropped 0
983 nonzeros on diagonal of U: 5
984 min abs. value on diagonal of U: 1.33e-01
985 max abs. value on diagonal of U: 1.00e+00
986 estimate of reciprocal of condition number: 1.33e-01
987 indices in compressed pattern: 2
988 numerical values stored in Numeric object: 9
989 numeric factorization defragmentations: 1
990 numeric factorization reallocations: 1
991 costly numeric factorization reallocations: 0
992 numeric factorization CPU time (sec): 0.00
993 numeric factorization wallclock time (sec): 0.00
994 symbolic + numeric CPU time (sec): 0.00
995 symbolic + numeric wall clock time (sec): 0.00
996
997 solve flops: 1.19000e+02
998 iterative refinement steps taken: 0
999 iterative refinement steps attempted: 0
1000 sparse backward error omega1: 3.70e-17
1001 sparse backward error omega2: 0.00e+00
1002 solve CPU time (sec): 0.00
1003 solve wall clock time (sec): 0.00
1004
1005 total symbolic + numeric + solve flops: 1.25000e+02
1006 total symbolic + numeric + solve CPU time: 0.00
1007 total symbolic+numeric+solve wall clock time: 0.00
1008
1009
1010 x (with completely modified A): dense vector, n = 5.
1011 0 : (8.50124)
1012 1 : (-0.692499)
1013 2 : (0.166667)
1014 3 : (-0.0217502)
1015 4 : (0.619594)
1016 dense vector OK
1017
1018 maxnorm of residual: 3.33067e-15
1019
1020
1021 C (transpose of A): column-form matrix, n_row 5 n_col 5, nz = 12.
1022
1023 column 0: start: 0 end: 1 entries: 2
1024 row 0 : (2)
1025 row 1 : (13)
1026
1027 column 1: start: 2 end: 4 entries: 3
1028 row 0 : (2)
1029 row 2 : (23)
1030 row 4 : (39)
1031
1032 column 2: start: 5 end: 7 entries: 3
1033 row 1 : (7)
1034 row 2 : (15)
1035 row 3 : (30)
1036
1037 column 3: start: 8 end: 8 entries: 1
1038 row 2 : (18)
1039
1040 column 4: start: 9 end: 11 entries: 3
1041 row 1 : (10)
1042 row 2 : (18)
1043 row 4 : (37)
1044 column-form matrix OK
1045
1046
1047 Symbolic factorization of C: Symbolic object:
1048 matrix to be factorized:
1049 n_row: 5 n_col: 5
1050 number of entries: 12
1051 block size used for dense matrix kernels: 32
1052 strategy used: unsymmetric
1053 ordering used: colamd on A
1054
1055 performn column etree postorder: yes
1056 prefer diagonal pivoting (attempt P=Q): no
1057 variable-size part of Numeric object:
1058 minimum initial size (Units): 75 (MBytes): 0.0
1059 estimated peak size (Units): 1302 (MBytes): 0.0
1060 estimated final size (Units): 16 (MBytes): 0.0
1061 symbolic factorization memory usage (Units): 144 (MBytes): 0.0
1062 frontal matrices / supercolumns:
1063 number of frontal chains: 1
1064 number of frontal matrices: 1
1065 largest frontal matrix row dimension: 3
1066 largest frontal matrix column dimension: 3
1067
1068 Frontal chain: 0. Frontal matrices 0 to 0
1069 Largest frontal matrix in Frontal chain: 3-by-3
1070 Front: 0 pivot cols: 3 (pivot columns 0 to 2)
1071 pivot row candidates: 2 to 4
1072 leftmost descendant: 0
1073 1st new candidate row : 2
1074 parent: (none)
1075
1076 Initial column permutation, Q1: permutation vector, n = 5.
1077 0 : 3
1078 1 : 2
1079 2 : 0
1080 3 : 4
1081 4 : 1
1082 permutation vector OK
1083
1084
1085 Initial row permutation, P1: permutation vector, n = 5.
1086 0 : 2
1087 1 : 3
1088 2 : 0
1089 3 : 1
1090 4 : 4
1091 permutation vector OK
1092
1093 Symbolic object: OK
1094
1095
1096 Get the contents of the Symbolic object for C:
1097 (compare with umfpack_di_report_symbolic output, above)
1098 From the Symbolic object, C is of dimension 5-by-5
1099 with nz = 12, number of fronts = 1,
1100 number of frontal matrix chains = 1
1101
1102 Pivot columns in each front, and parent of each front:
1103 Front 0: parent front: -1 number of pivot cols: 3
1104 0-th pivot column is column 3 in original matrix
1105 1-th pivot column is column 2 in original matrix
1106 2-th pivot column is column 0 in original matrix
1107
1108 Note that the column ordering, above, will be refined
1109 in the numeric factorization below. The assignment of pivot
1110 columns to frontal matrices will always remain unchanged.
1111
1112 Total number of pivot columns in frontal matrices: 3
1113
1114 Frontal matrix chains:
1115 Frontal matrices 0 to 0 are factorized in a single
1116 working array of size 3-by-3
1117
1118 Numeric factorization of C: Numeric object:
1119 n_row: 5 n_col: 5
1120 relative pivot tolerance used: 0.1
1121 relative symmetric pivot tolerance used: 0.001
1122 matrix scaled: yes (divided each row by sum abs value in each row)
1123 minimum sum (abs (rows of A)): 4.00000e+00
1124 maximum sum (abs (rows of A)): 7.60000e+01
1125 initial allocation parameter used: 0.7
1126 frontal matrix allocation parameter used: 0.5
1127 final total size of Numeric object (Units): 81
1128 final total size of Numeric object (MBytes): 0.0
1129 peak size of variable-size part (Units): 1293
1130 peak size of variable-size part (MBytes): 0.0
1131 largest actual frontal matrix size: 4
1132 memory defragmentations: 1
1133 memory reallocations: 1
1134 costly memory reallocations: 0
1135 entries in compressed pattern (L and U): 2
1136 number of nonzeros in L (excl diag): 3
1137 number of entries stored in L (excl diag): 2
1138 number of nonzeros in U (excl diag): 5
1139 number of entries stored in U (excl diag): 2
1140 factorization floating-point operations: 6
1141 number of nonzeros on diagonal of U: 5
1142 min abs. value on diagonal of U: 2.43243e-01
1143 max abs. value on diagonal of U: 1.00000e+00
1144 reciprocal condition number estimate: 2.43e-01
1145
1146 Scale factors applied via multiplication
1147 Scale factors, Rs: dense vector, n = 5.
1148 0 : (0.25)
1149 1 : (0.0333333)
1150 2 : (0.0135135)
1151 3 : (0.0333333)
1152 4 : (0.0131579)
1153 dense vector OK
1154
1155
1156 P: row permutation vector, n = 5.
1157 0 : 2
1158 1 : 3
1159 2 : 0
1160 3 : 4
1161 4 : 1
1162 permutation vector OK
1163
1164
1165 Q: column permutation vector, n = 5.
1166 0 : 3
1167 1 : 2
1168 2 : 0
1169 3 : 4
1170 4 : 1
1171 permutation vector OK
1172
1173
1174 L in Numeric object, in column-oriented compressed-pattern form:
1175 Diagonal entries are all equal to 1.0 (not stored)
1176
1177 column 0: length 0.
1178
1179 column 1: length 1.
1180 row 4 : (0.233333)
1181
1182 column 2: add 1 entries. length 1. Start of Lchain.
1183 row 4 : (0.866667)
1184
1185 column 3: length 1.
1186 row 4 : (0.684685)
1187
1188 column 4: length 0. Start of Lchain.
1189
1190
1191 U in Numeric object, in row-oriented compressed-pattern form:
1192 Diagonal is stored separately.
1193
1194 row 4: length 0. End of Uchain.
1195
1196 row 3: length 1. End of Uchain.
1197 col 4 : (0.513158)
1198
1199 row 2: length 1.
1200 col 4 : (0.5)
1201
1202 row 1: length 0. End of Uchain.
1203
1204 row 1: length 0.
1205
1206 row 0: length 3.
1207 col 1 : (0.202703)
1208 col 3 : (0.243243)
1209 col 4 : (0.310811)
1210
1211
1212 diagonal of U: dense vector, n = 5.
1213 0 : (0.243243)
1214 1 : (1)
1215 2 : (0.5)
1216 3 : (0.486842)
1217 4 : (-0.784685)
1218 dense vector OK
1219
1220 Numeric object: OK
1221
1222
1223 L (lower triangular factor of C): row-form matrix, n_row 5 n_col 5, nz = 8.
1224
1225 row 0: start: 0 end: 0 entries: 1
1226 column 0 : (1)
1227
1228 row 1: start: 1 end: 1 entries: 1
1229 column 1 : (1)
1230
1231 row 2: start: 2 end: 2 entries: 1
1232 column 2 : (1)
1233
1234 row 3: start: 3 end: 3 entries: 1
1235 column 3 : (1)
1236
1237 row 4: start: 4 end: 7 entries: 4
1238 column 1 : (0.233333)
1239 column 2 : (0.866667)
1240 column 3 : (0.684685)
1241 column 4 : (1)
1242 row-form matrix OK
1243
1244
1245 U (upper triangular factor of C): column-form matrix, n_row 5 n_col 5, nz = 10.
1246
1247 column 0: start: 0 end: 0 entries: 1
1248 row 0 : (0.243243)
1249
1250 column 1: start: 1 end: 2 entries: 2
1251 row 0 : (0.202703)
1252 row 1 : (1)
1253
1254 column 2: start: 3 end: 3 entries: 1
1255 row 2 : (0.5)
1256
1257 column 3: start: 4 end: 5 entries: 2
1258 row 0 : (0.243243)
1259 row 3 : (0.486842)
1260
1261 column 4: start: 6 end: 9 entries: 4
1262 row 0 : (0.310811)
1263 row 2 : (0.5)
1264 row 3 : (0.513158)
1265 row 4 : (-0.784685)
1266 column-form matrix OK
1267
1268
1269 P: permutation vector, n = 5.
1270 0 : 2
1271 1 : 3
1272 2 : 0
1273 3 : 4
1274 4 : 1
1275 permutation vector OK
1276
1277
1278 Q: permutation vector, n = 5.
1279 0 : 3
1280 1 : 2
1281 2 : 0
1282 3 : 4
1283 4 : 1
1284 permutation vector OK
1285
1286
1287 Scale factors: row i of A is to be multiplied by the ith scale factor
1288 0: 0.25
1289 1: 0.0333333
1290 2: 0.0135135
1291 3: 0.0333333
1292 4: 0.0131579
1293
1294 Converting L to triplet form, and printing it:
1295
1296 L, in triplet form: triplet-form matrix, n_row = 5, n_col = 5 nz = 8.
1297 0 : 0 0 (1)
1298 1 : 1 1 (1)
1299 2 : 2 2 (1)
1300 3 : 3 3 (1)
1301 4 : 4 1 (0.233333)
1302 5 : 4 2 (0.866667)
1303 6 : 4 3 (0.684685)
1304 7 : 4 4 (1)
1305 triplet-form matrix OK
1306
1307
1308 Saving numeric object:
1309
1310 Freeing numeric object:
1311
1312 Loading numeric object:
1313
1314 Done loading numeric object
1315
1316 UMFPACK V4.4 (Jan. 28, 2005), Info:
1317 matrix entry defined as: double
1318 Int (generic integer) defined as: int
1319 BLAS library used: none. UMFPACK will be slow.
1320 MATLAB: no.
1321 CPU timer: POSIX times ( ) routine.
1322 number of rows in matrix A: 5
1323 number of columns in matrix A: 5
1324 entries in matrix A: 12
1325 memory usage reported in: 8-byte Units
1326 size of int: 4 bytes
1327 size of long: 4 bytes
1328 size of pointer: 4 bytes
1329 size of numerical entry: 8 bytes
1330
1331 strategy used: unsymmetric
1332 ordering used: colamd on A
1333 modify Q during factorization: yes
1334 prefer diagonal pivoting: no
1335 pivots with zero Markowitz cost: 2
1336 submatrix S after removing zero-cost pivots:
1337 number of "dense" rows: 0
1338 number of "dense" columns: 0
1339 number of empty rows: 0
1340 number of empty columns 0
1341 submatrix S square and diagonal preserved
1342 pattern of square submatrix S:
1343 number rows and columns 3
1344 symmetry of nonzero pattern: 1.000000
1345 nz in S+S' (excl. diagonal): 4
1346 nz on diagonal of matrix S: 2
1347 fraction of nz on diagonal: 0.666667
1348 2-by-2 pivoting to place large entries on diagonal:
1349 # of small diagonal entries of S: 1
1350 # unmatched: 0
1351 symmetry of P2*S: 0.000000
1352 nz in P2*S+(P2*S)' (excl. diag.): 6
1353 nz on diagonal of P2*S: 3
1354 fraction of nz on diag of P2*S: 1.000000
1355 symbolic factorization defragmentations: 0
1356 symbolic memory usage (Units): 144
1357 symbolic memory usage (MBytes): 0.0
1358 Symbolic size (Units): 45
1359 Symbolic size (MBytes): 0
1360 symbolic factorization CPU time (sec): 0.00
1361 symbolic factorization wallclock time(sec): 0.00
1362
1363 matrix scaled: yes (divided each row by sum of abs values in each row)
1364 minimum sum (abs (rows of A)): 4.00000e+00
1365 maximum sum (abs (rows of A)): 7.60000e+01
1366
1367 symbolic/numeric factorization: upper bound actual %
1368 variable-sized part of Numeric object:
1369 initial size (Units) 75 70 93%
1370 peak size (Units) 1302 1293 99%
1371 final size (Units) 16 14 88%
1372 Numeric final size (Units) 86 82 95%
1373 Numeric final size (MBytes) 0.0 0.0 95%
1374 peak memory usage (Units) 1474 1465 99%
1375 peak memory usage (MBytes) 0.0 0.0 99%
1376 numeric factorization flops 1.30000e+01 6.00000e+00 46%
1377 nz in L (incl diagonal) 9 8 89%
1378 nz in U (incl diagonal) 11 10 91%
1379 nz in L+U (incl diagonal) 15 13 87%
1380 largest front (# entries) 9 4 44%
1381 largest # rows in front 3 2 67%
1382 largest # columns in front 3 2 67%
1383
1384 initial allocation ratio used: 0.7
1385 # of forced updates due to frontal growth: 0
1386 nz in L (incl diagonal), if none dropped 8
1387 nz in U (incl diagonal), if none dropped 10
1388 number of small entries dropped 0
1389 nonzeros on diagonal of U: 5
1390 min abs. value on diagonal of U: 2.43e-01
1391 max abs. value on diagonal of U: 1.00e+00
1392 estimate of reciprocal of condition number: 2.43e-01
1393 indices in compressed pattern: 2
1394 numerical values stored in Numeric object: 9
1395 numeric factorization defragmentations: 1
1396 numeric factorization reallocations: 1
1397 costly numeric factorization reallocations: 0
1398 numeric factorization CPU time (sec): 0.00
1399 numeric factorization wallclock time (sec): 0.00
1400 symbolic + numeric CPU time (sec): 0.00
1401 symbolic + numeric wall clock time (sec): 0.00
1402
1403 solve flops: 1.11000e+02
1404 iterative refinement steps taken: 0
1405 iterative refinement steps attempted: 0
1406 sparse backward error omega1: 7.60e-17
1407 sparse backward error omega2: 0.00e+00
1408 solve CPU time (sec): 0.00
1409 solve wall clock time (sec): 0.00
1410
1411 total symbolic + numeric + solve flops: 1.17000e+02
1412 total symbolic + numeric + solve CPU time: 0.00
1413 total symbolic+numeric+solve wall clock time: 0.00
1414
1415
1416 x (solution of C'x=b): dense vector, n = 5.
1417 0 : (8.50124)
1418 1 : (-0.692499)
1419 2 : (0.166667)
1420 3 : (-0.0217502)
1421 4 : (0.619594)
1422 dense vector OK
1423
1424 maxnorm of residual: 4.77396e-15
1425
1426
1427 Solving C'x=b again, using umfpack_di_wsolve instead:
1428
1429 UMFPACK V4.4 (Jan. 28, 2005), Info:
1430 matrix entry defined as: double
1431 Int (generic integer) defined as: int
1432 BLAS library used: none. UMFPACK will be slow.
1433 MATLAB: no.
1434 CPU timer: POSIX times ( ) routine.
1435 number of rows in matrix A: 5
1436 number of columns in matrix A: 5
1437 entries in matrix A: 12
1438 memory usage reported in: 8-byte Units
1439 size of int: 4 bytes
1440 size of long: 4 bytes
1441 size of pointer: 4 bytes
1442 size of numerical entry: 8 bytes
1443
1444 strategy used: unsymmetric
1445 ordering used: colamd on A
1446 modify Q during factorization: yes
1447 prefer diagonal pivoting: no
1448 pivots with zero Markowitz cost: 2
1449 submatrix S after removing zero-cost pivots:
1450 number of "dense" rows: 0
1451 number of "dense" columns: 0
1452 number of empty rows: 0
1453 number of empty columns 0
1454 submatrix S square and diagonal preserved
1455 pattern of square submatrix S:
1456 number rows and columns 3
1457 symmetry of nonzero pattern: 1.000000
1458 nz in S+S' (excl. diagonal): 4
1459 nz on diagonal of matrix S: 2
1460 fraction of nz on diagonal: 0.666667
1461 2-by-2 pivoting to place large entries on diagonal:
1462 # of small diagonal entries of S: 1
1463 # unmatched: 0
1464 symmetry of P2*S: 0.000000
1465 nz in P2*S+(P2*S)' (excl. diag.): 6
1466 nz on diagonal of P2*S: 3
1467 fraction of nz on diag of P2*S: 1.000000
1468 symbolic factorization defragmentations: 0
1469 symbolic memory usage (Units): 144
1470 symbolic memory usage (MBytes): 0.0
1471 Symbolic size (Units): 45
1472 Symbolic size (MBytes): 0
1473 symbolic factorization CPU time (sec): 0.00
1474 symbolic factorization wallclock time(sec): 0.00
1475
1476 matrix scaled: yes (divided each row by sum of abs values in each row)
1477 minimum sum (abs (rows of A)): 4.00000e+00
1478 maximum sum (abs (rows of A)): 7.60000e+01
1479
1480 symbolic/numeric factorization: upper bound actual %
1481 variable-sized part of Numeric object:
1482 initial size (Units) 75 70 93%
1483 peak size (Units) 1302 1293 99%
1484 final size (Units) 16 14 88%
1485 Numeric final size (Units) 86 82 95%
1486 Numeric final size (MBytes) 0.0 0.0 95%
1487 peak memory usage (Units) 1474 1465 99%
1488 peak memory usage (MBytes) 0.0 0.0 99%
1489 numeric factorization flops 1.30000e+01 6.00000e+00 46%
1490 nz in L (incl diagonal) 9 8 89%
1491 nz in U (incl diagonal) 11 10 91%
1492 nz in L+U (incl diagonal) 15 13 87%
1493 largest front (# entries) 9 4 44%
1494 largest # rows in front 3 2 67%
1495 largest # columns in front 3 2 67%
1496
1497 initial allocation ratio used: 0.7
1498 # of forced updates due to frontal growth: 0
1499 nz in L (incl diagonal), if none dropped 8
1500 nz in U (incl diagonal), if none dropped 10
1501 number of small entries dropped 0
1502 nonzeros on diagonal of U: 5
1503 min abs. value on diagonal of U: 2.43e-01
1504 max abs. value on diagonal of U: 1.00e+00
1505 estimate of reciprocal of condition number: 2.43e-01
1506 indices in compressed pattern: 2
1507 numerical values stored in Numeric object: 9
1508 numeric factorization defragmentations: 1
1509 numeric factorization reallocations: 1
1510 costly numeric factorization reallocations: 0
1511 numeric factorization CPU time (sec): 0.00
1512 numeric factorization wallclock time (sec): 0.00
1513 symbolic + numeric CPU time (sec): 0.00
1514 symbolic + numeric wall clock time (sec): 0.00
1515
1516 solve flops: 1.11000e+02
1517 iterative refinement steps taken: 0
1518 iterative refinement steps attempted: 0
1519 sparse backward error omega1: 7.60e-17
1520 sparse backward error omega2: 0.00e+00
1521 solve CPU time (sec): 0.00
1522 solve wall clock time (sec): 0.00
1523
1524 total symbolic + numeric + solve flops: 1.17000e+02
1525 total symbolic + numeric + solve CPU time: 0.00
1526 total symbolic+numeric+solve wall clock time: 0.00
1527
1528
1529 x (solution of C'x=b): dense vector, n = 5.
1530 0 : (8.50124)
1531 1 : (-0.692499)
1532 2 : (0.166667)
1533 3 : (-0.0217502)
1534 4 : (0.619594)
1535 dense vector OK
1536
1537 maxnorm of residual: 4.77396e-15
1538
1539
1540 umfpack_di_demo complete.
1541 Total time: 0.00 seconds (CPU time), 0.00 seconds (wallclock time)