|
5164
|
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)
|
