Mercurial > octave-nkf
comparison liboctave/UMFPACK/UMFPACK/Demo/umfpack_dl_demo.out @ 5164:57077d0ddc8e
[project @ 2005-02-25 19:55:24 by jwe]
author | jwe |
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date | Fri, 25 Feb 2005 19:55:28 +0000 |
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1 | |
2 UMFPACK V4.4 (Jan. 28, 2005) demo: _dl_ 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: long | |
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: long | |
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: long | |
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: long | |
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: long | |
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_dl_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: long | |
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_dl_wsolve instead: | |
1428 | |
1429 UMFPACK V4.4 (Jan. 28, 2005), Info: | |
1430 matrix entry defined as: double | |
1431 Int (generic integer) defined as: long | |
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_dl_demo complete. | |
1541 Total time: 0.00 seconds (CPU time), 0.00 seconds (wallclock time) |