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test_spqr_coverage
Exhaustive test of spqr_rank functions
SJget from the SJSU Singular Matrix Database and some of
its matrices from the database need to be installed
to run the tests and demos. This requires about
2.5 Mbytes of disk space and an internet connection.
The current MATLAB path will be augmented to include a path
to access these matrices and the new path will be saved.
downloading http://www.math.sjsu.edu/singular/matrices/mat/SJ_Index.mat
to /Users/davis/sparse/MyPapers/Foster/spqr_rank/SJget/mat/SJ_Index.mat
SJSU Singular matrix collection index: 18-Apr-2009 20:02:50
Legend:
num. rank: numerical rank
struc. rank: structural rank
type: real
complex
binary: all entries are 0 or 1
ID Group/Name nrows-by- ncols num. rank struct. rank type
1 Pajek/CSphd 1882-by- 1882 705 706 binary
2 Pajek/EPA 4772-by- 4772 951 986 binary
3 Pajek/Erdos971 472-by- 472 413 414 binary
4 Pajek/Erdos981 485-by- 485 427 427 binary
5 Pajek/Erdos991 492-by- 492 435 436 binary
6 Gset/G48 3000-by- 3000 2982 3000 binary
7 Gset/G49 3000-by- 3000 2982 3000 binary
8 Gset/G50 3000-by- 3000 2991 3000 binary
9 Gset/G55 5000-by- 5000 4966 4966 binary
10 Gset/G56 5000-by- 5000 4966 4966 real
11 Pajek/GD00_a 352-by- 352 178 179 binary
12 Pajek/GD00_c 638-by- 638 300 302 real
13 Pajek/GD01_a 311-by- 311 155 158 real
14 Pajek/GD01_b 18-by- 18 17 17 binary
15 Pajek/GD01_c 33-by- 33 25 27 real
16 Pajek/GD02_a 23-by- 23 18 19 binary
17 Pajek/GD02_b 80-by- 80 77 77 binary
18 Pajek/GD06_Java 1538-by- 1538 744 759 binary
19 Pajek/GD06_theory 101-by- 101 20 20 binary
20 Pajek/GD95_a 36-by- 36 31 32 binary
21 Pajek/GD95_b 73-by- 73 34 34 binary
22 Pajek/GD96_a 1096-by- 1096 827 827 real
23 Pajek/GD96_b 111-by- 111 19 20 binary
24 Pajek/GD96_c 65-by- 65 63 64 binary
25 Pajek/GD96_d 180-by- 180 73 73 binary
ID Group/Name nrows-by- ncols num. rank struct. rank type
26 Pajek/GD97_a 84-by- 84 80 84 binary
27 Pajek/GD97_b 47-by- 47 44 44 real
28 Pajek/GD97_c 452-by- 452 63 63 real
29 Pajek/GD98_a 38-by- 38 14 14 binary
30 Pajek/GD98_b 121-by- 121 87 87 binary
31 Pajek/GD98_c 112-by- 112 100 112 binary
32 Pajek/GD99_b 64-by- 64 45 64 real
33 Pajek/GD99_c 105-by- 105 64 64 binary
34 Pajek/GlossGT 72-by- 72 35 35 binary
35 MathWorks/Harvard500 500-by- 500 170 233 binary
36 Pajek/Kohonen 4470-by- 4470 1652 1658 binary
37 Barabasi/NotreDame_yeast 2114-by- 2114 1263 1273 binary
38 Pajek/ODLIS 2909-by- 2909 1959 1961 real
39 Pajek/Ragusa16 24-by- 24 18 18 real
40 Pajek/Ragusa18 23-by- 23 15 15 real
41 Pajek/Roget 1022-by- 1022 984 986 binary
42 Pajek/Sandi_authors 86-by- 86 72 72 real
43 Pajek/SciMet 3084-by- 3084 1569 1573 real
44 Pajek/SmaGri 1059-by- 1059 511 513 real
45 Pajek/SmallW 396-by- 396 92 93 real
46 Pajek/Tina_AskCal 11-by- 11 9 9 binary
47 Pajek/Tina_DisCal 11-by- 11 10 10 binary
48 Pajek/Tina_DisCog 11-by- 11 10 11 binary
49 Pajek/USAir97 332-by- 332 281 281 real
50 Pajek/USpowerGrid 4941-by- 4941 4348 4366 binary
ID Group/Name nrows-by- ncols num. rank struct. rank type
51 Sandia/adder_dcop_02 1813-by- 1813 1790 1813 real
52 HB/ash292 292-by- 292 289 292 binary
53 Grund/b_dyn 1089-by- 1089 1028 1089 real
54 Grund/bayer05 3268-by- 3268 1666 3268 real
55 Grund/bayer06 3008-by- 3008 1710 3008 real
56 Grund/bayer07 3268-by- 3268 1666 3268 real
57 Grund/bayer08 3008-by- 3008 2563 3008 real
58 Grund/bayer09 3083-by- 3083 2667 3083 real
59 HB/bcspwr02 49-by- 49 48 49 binary
60 HB/bcspwr04 274-by- 274 262 274 binary
61 HB/bcspwr05 443-by- 443 437 443 binary
62 HB/bcspwr06 1454-by- 1454 1446 1454 binary
63 HB/bcspwr07 1612-by- 1612 1601 1612 binary
64 HB/bcspwr08 1624-by- 1624 1613 1624 binary
65 HB/bcspwr09 1723-by- 1723 1712 1723 binary
66 HB/bcsstm01 48-by- 48 24 24 real
67 HB/bcsstm03 112-by- 112 72 72 real
68 HB/bcsstm04 132-by- 132 66 66 real
69 HB/bcsstm13 2003-by- 2003 1241 1241 real
70 HB/can_1054 1054-by- 1054 1031 1054 binary
71 HB/can_1072 1072-by- 1072 1050 1072 binary
72 HB/can_144 144-by- 144 96 144 binary
73 HB/can_187 187-by- 187 184 187 binary
74 HB/can_229 229-by- 229 200 229 binary
75 HB/can_256 256-by- 256 250 256 binary
ID Group/Name nrows-by- ncols num. rank struct. rank type
76 HB/can_268 268-by- 268 261 268 binary
77 HB/can_292 292-by- 292 272 292 binary
78 HB/can_445 445-by- 445 443 445 binary
79 HB/can_61 61-by- 61 49 61 binary
80 HB/can_634 634-by- 634 586 634 binary
81 HB/can_715 715-by- 715 702 715 binary
82 HB/cegb2802 2802-by- 2802 289 2694 binary
83 HB/cegb2919 2919-by- 2919 444 2859 binary
84 HB/cegb3024 3024-by- 3024 1411 2996 binary
85 HB/cegb3306 3306-by- 3306 537 3222 binary
86 Brethour/coater1 1348-by- 1348 1330 1331 real
87 Bai/cryg2500 2500-by- 2500 2499 2500 real
88 Boeing/crystk01 4875-by- 4875 4869 4875 real
89 HB/curtis54 54-by- 54 50 54 binary
90 Bai/dwg961a 961-by- 961 705 705 complex
91 HB/dwt_1005 1005-by- 1005 995 1005 binary
92 HB/dwt_1007 1007-by- 1007 1000 1007 binary
93 HB/dwt_1242 1242-by- 1242 1178 1242 binary
94 HB/dwt_162 162-by- 162 144 162 binary
95 HB/dwt_193 193-by- 193 136 193 binary
96 HB/dwt_198 198-by- 198 192 198 binary
97 HB/dwt_209 209-by- 209 208 209 binary
98 HB/dwt_221 221-by- 221 220 221 binary
99 HB/dwt_245 245-by- 245 239 245 binary
100 HB/dwt_2680 2680-by- 2680 2640 2680 binary
ID Group/Name nrows-by- ncols num. rank struct. rank type
101 HB/dwt_307 307-by- 307 288 307 binary
102 HB/dwt_346 346-by- 346 341 346 binary
103 HB/dwt_361 361-by- 361 358 361 binary
104 HB/dwt_419 419-by- 419 370 419 binary
105 HB/dwt_492 492-by- 492 488 492 binary
106 HB/dwt_503 503-by- 503 499 503 binary
107 HB/dwt_512 512-by- 512 477 512 binary
108 HB/dwt_592 592-by- 592 580 592 binary
109 HB/dwt_607 607-by- 607 547 607 binary
110 HB/dwt_72 72-by- 72 70 72 binary
111 HB/dwt_758 758-by- 758 700 758 binary
112 HB/dwt_869 869-by- 869 845 869 binary
113 HB/dwt_878 878-by- 878 850 878 binary
114 HB/dwt_918 918-by- 918 891 918 binary
115 HB/dwt_992 992-by- 992 496 992 binary
116 HB/eris1176 1176-by- 1176 774 1176 binary
117 FIDAP/ex12 3973-by- 3973 3972 3973 real
118 FIDAP/ex13 2568-by- 2568 1434 2568 real
119 FIDAP/ex14 3251-by- 3251 2925 3251 real
120 FIDAP/ex26 2163-by- 2163 2162 2163 real
121 FIDAP/ex32 1159-by- 1159 1158 1159 real
122 FIDAP/ex6 1651-by- 1651 1650 1651 real
123 Pajek/football 35-by- 35 19 19 real
124 Sandia/fpga_dcop_01 1220-by- 1220 1219 1220 real
125 Sandia/fpga_dcop_02 1220-by- 1220 1219 1220 real
ID Group/Name nrows-by- ncols num. rank struct. rank type
126 Sandia/fpga_dcop_04 1220-by- 1220 1209 1220 real
127 Sandia/fpga_dcop_07 1220-by- 1220 1210 1220 real
128 HB/fs_760_2 760-by- 760 411 760 real
129 HB/fs_760_3 760-by- 760 381 760 real
130 Hollinger/g7jac010 2880-by- 2880 2282 2880 real
131 HB/gent113 113-by- 113 107 113 binary
132 HB/gre_216b 216-by- 216 215 216 real
133 Meszaros/iprob 3001-by- 3001 3000 3001 real
134 HB/jgl009 9-by- 9 5 9 binary
135 HB/jgl011 11-by- 11 5 11 binary
136 HB/lap_25 25-by- 25 16 25 binary
137 GHS_indef/laser 3002-by- 3002 3000 3000 real
138 Mallya/lhr04 4101-by- 4101 4096 4101 real
139 HB/lns_131 131-by- 131 125 131 real
140 HB/lns_3937 3937-by- 3937 2895 3937 real
141 HB/lns_511 511-by- 511 469 511 real
142 HB/lnsp3937 3937-by- 3937 2895 3937 real
143 HB/lnsp_131 131-by- 131 125 131 real
144 HB/lnsp_511 511-by- 511 469 511 real
145 HB/lock1074 1074-by- 1074 155 1038 binary
146 HB/lock2232 2232-by- 2232 368 2208 binary
147 HB/lock3491 3491-by- 3491 603 3416 binary
148 HB/lock_700 700-by- 700 165 691 binary
149 HB/mbeacxc 496-by- 496 448 448 real
150 HB/mbeaflw 496-by- 496 448 448 real
ID Group/Name nrows-by- ncols num. rank struct. rank type
151 HB/mbeause 496-by- 496 447 447 real
152 HB/mcca 180-by- 180 143 180 real
153 HB/mcfe 765-by- 765 759 765 real
154 Bai/mhd1280a 1280-by- 1280 963 1280 complex
155 Bai/mhd3200a 3200-by- 3200 2244 3200 real
156 Bai/mhd4800a 4800-by- 4800 3302 4800 real
157 Bai/mhd4800b 4800-by- 4800 4798 4800 real
158 Bai/mhda416 416-by- 416 322 416 real
159 Boeing/msc01050 1050-by- 1050 1049 1050 real
160 HB/nnc1374 1374-by- 1374 1308 1374 real
161 HB/nnc261 261-by- 261 260 261 real
162 Bai/odepb400 400-by- 400 399 399 real
163 Sandia/oscil_dcop_06 430-by- 430 426 430 real
164 Sandia/oscil_dcop_07 430-by- 430 426 430 real
165 Sandia/oscil_dcop_08 430-by- 430 428 430 real
166 Sandia/oscil_dcop_17 430-by- 430 427 430 real
167 Sandia/oscil_dcop_18 430-by- 430 427 430 real
168 Sandia/oscil_dcop_19 430-by- 430 427 430 real
169 Sandia/oscil_dcop_20 430-by- 430 427 430 real
170 Sandia/oscil_dcop_21 430-by- 430 427 430 real
171 Sandia/oscil_dcop_22 430-by- 430 427 430 real
172 Sandia/oscil_dcop_23 430-by- 430 426 430 real
173 Sandia/oscil_dcop_24 430-by- 430 425 430 real
174 Sandia/oscil_dcop_25 430-by- 430 427 430 real
175 Sandia/oscil_dcop_26 430-by- 430 427 430 real
ID Group/Name nrows-by- ncols num. rank struct. rank type
176 Sandia/oscil_dcop_27 430-by- 430 427 430 real
177 Sandia/oscil_dcop_28 430-by- 430 425 430 real
178 Sandia/oscil_dcop_29 430-by- 430 425 430 real
179 Sandia/oscil_dcop_30 430-by- 430 423 430 real
180 Sandia/oscil_dcop_31 430-by- 430 423 430 real
181 Sandia/oscil_dcop_32 430-by- 430 422 430 real
182 Sandia/oscil_dcop_33 430-by- 430 422 430 real
183 Sandia/oscil_dcop_34 430-by- 430 420 430 real
184 Sandia/oscil_dcop_35 430-by- 430 418 430 real
185 Sandia/oscil_dcop_36 430-by- 430 415 430 real
186 Sandia/oscil_dcop_37 430-by- 430 413 430 real
187 Sandia/oscil_dcop_38 430-by- 430 412 430 real
188 Sandia/oscil_dcop_39 430-by- 430 411 430 real
189 Sandia/oscil_dcop_40 430-by- 430 411 430 real
190 Sandia/oscil_dcop_41 430-by- 430 410 430 real
191 Sandia/oscil_dcop_42 430-by- 430 410 430 real
192 Sandia/oscil_dcop_43 430-by- 430 410 430 real
193 Sandia/oscil_dcop_44 430-by- 430 410 430 real
194 Sandia/oscil_dcop_45 430-by- 430 410 430 real
195 Sandia/oscil_dcop_46 430-by- 430 410 430 real
196 Sandia/oscil_dcop_47 430-by- 430 410 430 real
197 Sandia/oscil_dcop_48 430-by- 430 410 430 real
198 Sandia/oscil_dcop_49 430-by- 430 410 430 real
199 Sandia/oscil_dcop_50 430-by- 430 410 430 real
200 Sandia/oscil_dcop_51 430-by- 430 410 430 real
ID Group/Name nrows-by- ncols num. rank struct. rank type
201 Sandia/oscil_dcop_52 430-by- 430 410 430 real
202 Sandia/oscil_dcop_53 430-by- 430 410 430 real
203 Sandia/oscil_dcop_54 430-by- 430 410 430 real
204 Sandia/oscil_dcop_55 430-by- 430 410 430 real
205 Sandia/oscil_dcop_56 430-by- 430 410 430 real
206 Sandia/oscil_dcop_57 430-by- 430 410 430 real
207 HB/plat1919 1919-by- 1919 1916 1919 real
208 HB/plsk1919 1919-by- 1919 1918 1919 real
209 FEMLAB/problem1 415-by- 415 414 415 real
210 Bai/qh1484 1484-by- 1484 708 1484 real
211 Bai/qh768 768-by- 768 644 768 real
212 Bai/qh882 882-by- 882 821 882 real
213 Simon/raefsky6 3402-by- 3402 2586 3402 real
214 Rajat/rajat02 1960-by- 1960 1508 1960 binary
215 HB/rgg010 10-by- 10 4 10 binary
216 HB/saylr3 1000-by- 1000 998 1000 real
217 Shyy/shyy41 4720-by- 4720 4712 4720 real
218 Pothen/sphere2 66-by- 66 64 66 binary
219 Pothen/sphere3 258-by- 258 253 258 binary
220 HB/sstmodel 3345-by- 3345 3326 3345 binary
221 Oberwolfach/t2dal 4257-by- 4257 4256 4257 real
222 Oberwolfach/t2dal_a 4257-by- 4257 4256 4257 real
223 Oberwolfach/t2dal_bci 4257-by- 4257 4256 4257 real
224 HB/west0156 156-by- 156 154 156 real
225 HB/will199 199-by- 199 191 199 binary
ID Group/Name nrows-by- ncols num. rank struct. rank type
226 HB/will57 57-by- 57 50 57 binary
227 Pajek/yeast 2361-by- 2361 1644 1659 binary
228 HB/zenios 2873-by- 2873 265 266 real
229 Regtools/foxgood_100 100-by- 100 23 100 real
230 Regtools/foxgood_200 200-by- 200 26 200 real
231 Regtools/foxgood_500 500-by- 500 29 500 real
232 Regtools/foxgood_1000 1000-by- 1000 30 1000 real
233 Regtools/baart_100 100-by- 100 12 100 real
234 Regtools/baart_200 200-by- 200 12 200 real
235 Regtools/baart_500 500-by- 500 12 500 real
236 Regtools/baart_1000 1000-by- 1000 13 1000 real
237 Regtools/gravity_100 100-by- 100 48 100 real
238 Regtools/gravity_200 200-by- 200 47 200 real
239 Regtools/gravity_500 500-by- 500 46 500 real
240 Regtools/gravity_1000 1000-by- 1000 45 1000 real
241 Regtools/heat_100 100-by- 100 97 100 real
242 Regtools/heat_200 200-by- 200 195 200 real
243 Regtools/heat_500 500-by- 500 492 500 real
244 Regtools/heat_1000 1000-by- 1000 588 1000 real
245 Regtools/i_laplace_100 100-by- 100 28 100 real
246 Regtools/i_laplace_200 200-by- 200 34 193 real
247 Regtools/i_laplace_500 500-by- 500 39 363 real
248 Regtools/i_laplace_1000 1000-by- 1000 43 581 real
249 Regtools/parallax_100 26-by- 100 25 26 real
250 Regtools/parallax_200 26-by- 200 25 26 real
ID Group/Name nrows-by- ncols num. rank struct. rank type
251 Regtools/parallax_500 26-by- 500 24 26 real
252 Regtools/parallax_1000 26-by- 1000 24 26 real
253 Regtools/shaw_100 100-by- 100 20 100 real
254 Regtools/shaw_200 200-by- 200 20 200 real
255 Regtools/shaw_500 500-by- 500 20 500 real
256 Regtools/shaw_1000 1000-by- 1000 20 1000 real
257 Regtools/ursell_100 100-by- 100 98 100 real
258 Regtools/ursell_200 200-by- 200 198 200 real
259 Regtools/ursell_500 500-by- 500 497 500 real
260 Regtools/ursell_1000 1000-by- 1000 999 1000 real
261 Regtools/wing_100 100-by- 100 8 100 real
262 Regtools/wing_200 200-by- 200 8 200 real
263 Regtools/wing_500 500-by- 500 8 500 real
264 Regtools/wing_1000 1000-by- 1000 8 1000 real
265 Regtools/tomo_100 100-by- 100 98 100 real
266 Regtools/tomo_900 900-by- 900 893 900 real
267 Regtools/tomo_2500 2500-by- 2500 2496 2500 real
268 Regtools/tomo_4900 4900-by- 4900 4897 4900 real
269 Pajek/Sandi_sandi 314-by- 360 239 246 binary
270 LPnetlib/lpi_ex73a 193-by- 211 188 193 real
271 LPnetlib/lpi_ex72a 197-by- 215 192 197 real
272 LPnetlib/lpi_box1 231-by- 261 214 231 real
273 LPnetlib/lpi_mondou2 312-by- 604 311 312 real
274 LPnetlib/lp_scorpion 388-by- 466 358 388 real
275 LPnetlib/lpi_cplex2 224-by- 378 223 224 real
ID Group/Name nrows-by- ncols num. rank struct. rank type
276 HB/abb313 313-by- 176 128 176 binary
277 HB/fs_183_3 183-by- 183 182 183 real
278 LPnetlib/lp_bore3d 233-by- 334 231 232 real
279 Muite/Chebyshev1 261-by- 261 259 261 real
280 Sandia/oscil_dcop_05 430-by- 430 428 430 real
281 Sandia/oscil_dcop_16 430-by- 430 428 430 real
282 LPnetlib/lp_brandy 220-by- 303 193 193 real
283 LPnetlib/lp_standgub 361-by- 1383 360 360 real
284 Pajek/EVA 8497-by- 8497 1301 1303 binary
285 Cunningham/m3plates 11107-by- 11107 6639 6639 real
286 LPnetlib/lp_ship04s 402-by- 1506 360 360 real
287 Sandia/fpga_dcop_08 1220-by- 1220 1210 1220 real
288 Sandia/fpga_dcop_05 1220-by- 1220 1206 1220 real
289 Sandia/fpga_dcop_10 1220-by- 1220 1207 1220 real
290 Boeing/bcsstm38 8032-by- 8032 5112 5199 real
291 Sandia/fpga_dcop_06 1220-by- 1220 1208 1220 real
292 Sandia/fpga_dcop_09 1220-by- 1220 1208 1220 real
293 Sandia/fpga_dcop_12 1220-by- 1220 1219 1220 real
294 Sandia/fpga_dcop_03 1220-by- 1220 1214 1220 real
295 HB/bcsstm24 3562-by- 3562 3496 3562 real
296 HB/mahindas 1258-by- 1258 1257 1258 real
297 Pajek/California 9664-by- 9664 1647 1686 binary
298 LPnetlib/lp_modszk1 687-by- 1620 686 686 real
299 LPnetlib/lp_tuff 333-by- 628 302 302 real
300 LPnetlib/lp_shell 536-by- 1777 535 536 real
ID Group/Name nrows-by- ncols num. rank struct. rank type
301 Norris/lung1 1650-by- 1650 1549 1650 real
302 Pajek/Lederberg 8843-by- 8843 4170 4179 real
303 LPnetlib/lp_ship04l 402-by- 2166 360 360 real
304 Pajek/Zewail 6752-by- 6752 4301 4325 real
305 MathWorks/Pd_rhs 8081-by- 12406 4368 4368 real
306 Pajek/geom 7343-by- 7343 5499 5517 real
307 LPnetlib/lp_ship12s 1151-by- 2869 1042 1042 real
308 LPnetlib/lp_ship08s 778-by- 2467 712 712 real
309 Zitney/extr1 2837-by- 2837 2836 2837 real
310 Bai/mhd3200b 3200-by- 3200 3199 3200 real
311 Meszaros/de063155 852-by- 1848 841 852 real
312 LPnetlib/lp_degen2 444-by- 757 442 444 real
313 Boeing/bcsstm35 30237-by- 30237 15609 15803 real
314 Zitney/extr1b 2836-by- 2836 2835 2836 real
315 Muite/Chebyshev2 2053-by- 2053 2051 2053 real
316 LPnetlib/lp_ship08l 778-by- 4363 712 712 real
317 LPnetlib/lp_sierra 1227-by- 2735 1217 1227 real
318 LPnetlib/lp_ken_07 2426-by- 3602 2377 2426 real
319 Gleich/wb-cs-stanford 9914-by- 9914 5475 5782 binary
320 FIDAP/ex33 1733-by- 1733 1732 1733 real
321 GHS_indef/aug2dc 30200-by- 30200 20000 20000 real
322 LPnetlib/lp_ship12l 1151-by- 5533 1042 1042 real
323 LPnetlib/lp_bnl1 643-by- 1586 642 642 real
324 HB/bcspwr10 5300-by- 5300 5276 5300 binary
325 Nasa/barth 6691-by- 6691 6690 6691 binary
ID Group/Name nrows-by- ncols num. rank struct. rank type
326 GHS_indef/aug2d 29008-by- 29008 19208 19208 real
327 Rajat/rajat01 6833-by- 6833 6777 6833 binary
328 Meszaros/model2 379-by- 1321 377 379 real
329 Zitney/hydr1 5308-by- 5308 5191 5308 real
330 Zitney/hydr1c 5308-by- 5308 5191 5308 real
331 Meszaros/de063157 936-by- 1908 111 936 real
332 Muite/Chebyshev3 4101-by- 4101 4099 4101 real
333 Nasa/barth4 6019-by- 6019 6018 6019 binary
334 Bates/Chem97Zt 2541-by- 31022 2410 2541 binary
335 Grund/bayer03 6747-by- 6747 5680 6747 real
336 HB/sherman3 5005-by- 5005 2898 5005 real
337 Schenk_IBMNA/c-30 5321-by- 5321 5320 5321 real
338 Andrianov/fxm3_6 5026-by- 5026 4087 5026 binary
339 LPnetlib/lp_25fv47 821-by- 1876 820 820 real
340 MathWorks/Kaufhold 8765-by- 8765 8759 8765 real
341 Hollinger/g7jac010sc 2880-by- 2880 2878 2880 real
342 GHS_indef/bloweybq 10001-by- 10001 9964 10001 real
343 Boeing/nasa2910 2910-by- 2910 1623 2910 binary
344 FIDAP/ex9 3363-by- 3363 3344 3363 real
345 LPnetlib/lp_cre_c 3068-by- 6411 2981 2986 real
346 Lucifora/cell1 7055-by- 7055 7054 7055 real
347 Lucifora/cell2 7055-by- 7055 7054 7055 real
348 LPnetlib/lp_cre_a 3516-by- 7248 3423 3428 real
349 Mallya/lhr04c 4101-by- 4101 4100 4101 real
350 Hollinger/jan99jac020 6774-by- 6774 6525 6774 real
ID Group/Name nrows-by- ncols num. rank struct. rank type
351 HB/beacxc 497-by- 506 449 449 real
352 FIDAP/ex18 5773-by- 5773 5772 5773 real
353 HB/beause 497-by- 507 459 459 real
354 Pajek/internet 124651-by- 124651 66598 66679 real
355 FIDAP/ex23 1409-by- 1409 1408 1409 real
356 Gaertner/nopoly 10774-by- 10774 10773 10774 real
357 HB/beaflw 497-by- 507 460 460 real
358 LPnetlib/lp_wood1p 244-by- 2595 243 244 real
359 Grund/bayer10 13436-by- 13436 13309 13436 real
360 LPnetlib/lp_cycle 1903-by- 3371 1875 1875 real
361 LPnetlib/lp_pds_02 2953-by- 7716 2942 2953 real
362 Pothen/shuttle_eddy 10429-by- 10429 9757 10429 binary
363 Nasa/shuttle_eddy 10429-by- 10429 9757 10429 binary
364 Grund/bayer02 13935-by- 13935 12610 13935 real
365 Grund/bayer04 20545-by- 20545 14831 20545 real
366 Rajat/rajat27 20640-by- 20640 20542 20640 real
367 Mallya/lhr07c 7337-by- 7337 7336 7337 real
368 Mallya/lhr07 7337-by- 7337 7315 7337 real
369 Bai/cryg10000 10000-by- 10000 9999 10000 real
370 Meszaros/model9 2879-by- 10939 2787 2787 real
371 Meszaros/stormg2-8 4409-by- 11322 4393 4393 real
372 LPnetlib/lpi_greenbea 2393-by- 5596 2390 2390 real
373 Bindel/ted_A 10605-by- 10605 10604 10605 real
374 Okunbor/aft01 8205-by- 8205 1 8205 real
375 Mallya/lhr14 14270-by- 14270 13996 14270 real
ID Group/Name nrows-by- ncols num. rank struct. rank type
376 Boeing/bcsstm36 23052-by- 23052 12172 12172 real
377 LPnetlib/lp_greenbeb 2392-by- 5598 2389 2389 real
378 Hollinger/g7jac020 5850-by- 5850 4488 5850 real
379 LPnetlib/lp_greenbea 2392-by- 5598 2389 2389 real
380 Hollinger/jan99jac040 13694-by- 13694 13044 13694 real
381 FIDAP/ex19 12005-by- 12005 11966 12005 real
382 LPnetlib/lp_degen3 1503-by- 2604 1501 1503 real
383 GHS_psdef/ford1 18728-by- 18728 18194 18728 binary
384 Hollinger/g7jac020sc 5850-by- 5850 5848 5850 real
385 Mallya/lhr10c 10672-by- 10672 10670 10672 real
386 Andrianov/fxm4_6 18892-by- 18892 14569 18892 binary
387 Mallya/lhr10 10672-by- 10672 10602 10672 real
388 Hohn/fd15 11532-by- 11532 11519 11532 real
389 Mallya/lhr11 10964-by- 10964 10810 10964 real
390 Boeing/nasa4704 4704-by- 4704 2264 4704 binary
391 LPnetlib/lpi_gran 2658-by- 2525 1938 2311 real
392 HB/man_5976 5976-by- 5976 2341 5882 binary
393 HB/bcsstk23 3134-by- 3134 3133 3134 real
394 Pothen/skirt 12598-by- 12598 9831 12598 binary
395 Nasa/skirt 12598-by- 12598 9831 12598 binary
396 Hohn/fd18 16428-by- 16428 16356 16428 real
397 Sandia/mult_dcop_01 25187-by- 25187 25165 25187 real
398 GHS_indef/ncvxqp9 16554-by- 16554 14617 16554 real
399 Oberwolfach/t2dah 11445-by- 11445 11444 11445 real
400 Mallya/lhr11c 10964-by- 10964 10961 10964 real
ID Group/Name nrows-by- ncols num. rank struct. rank type
401 Schenk_IBMNA/c-52 23948-by- 23948 9 23948 real
402 Cunningham/k3plates 11107-by- 11107 11101 11107 real
403 Meszaros/model6 2096-by- 5289 2094 2094 real
404 Mallya/lhr14c 14270-by- 14270 14267 14270 real
405 DNVS/trdheim 22098-by- 22098 2819 22098 binary
406 Rajat/rajat22 39899-by- 39899 39827 39899 real
407 Hollinger/jan99jac060 20614-by- 20614 19484 20614 real
408 Oberwolfach/t2dah_a 11445-by- 11445 11444 11445 real
409 Mallya/lhr17 17576-by- 17576 17182 17576 real
410 Mallya/lhr17c 17576-by- 17576 17572 17576 real
411 Meszaros/nemspmm1 2372-by- 8903 2362 2362 real
412 Rajat/rajat26 51032-by- 51032 50853 51032 real
413 Schenk_IBMNA/c-41 9769-by- 9769 9705 9769 real
414 IBM_EDA/ckt11752_tr_0 49702-by- 49702 49698 49702 real
415 FIDAP/ex35 19716-by- 19716 19673 19716 real
416 Brethour/coater2 9540-by- 9540 9426 9434 real
417 GHS_indef/sit100 10262-by- 10262 10261 10262 real
418 Grund/bayer01 57735-by- 57735 51609 57735 real
419 Boeing/bcsstk38 8032-by- 8032 8008 8032 real
420 Andrianov/net25 9520-by- 9520 9058 9520 binary
421 Gset/G61 7000-by- 7000 6953 6953 real
422 Gset/G60 7000-by- 7000 6953 6953 binary
423 HB/bcsstk25 15439-by- 15439 15435 15439 real
424 Hollinger/mark3jac020 9129-by- 9129 8934 9129 real
425 Sandia/mult_dcop_03 25187-by- 25187 18271 25187 real
ID Group/Name nrows-by- ncols num. rank struct. rank type
426 LPnetlib/lp_d6cube 415-by- 6184 404 404 real
427 Mallya/lhr34 35152-by- 35152 34366 35152 real
428 Hollinger/jan99jac100 34454-by- 34454 32490 34454 real
429 Mallya/lhr71 70304-by- 70304 68728 70304 real
430 Hollinger/mark3jac020sc 9129-by- 9129 9102 9129 real
431 Norris/lung2 109460-by- 109460 55103 109460 real
432 Schenk_ISEI/igbt3 10938-by- 10938 7592 10938 real
433 VanVelzen/std1_Jac2_db 21982-by- 21982 8940 21982 real
434 Hollinger/jan99jac120 41374-by- 41374 38925 41374 real
435 Schenk_IBMNA/c-56 35910-by- 35910 35904 35910 real
436 Bomhof/circuit_4 80209-by- 80209 80185 80209 real
437 GHS_indef/stokes64s 12546-by- 12546 12544 12546 real
438 Shyy/shyy161 76480-by- 76480 76432 76480 real
439 Mallya/lhr34c 35152-by- 35152 35143 35152 real
440 Hollinger/g7jac040sc 11790-by- 11790 11786 11790 real
441 Schenk_IBMNA/c-67 57975-by- 57975 57348 57975 real
442 Meszaros/model5 1888-by- 11802 1744 1744 real
443 GHS_indef/stokes64 12546-by- 12546 12544 12546 real
444 IBM_EDA/ckt11752_dc_1 49702-by- 49702 48868 49702 real
445 Rajat/rajat23 110355-by- 110355 109820 110355 real
446 Meszaros/aa4 426-by- 7195 367 426 binary
447 VanVelzen/Zd_Jac2_db 22835-by- 22835 22360 22835 real
448 Boeing/bcsstk35 30237-by- 30237 30231 30237 real
449 Meszaros/air05 426-by- 7195 367 426 binary
450 Graham/graham1 9035-by- 9035 8924 9035 real
ID Group/Name nrows-by- ncols num. rank struct. rank type
451 Chen/pkustk02 10800-by- 10800 1224 10800 binary
452 Hollinger/g7jac050sc 14760-by- 14760 14754 14760 real
453 Meszaros/stormg2-27 14441-by- 37485 14387 14387 real
454 Hollinger/g7jac040 11790-by- 11790 8838 11790 real
455 GHS_indef/aug3dcqp 35543-by- 35543 28387 35543 real
456 Simon/olafu 16146-by- 16146 16145 16146 real
457 Meszaros/nsir 4453-by- 10057 4391 4453 real
458 Mallya/lhr71c 70304-by- 70304 70284 70304 real
459 Hollinger/mark3jac040sc 18289-by- 18289 18223 18289 real
460 Hollinger/g7jac060sc 17730-by- 17730 17724 17730 real
461 Nasa/pwt 36519-by- 36519 35475 36519 binary
462 GHS_psdef/pwt 36519-by- 36519 35475 36519 binary
463 Pothen/pwt 36519-by- 36519 35475 36519 binary
464 DNVS/crplat2 18010-by- 18010 2912 18010 binary
465 Meszaros/aa6 646-by- 7292 563 646 binary
466 Pajek/dictionary28 52652-by- 52652 37774 38108 binary
467 DNVS/tsyl201 20685-by- 20685 2866 20685 binary
468 GHS_psdef/finance256 37376-by- 37376 35822 37376 binary
469 Schenk_IBMNA/c-64 51035-by- 51035 50941 51035 real
470 Boeing/crystk02 13965-by- 13965 13959 13965 real
471 Boeing/bcsstk36 23052-by- 23052 23020 23052 real
472 Andrianov/net4-1 88343-by- 88343 86176 88343 binary
473 Mulvey/pfinan512 74752-by- 74752 71614 74752 binary
474 Hollinger/mark3jac060sc 27449-by- 27449 27335 27449 real
475 Sandia/ASIC_680ks 682712-by- 682712 583662 682712 real
ID Group/Name nrows-by- ncols num. rank struct. rank type
476 Hollinger/g7jac080sc 23670-by- 23670 23661 23670 real
477 Boeing/bcsstk37 25503-by- 25503 25395 25503 real
478 Simon/raefsky4 19779-by- 19779 19771 19779 real
479 Schenk_IBMSDS/2D_27628_bjtcai 27628-by- 27628 18442 27628 real
480 GHS_indef/k1_san 67759-by- 67759 67758 67758 real
481 GHS_indef/ncvxqp1 12111-by- 12111 7087 12111 real
482 GHS_psdef/ford2 100196-by- 100196 97892 100196 binary
483 Meszaros/air06 825-by- 8627 706 822 binary
484 Hollinger/g7jac100sc 29610-by- 29610 29596 29610 real
485 Meszaros/aa3 825-by- 8627 706 822 binary
486 Chen/pkustk01 22044-by- 22044 3732 22044 binary
487 GHS_psdef/opt1 15449-by- 15449 3442 15449 binary
488 Oberwolfach/t3dl 20360-by- 20360 20359 20360 real
489 Hollinger/mark3jac080sc 36609-by- 36609 36451 36609 real
490 Schenk_IBMNA/c-54 31793-by- 31793 31404 31793 real
491 Hollinger/mark3jac100sc 45769-by- 45769 45571 45769 real
492 GHS_psdef/pds10 16558-by- 16558 16519 16558 binary
493 VanVelzen/Zd_Jac6_db 22835-by- 22835 22505 22835 real
494 VanVelzen/std1_Jac3_db 21982-by- 21982 8940 21982 real
495 HB/bcsstk33 8738-by- 8738 3979 8738 binary
496 Hollinger/g7jac120sc 35550-by- 35550 35530 35550 real
497 Goodwin/rim 22560-by- 22560 22479 22560 real
498 VanVelzen/Zd_Jac3_db 22835-by- 22835 22374 22835 real
499 HB/bcsstk30 28924-by- 28924 8935 28924 binary
500 Boeing/crystk03 24696-by- 24696 24690 24696 real
ID Group/Name nrows-by- ncols num. rank struct. rank type
501 Hollinger/mark3jac120sc 54929-by- 54929 54691 54929 real
502 Chen/pkustk09 33960-by- 33960 5583 33960 binary
503 Sandia/ASIC_320ks 321671-by- 321671 99190 321671 real
504 GHS_psdef/srb1 54924-by- 54924 9154 54924 binary
505 Hollinger/g7jac180 53370-by- 53370 39522 53370 real
506 GHS_indef/olesnik0 88263-by- 88263 88262 88263 real
507 Meszaros/pf2177 9728-by- 10178 9662 9728 binary
508 Andrianov/lpl1 32460-by- 32460 31143 32460 binary
509 HB/bcsstk32 44609-by- 44609 14152 44609 binary
510 Rothberg/struct3 53570-by- 53570 41593 53570 binary
511 Chen/pkustk03 63336-by- 63336 9477 63336 binary
512 LPnetlib/lp_dfl001 6071-by- 12230 6058 6071 real
513 Boeing/pcrystk02 13965-by- 13965 4624 13965 binary
514 GHS_indef/c-68 64810-by- 64810 64801 64810 real
515 Meszaros/stormg2-125 66185-by- 172431 65935 65935 real
516 HB/bcsstk31 35588-by- 35588 16803 35588 binary
517 Schenk_IBMSDS/3D_28984_Tetra 28984-by- 28984 846 28984 real
518 GHS_indef/exdata_1 6001-by- 6001 6000 6001 real
519 Schenk_IBMSDS/2D_54019_highK 54019-by- 54019 45 54019 real
520 Gupta/gupta1 31802-by- 31802 30782 31802 binary
521 Boeing/pcrystk03 24696-by- 24696 7301 24696 binary
522 NYPA/Maragal_1 32-by- 14 10 14 real
523 NYPA/Maragal_2 555-by- 350 171 220 real
524 NYPA/Maragal_3 1690-by- 860 613 765 real
525 NYPA/Maragal_4 1964-by- 1034 801 995 real
ID Group/Name nrows-by- ncols num. rank struct. rank type
526 NYPA/Maragal_5 4654-by- 3320 2147 2690 real
527 Mancktelow/viscorocks 37762-by- 37762 37752 37762 real
528 Pajek/GD01_A 953-by- 953 155 158 real
529 Pajek/Erdos972 5488-by- 5488 882 882 binary
530 Pajek/Erdos982 5822-by- 5822 908 908 binary
531 Pajek/Erdos992 6100-by- 6100 922 922 binary
532 Pajek/Erdos02 6927-by- 6927 938 938 binary
533 Meszaros/aa5 801-by- 8308 692 800 binary
534 Meszaros/aa03 825-by- 8627 706 822 binary
535 Meszaros/us04 163-by- 28016 115 162 binary
536 LPnetlib/lpi_gosh 3792-by- 13455 3790 3790 real
537 Pereyra/landmark 71952-by- 2704 2671 2673 real
538 Meszaros/stat96v5 2307-by- 75779 2305 2305 real
539 TKK/g3rmt3m3 5357-by- 5357 938 5357 binary
540 JGD_Relat/rel3 12-by- 5 1 3 real
541 JGD_Relat/relat3 12-by- 5 1 3 real
542 JGD_Homology/n3c4-b1 15-by- 6 5 6 real
543 JGD_Homology/n3c4-b4 6-by- 15 5 6 real
544 JGD_Homology/ch3-3-b1 18-by- 9 8 9 real
545 JGD_Homology/klein-b1 30-by- 10 9 10 real
546 JGD_Homology/n3c4-b2 20-by- 15 10 15 real
547 JGD_Homology/n3c4-b3 15-by- 20 10 15 real
548 JGD_Homology/n3c5-b1 45-by- 10 9 10 real
549 JGD_Relat/rel4 66-by- 12 5 10 real
550 JGD_Relat/relat4 66-by- 12 5 10 real
ID Group/Name nrows-by- ncols num. rank struct. rank type
551 JGD_Margulies/wheel_3_1 21-by- 25 20 21 binary
552 JGD_Homology/ch4-4-b1 72-by- 16 15 16 real
553 JGD_Homology/n2c6-b1 105-by- 15 14 15 real
554 JGD_Homology/n4c5-b1 105-by- 15 14 15 real
555 JGD_Margulies/wheel_4_1 36-by- 41 32 36 binary
556 JGD_Homology/cis-n4c6-b1 210-by- 21 20 21 real
557 JGD_Homology/n4c6-b1 210-by- 21 20 21 real
558 JGD_Homology/ch5-5-b1 200-by- 25 24 25 real
559 JGD_Margulies/wheel_5_1 57-by- 61 51 57 binary
560 JGD_Homology/n3c5-b2 120-by- 45 36 45 real
561 JGD_Relat/rel5 340-by- 35 24 33 real
562 JGD_Relat/relat5 340-by- 35 24 33 real
563 JGD_Homology/mk9-b1 378-by- 36 35 36 real
564 JGD_Homology/ch4-4-b2 96-by- 72 57 72 real
565 JGD_Homology/ch6-6-b1 450-by- 36 35 36 real
566 JGD_Margulies/wheel_6_1 83-by- 85 72 80 binary
567 JGD_Margulies/cat_ears_2_1 85-by- 85 74 82 binary
568 JGD_Homology/ch7-6-b1 630-by- 42 41 42 real
569 JGD_Homology/n3c6-b1 105-by- 105 14 15 real
570 JGD_Homology/mk10-b1 630-by- 45 44 45 real
571 JGD_Margulies/wheel_7_1 114-by- 113 99 107 binary
572 JGD_Margulies/flower_4_1 121-by- 129 108 121 binary
573 JGD_Homology/ch7-7-b1 882-by- 49 48 49 real
574 JGD_Homology/mk11-b1 990-by- 55 54 55 real
575 JGD_Homology/n3c5-b3 210-by- 120 84 120 real
ID Group/Name nrows-by- ncols num. rank struct. rank type
576 JGD_Homology/n3c5-b6 120-by- 210 84 120 real
577 JGD_GL7d/GL7d11 1019-by- 60 59 60 real
578 JGD_Homology/ch7-8-b1 1176-by- 56 55 56 real
579 JGD_Homology/n2c6-b2 455-by- 105 91 105 real
580 JGD_Homology/n3c6-b2 455-by- 105 91 105 real
581 JGD_Homology/n4c5-b2 455-by- 105 91 105 real
582 JGD_SL6/D_5 434-by- 115 95 114 real
583 JGD_Homology/ch7-9-b1 1512-by- 63 62 63 real
584 JGD_Homology/ch8-8-b1 1568-by- 64 63 64 real
585 JGD_Homology/mk12-b1 1485-by- 66 65 66 real
586 JGD_Margulies/cat_ears_3_1 204-by- 181 165 175 binary
587 JGD_G5/IG5-8 156-by- 292 154 156 real
588 JGD_Margulies/flower_5_1 211-by- 201 179 191 binary
589 JGD_GL6/GL6_D_10 163-by- 341 120 158 real
590 JGD_Homology/n4c5-b10 120-by- 630 110 120 real
591 JGD_Homology/n3c5-b4 252-by- 210 126 210 real
592 JGD_Homology/n3c5-b5 210-by- 252 126 210 real
593 JGD_SL6/D_11 169-by- 461 136 168 real
594 JGD_GL6/GL6_D_6 469-by- 201 156 199 real
595 JGD_Homology/ch5-5-b2 600-by- 200 176 200 real
596 JGD_Margulies/cat_ears_4_1 377-by- 313 291 304 binary
597 JGD_Relat/rel6 2340-by- 157 137 155 real
598 JGD_Relat/relat6 2340-by- 157 137 155 real
599 JGD_Homology/cis-n4c6-b2 1330-by- 210 190 210 real
600 JGD_Homology/n4c6-b2 1330-by- 210 190 210 real
ID Group/Name nrows-by- ncols num. rank struct. rank type
601 JGD_GL6/GL6_D_9 340-by- 545 220 337 real
602 JGD_G5/IG5-9 342-by- 540 308 310 real
603 JGD_Margulies/flower_7_1 463-by- 393 363 379 binary
604 JGD_Homology/n2c6-b9 306-by- 1470 276 306 real
605 JGD_GL6/GL6_D_7 636-by- 470 312 467 real
606 JGD_Margulies/flower_8_1 625-by- 513 479 497 binary
607 JGD_SL6/D_10 460-by- 816 323 455 real
608 JGD_SPG/EX1 560-by- 560 547 560 binary
609 JGD_SPG/EX2 560-by- 560 553 560 binary
610 JGD_Homology/mk9-b2 1260-by- 378 343 378 real
611 JGD_SL6/D_6 970-by- 435 339 433 real
612 JGD_GL6/GL6_D_8 544-by- 637 324 542 real
613 JGD_Homology/ch5-5-b3 600-by- 600 424 600 real
614 JGD_Margulies/kneser_6_2_1 601-by- 676 540 601 binary
615 JGD_GL7d/GL7d26 305-by- 2798 273 303 real
616 JGD_Homology/n4c5-b3 1350-by- 455 364 455 real
617 JGD_Homology/n2c6-b3 1365-by- 455 364 455 real
618 JGD_Homology/n3c6-b3 1365-by- 455 364 455 real
619 JGD_G5/IG5-10 652-by- 976 527 527 real
620 JGD_Homology/ch6-6-b2 2400-by- 450 415 450 real
621 JGD_Homology/n4c5-b9 630-by- 1895 520 630 real
622 JGD_SL6/D_9 815-by- 1133 491 810 real
623 JGD_Kocay/Trec12 551-by- 2726 550 551 real
624 JGD_Homology/mk9-b3 945-by- 1260 875 945 real
625 JGD_Homology/n3c6-b10 675-by- 2511 615 675 real
ID Group/Name nrows-by- ncols num. rank struct. rank type
626 JGD_SL6/D_7 1270-by- 971 629 968 real
627 JGD_Homology/mk10-b2 3150-by- 630 586 630 real
628 JGD_Franz/Franz1 2240-by- 768 755 768 real
629 JGD_Homology/shar_te2-b1 17160-by- 286 285 286 real
630 JGD_SL6/D_8 1132-by- 1271 641 1126 real
631 JGD_Homology/ch7-6-b2 4200-by- 630 589 630 real
632 JGD_G5/IG5-11 1227-by- 1692 902 902 real
633 JGD_Franz/Franz3 1280-by- 2800 1025 1280 real
634 JGD_Homology/n4c5-b4 2852-by- 1350 986 1350 real
635 JGD_Homology/cis-n4c6-b14 920-by- 6300 860 920 real
636 JGD_Homology/n4c6-b14 920-by- 6300 860 920 real
637 JGD_Homology/n2c6-b4 3003-by- 1365 1001 1365 real
638 JGD_Homology/n3c6-b4 3003-by- 1365 1001 1365 real
639 JGD_Homology/ch7-7-b2 7350-by- 882 834 882 real
640 JGD_Homology/mk11-b2 6930-by- 990 936 990 real
641 JGD_Homology/n2c6-b8 1470-by- 3990 1194 1470 real
642 JGD_Homology/lutz30-23-b6 1716-by- 3003 1702 1716 real
643 JGD_GL7d/GL7d12 8899-by- 1019 960 1019 real
644 JGD_Homology/cis-n4c6-b3 5970-by- 1330 1140 1330 real
645 JGD_Homology/n4c6-b3 5970-by- 1330 1140 1330 real
646 JGD_Kocay/Trec13 1301-by- 6561 1295 1301 real
647 JGD_Homology/n4c5-b8 1895-by- 3635 1374 1895 real
648 JGD_Groebner/f855_mat9 2456-by- 2511 2228 2456 real
649 JGD_Groebner/f855_mat9_I 2456-by- 2511 2228 2456 real
650 JGD_G5/IG5-12 2296-by- 2875 1578 1578 real
ID Group/Name nrows-by- ncols num. rank struct. rank type
651 JGD_Homology/ch7-8-b2 11760-by- 1176 1121 1176 real
652 JGD_Groebner/HFE18_96_in 2372-by- 4096 2371 2371 binary
653 JGD_Relat/rel7 21924-by- 1045 1012 1043 real
654 JGD_Relat/relat7b 21924-by- 1045 1012 1043 real
655 JGD_Relat/relat7 21924-by- 1045 1012 1043 real
656 JGD_Homology/mk12-b2 13860-by- 1485 1420 1485 real
657 JGD_Franz/Franz7 10164-by- 1740 1627 1740 real
658 JGD_Homology/ch6-6-b3 5400-by- 2400 1985 2400 real
659 JGD_Homology/n3c6-b9 2511-by- 4935 1896 2511 real
660 JGD_Homology/n4c5-b5 4340-by- 2852 1866 2852 real
661 JGD_Homology/ch7-9-b2 17640-by- 1512 1450 1512 real
662 JGD_Homology/n2c6-b5 4945-by- 3003 2002 3003 real
663 JGD_Homology/n3c6-b5 5005-by- 3003 2002 3003 real
664 JGD_Homology/ch8-8-b2 18816-by- 1568 1505 1568 real
665 JGD_Homology/mk10-b3 4725-by- 3150 2564 3150 real
666 JGD_Franz/Franz5 7382-by- 2882 2229 2882 real
667 JGD_Homology/n4c5-b7 3635-by- 4735 2261 3635 real
668 JGD_Franz/Franz6 7576-by- 3016 2327 3016 real
669 JGD_Franz/Franz2 4032-by- 4480 2631 4032 real
670 JGD_G5/IG5-13 3994-by- 4731 2532 2532 real
671 JGD_Homology/n4c5-b6 4735-by- 4340 2474 4340 real
672 JGD_Homology/n2c6-b7 3990-by- 5715 2772 3990 real
673 JGD_Homology/ch6-6-b4 4320-by- 5400 3390 4320 real
674 JGD_Homology/n2c6-b6 5715-by- 4945 2943 4945 real
675 JGD_Homology/n3c6-b8 4935-by- 6435 3003 4935 real
ID Group/Name nrows-by- ncols num. rank struct. rank type
676 JGD_Kocay/Trec14 3159-by- 15905 3133 3159 real
677 JGD_Homology/n3c6-b6 6435-by- 5005 3003 5005 real
678 JGD_GL7d/GL7d25 2798-by- 21074 2525 2798 real
679 TKK/t520 5563-by- 5563 882 5563 real
680 JGD_Franz/Franz4 6784-by- 5252 3297 5252 real
681 JGD_Homology/ch7-6-b3 12600-by- 4200 3611 4200 real
682 JGD_Homology/n3c6-b7 6435-by- 6435 3432 6435 real
683 JGD_SPG/EX5 6545-by- 6545 4740 6545 binary
684 JGD_SPG/EX6 6545-by- 6545 4740 6545 binary
685 JGD_Franz/Franz9 19588-by- 4164 3545 4164 real
686 JGD_Franz/Franz10 19588-by- 4164 3545 4164 real
687 JGD_G5/IG5-14 6735-by- 7621 3906 3906 real
688 Marini/eurqsa 7245-by- 7245 7035 7245 real
689 JGD_Homology/ch7-6-b5 5040-by- 15120 5039 5040 real
690 JGD_Homology/cis-n4c6-b4 20058-by- 5970 4830 5970 real
691 JGD_Homology/n4c6-b4 20058-by- 5970 4830 5970 real
692 JGD_Homology/mk11-b3 17325-by- 6930 5994 6930 real
693 JGD_Franz/Franz8 16728-by- 7176 5463 7176 real
694 TKK/cyl6 13681-by- 13681 2243 13681 real
695 QY/case9 14454-by- 14454 14444 14454 real
696 TSOPF/TSOPF_FS_b9_c6 14454-by- 14454 14444 14454 real
697 TKK/tube1 21498-by- 21498 3583 21498 binary
698 TKK/tube2 21498-by- 21498 3583 21498 real
699 JGD_Homology/D6-6 120576-by- 23740 14409 18660 real
Your path has been modified by:
addpath /Users/davis/sparse/MyPapers/Foster/spqr_rank/SJget
SJget toolbox successfully installed.
Remember to save your path using savepath or pathtool!
Saving the current MATLAB path so that access to the matrices
is available when restarting MATLAB.
downloading http://www.math.sjsu.edu/singular/matrices/mat/Pajek/Erdos971.mat
to /Users/davis/sparse/MyPapers/Foster/spqr_rank/SJget/mat/Pajek/Erdos971.mat
Expected error caught: Input argument "A" is undefined.
Expected error caught: invalid stats
Expected error caught: usage: [x,stats,NT] = spqr_basic (A,B,opts)
Expected error caught: A and B must have the same number of rows
Expected error caught: usage: [x,stats,NT] = spqr_basic (A,B,opts)
Expected error caught: usage: [U,S,V,stats] = spqr_ssi (R,opts)
Expected error caught: usage: [x,stats,N,NT] = spqr_cod (A,B,opts)
Expected error caught: usage: [N,stats] = spqr_null (A,opts)
Expected error caught: usage: [U,S,V,stats] = spqr_ssp (A,N,k,opts)
Expected error caught: usage: [x,stats,N,NT] = spqr_pinv (A,B,opts)
Expected error caught: R must be square
opts for spqr_ssi with get_details = 1:
options for the spqr_rank functions:
get_details : 1 : extensive statistics returned
tol : default : max(m,n)*eps(normest(A,0.01))
nsvals_large : 1 : # of large singular values to estimate.
nsvals_small : 1 : # of small singular values to estimate.
implicit_null_space_basis : true : N represented in Householder form.
start_with_A_transpose : false : spqr_cod computes qr(A).
ssi_tol : default : same as tol.
ssi_min_block : 3 : ssi initial block size.
ssi_max_block : 10 : spqr_ssi max block size.
ssi_min_iters : 3 : min # of iterations before checking convergence
ssi_max_iters : 100 : max # of iterations before stopping spqr_ssi iterations
ssi_nblock_increment : 5 : block size inc. if convergence not met.
ssi_convergence_factor : 0.1 : spqr_ssi termination criterion.
k : ssp_min_iters : 4 : min # of iterations before checking convergence
ssp_max_iters : 10 : max # of ssp iterations before stopping iterations
ssp_convergence_factor : 0.1 ssp terminates when relative error drops below this value.
repeatable : true : internal random stream used to guarantee repeatability
flag : 0 : ok. stats.rank very likely to be correct.
rank : 4 : estimate of numerical rank.
tol : 2.84217e-14 : numerical tolerance used.
normest_R : 51.6479 : estimate of Euclidean norm of R (calculated for spqr_ssi).
est_svals_of_R : 3.22608
: estimated singular value(s) of triangular matrix R.
est_error_bounds : 5.77104e-05
: error bounds for each singular value.
sval_numbers_for_bounds : 4
: index of singular value(s), for bounds.
norm_R_times_N : 0 : norm of (R*N), from spqr_ssi.
norm_R_transpose_times_NT : 0 : norm of (R'*NT), from spqr_ssi.
iters : 3 : iterations in spqr_ssi or spqr_ssp.
nsvals_large_found : 1 : number of large singular values found.
final_blocksize : 3 : final block size in spqr_ssi.
ssi_max_block_used : 4 : max block size for spqr_ssi.
ssi_min_block_used : 3 : initial block size for spqr_ssi.
time : 0.155409 : total time taken (includes all timings below).
time_initialize : 0.00524966 : time to initialize including estimating the norm of A or R.
time_svd : 0.0301843 : total time taken by svd.
time_iters : 0.0882315 : time for spqr_ssi iterations.
time_est_error_bounds : 0.0150126 : time taken to estimate error bounds in spqr_ssi.
opts for spqr_cod with get_details = 0:
options for the spqr_rank functions:
get_details : 0 : basic statistics returned
tol : 1e-06
nsvals_large : 1 : # of large singular values to estimate.
nsvals_small : 1 : # of small singular values to estimate.
implicit_null_space_basis : true : N represented in Householder form.
start_with_A_transpose : false : spqr_cod computes qr(A).
ssi_tol : default : same as tol.
ssi_min_block : 3 : ssi initial block size.
ssi_max_block : 10 : spqr_ssi max block size.
ssi_min_iters : 3 : min # of iterations before checking convergence
ssi_max_iters : 100 : max # of iterations before stopping spqr_ssi iterations
ssi_nblock_increment : 5 : block size inc. if convergence not met.
ssi_convergence_factor : 0.1 : spqr_ssi termination criterion.
k : ssp_min_iters : 4 : min # of iterations before checking convergence
ssp_max_iters : 10 : max # of ssp iterations before stopping iterations
ssp_convergence_factor : 0.1 ssp terminates when relative error drops below this value.
repeatable : true : internal random stream used to guarantee repeatability
results from spqr_cod with get_details = 0: err 2.1528e-15
flag : 0 : ok. stats.rank very likely to be correct.
rank : 4 : estimate of numerical rank.
tol : 1e-06 : numerical tolerance used.
est_sval_upper_bounds : 13.135
: estimated upper bounds on singular value(s).
est_sval_lower_bounds : 13.0823
: estimated lower bounds on singular value(s).
sval_numbers_for_bounds : 4
: index of singular value(s), for bounds.
results from spqr_pinv with get_details = 0: err 1.40433e-15
flag : 0 : ok. stats.rank very likely to be correct.
rank : 4 : estimate of numerical rank.
tol : 1e-06 : numerical tolerance used.
est_sval_upper_bounds : 17.1615
: estimated upper bounds on singular value(s).
est_sval_lower_bounds : 3.60039
: estimated lower bounds on singular value(s).
sval_numbers_for_bounds : 4
: index of singular value(s), for bounds.
est_norm_A_times_N : 4.98489e-15 : estimated norm(A*N).
est_norm_A_transpose_times_NT : 0 : estimated norm(A'*NT).
results from spqr_basic with get_details = 0: err 2.22045e-16
flag : 0 : ok. stats.rank very likely to be correct.
rank : 4 : estimate of numerical rank.
tol : 1e-06 : numerical tolerance used.
est_sval_upper_bounds : 17.1615
: estimated upper bounds on singular value(s).
est_sval_lower_bounds : 3.60039
: estimated lower bounds on singular value(s).
sval_numbers_for_bounds : 4
: index of singular value(s), for bounds.
est_norm_A_transpose_times_NT : 0 : estimated norm(A'*NT).
opts for spqr_cod with get_details = 1:
options for the spqr_rank functions:
get_details : 1 : extensive statistics returned
tol : 1e-06
nsvals_large : 1 : # of large singular values to estimate.
nsvals_small : 1 : # of small singular values to estimate.
implicit_null_space_basis : true : N represented in Householder form.
start_with_A_transpose : false : spqr_cod computes qr(A).
ssi_tol : default : same as tol.
ssi_min_block : 3 : ssi initial block size.
ssi_max_block : 10 : spqr_ssi max block size.
ssi_min_iters : 3 : min # of iterations before checking convergence
ssi_max_iters : 100 : max # of iterations before stopping spqr_ssi iterations
ssi_nblock_increment : 5 : block size inc. if convergence not met.
ssi_convergence_factor : 0.1 : spqr_ssi termination criterion.
k : ssp_min_iters : 4 : min # of iterations before checking convergence
ssp_max_iters : 10 : max # of ssp iterations before stopping iterations
ssp_convergence_factor : 0.1 ssp terminates when relative error drops below this value.
repeatable : true : internal random stream used to guarantee repeatability
results from spqr_cod with get_details = 1: err 2.1528e-15
flag : 0 : ok. stats.rank very likely to be correct.
rank : 4 : estimate of numerical rank.
rank_spqr : 4 : estimate of numerical rank from spqr.
This is normally an upper bound on the true rank.
tol : 1e-06 : numerical tolerance used.
est_sval_upper_bounds : 13.135
: estimated upper bounds on singular value(s).
est_sval_lower_bounds : 13.0823
: estimated lower bounds on singular value(s).
sval_numbers_for_bounds : 4
: index of singular value(s), for bounds.
est_norm_A_times_N : 1.35229e-14 : estimated norm(A*N).
est_err_bound_norm_A_times_N : 2.68461e-15 : estimated error bound for norm(A*N).
time : 0.0766464 : total time taken (includes all timings below).
time_initialize : 0.000894783 : time to initialize.
time_svd : 0.021441 : total time taken by svd.
time_basis : 0.00508991 : time to compute basis.
info_spqr1 : statistics from first QR factorization.
nnzR_upper_bound: 18
nnzH_upper_bound: 6
number_of_frontal_matrices: 1
number_of_TBB_tasks: 1
rank_A_estimate: 4
number_of_column_singletons: 0
number_of_singleton_rows: 0
ordering: 'colamd'
memory_usage_in_bytes: 2518
flops_upper_bound: 190
tol: 1.0000e-06
number_of_TBB_threads: 'default'
norm_E_fro: 0
spqr_compiled_with_TBB: 'no'
spqr_compiled_with_METIS: 'yes'
time: 3.6561e-04
info_spqr2 : statistics from second QR factorization.
nnzR_upper_bound: 10
nnzH_upper_bound: 8
number_of_frontal_matrices: 1
number_of_TBB_tasks: 1
rank_A_estimate: 4
number_of_column_singletons: 0
number_of_singleton_rows: 0
ordering: 'colamd'
memory_usage_in_bytes: 2420
flops_upper_bound: 116
tol: 0
number_of_TBB_threads: 'default'
norm_E_fro: 0
spqr_compiled_with_TBB: 'no'
spqr_compiled_with_METIS: 'yes'
time: 2.6390e-04
stats_ssi : statistics from spqr_ssi.
flag : 0 : ok. stats.rank very likely to be correct.
rank : 4 : estimate of numerical rank.
tol : 1e-06 : numerical tolerance used.
est_svals_of_R : 13.1087
: estimated singular value(s) of triangular matrix R.
est_error_bounds : 0.0263153
: error bounds for each singular value.
sval_numbers_for_bounds : 4
: index of singular value(s), for bounds.
norm_R_times_N : 0 : norm of (R*N), from spqr_ssi.
norm_R_transpose_times_NT : 0 : norm of (R'*NT), from spqr_ssi.
iters : 3 : iterations in spqr_ssi or spqr_ssp.
nsvals_large_found : 1 : number of large singular values found.
final_blocksize : 3 : final block size in spqr_ssi.
ssi_max_block_used : 4 : max block size for spqr_ssi.
ssi_min_block_used : 3 : initial block size for spqr_ssi.
time : 0.0260141 : total time taken (includes all timings below).
time_initialize : 0.000476977 : time to initialize.
time_svd : 0.0139333 : total time taken by svd.
time_iters : 0.0149111 : time for spqr_ssi iterations.
time_est_error_bounds : 0.00068853 : time taken to estimate error bounds in spqr_ssi.
stats_ssp_N : statistics from spqr_ssp (A,N).
flag : 1 : spqr_ssp did not converge with est. relative error <= opts_ssp.convergence_factor.
est_svals : 1.35229e-14
: estimated singular value(s) of A*N or A'*NT, from spqr_ssp.
est_error_bounds : 2.68461e-15
: error bounds for each singular value.
sval_numbers_for_bounds : 1
: index of singular value(s), for bounds.
iters : 10 : iterations in spqr_ssi or spqr_ssp.
time : 0.0200954 : total time taken (includes all timings below).
time_initialize : 0.00130859 : time to initialize.
time_svd : 0.00750766 : total time taken by svd.
time_iters : 0.0151055 : time for spqr_ssi iterations.
time_est_error_bounds : 3.1059e-05 : time taken to estimate error bounds in spqr_ssi.
results from spqr_pinv with get_details = 1: err 1.40433e-15
flag : 0 : ok. stats.rank very likely to be correct.
rank : 4 : estimate of numerical rank.
rank_spqr : 4 : estimate of numerical rank from spqr.
This is normally an upper bound on the true rank.
tol : 1e-06 : numerical tolerance used.
est_sval_upper_bounds : 17.1615
: estimated upper bounds on singular value(s).
est_sval_lower_bounds : 3.60039
: estimated lower bounds on singular value(s).
sval_numbers_for_bounds : 4
: index of singular value(s), for bounds.
est_norm_A_times_N : 4.98489e-15 : estimated norm(A*N).
est_err_bound_norm_A_times_N : 2.26877e-15 : estimated error bound for norm(A*N).
est_norm_A_transpose_times_NT : 0 : estimated norm(A'*NT).
est_err_bound_norm_A_transpose_times_NT : 0 : estimated error bound for norm(A'*NT).
time : 0.0526774 : total time taken (includes all timings below).
time_initialize : 0.000870357 : time to initialize.
time_svd : 0.00369433 : total time taken by svd.
time_basis : 0.00482744 : time to compute basis.
opts_used : options for the spqr_rank functions:
get_details : 1 : extensive statistics returned
tol : 1e-06
nsvals_large : 1 : # of large singular values to estimate.
nsvals_small : 1 : # of small singular values to estimate.
implicit_null_space_basis : true : N represented in Householder form.
start_with_A_transpose : false : spqr_cod computes qr(A).
ssi_tol : 1e-06
ssi_min_block : 3 : ssi initial block size.
ssi_max_block : 10 : spqr_ssi max block size.
ssi_min_iters : 3 : min # of iterations before checking convergence
ssi_max_iters : 100 : max # of iterations before stopping spqr_ssi iterations
ssi_nblock_increment : 5 : block size inc. if convergence not met.
ssi_convergence_factor : 0.1 : spqr_ssi termination criterion.
k : ssp_min_iters : 4 : min # of iterations before checking convergence
ssp_max_iters : 10 : max # of ssp iterations before stopping iterations
ssp_convergence_factor : 0.1 ssp terminates when relative error drops below this value.
repeatable : true : internal random stream used to guarantee repeatability
stats_spqr_basic : statistics from spqr_basic.
flag : 0 : ok. stats.rank very likely to be correct.
rank : 4 : estimate of numerical rank.
rank_spqr : 4 : estimate of numerical rank from spqr.
This is normally an upper bound on the true rank.
tol : 1e-06 : numerical tolerance used.
est_sval_upper_bounds : 17.1615
: estimated upper bounds on singular value(s).
est_sval_lower_bounds : 3.60039
: estimated lower bounds on singular value(s).
sval_numbers_for_bounds : 4
: index of singular value(s), for bounds.
est_norm_A_transpose_times_NT : 0 : estimated norm(A'*NT).
est_err_bound_norm_A_transpose_times_NT : 0 : estimated error bound for norm(A'*NT).
time : 0.0208919 : total time taken (includes all timings below).
time_initialize : 0.000480994 : time to initialize.
time_svd : 0.000530932 : total time taken by svd.
time_basis : 0.00470466 : time to compute basis.
info_spqr1 : statistics from first QR factorization.
nnzR_upper_bound: 14
nnzH_upper_bound: 6
number_of_frontal_matrices: 1
number_of_TBB_tasks: 1
rank_A_estimate: 4
number_of_column_singletons: 0
number_of_singleton_rows: 0
ordering: 'colamd'
memory_usage_in_bytes: 2645
flops_upper_bound: 150
tol: 1.0000e-06
number_of_TBB_threads: 'default'
norm_E_fro: 0
spqr_compiled_with_TBB: 'no'
spqr_compiled_with_METIS: 'yes'
time: 4.0852e-04
stats_ssi : statistics from spqr_ssi.
flag : 0 : ok. stats.rank very likely to be correct.
rank : 4 : estimate of numerical rank.
tol : 1e-06 : numerical tolerance used.
est_svals_of_R : 3.6005
: estimated singular value(s) of triangular matrix R.
est_error_bounds : 0.000103967
: error bounds for each singular value.
sval_numbers_for_bounds : 4
: index of singular value(s), for bounds.
norm_R_times_N : 0 : norm of (R*N), from spqr_ssi.
norm_R_transpose_times_NT : 0 : norm of (R'*NT), from spqr_ssi.
iters : 3 : iterations in spqr_ssi or spqr_ssp.
nsvals_large_found : 1 : number of large singular values found.
final_blocksize : 3 : final block size in spqr_ssi.
ssi_max_block_used : 4 : max block size for spqr_ssi.
ssi_min_block_used : 3 : initial block size for spqr_ssi.
time : 0.00467957 : total time taken (includes all timings below).
time_initialize : 0.000453893 : time to initialize.
time_svd : 0.000462889 : total time taken by svd.
time_iters : 0.00147939 : time for spqr_ssi iterations.
time_est_error_bounds : 0.000284898 : time taken to estimate error bounds in spqr_ssi.
stats_ssp_NT : statistics from spqr_ssp (A',NT).
flag : 0 : ok. spqr_ssp converged with est. relative error <= opts_ssp.convergence_factor.
est_svals : 0
: estimated singular value(s) of A*N or A'*NT, from spqr_ssp.
est_error_bounds : 0
: error bounds for each singular value.
sval_numbers_for_bounds : 0
: index of singular value(s), for bounds.
iters : 0 : iterations in spqr_ssi or spqr_ssp.
time : 0 : total time taken (includes all timings below).
time_initialize : 0.000458996 : time to initialize.
time_svd : 0 : total time taken by svd.
time_iters : 0 : time for spqr_ssi iterations.
time_est_error_bounds : 0 : time taken to estimate error bounds in spqr_ssi.
stats_spqr_null : statistics from spqr_null.
stats_spqr_null.opts_used.ssi_min_block : 3 : initial block size in spqr_ssi as used by spqr_null.
flag : 0 : ok. stats.rank very likely to be correct.
rank : 4 : estimate of numerical rank.
rank_spqr : 4 : estimate of numerical rank from spqr.
This is normally an upper bound on the true rank.
tol : 1e-06 : numerical tolerance used.
est_sval_upper_bounds : 13.1087
: estimated upper bounds on singular value(s).
est_sval_lower_bounds : 13.0996
: estimated lower bounds on singular value(s).
sval_numbers_for_bounds : 4
: index of singular value(s), for bounds.
est_norm_A_times_N : 4.98489e-15 : estimated norm(A*N).
est_err_bound_norm_A_times_N : 2.26877e-15 : estimated error bound for norm(A*N).
time : 0.0252396 : total time taken (includes all timings below).
time_initialize : 0.000428747 : time to initialize.
time_svd : 0.00137542 : total time taken by svd.
time_basis : 0.000122782 : time to compute basis.
info_spqr1 : statistics from first QR factorization.
nnzR_upper_bound: 10
nnzH_upper_bound: 10
number_of_frontal_matrices: 1
number_of_TBB_tasks: 1
rank_A_estimate: 4
number_of_column_singletons: 0
number_of_singleton_rows: 0
ordering: 'colamd'
memory_usage_in_bytes: 2516
flops_upper_bound: 146
tol: 1.0000e-06
number_of_TBB_threads: 'default'
norm_E_fro: 0
spqr_compiled_with_TBB: 'no'
spqr_compiled_with_METIS: 'yes'
time: 3.1628e-04
stats_ssi : statistics from spqr_ssi.
flag : 0 : ok. stats.rank very likely to be correct.
rank : 4 : estimate of numerical rank.
tol : 1e-06 : numerical tolerance used.
est_svals_of_R : 13.1087
: estimated singular value(s) of triangular matrix R.
est_error_bounds : 0.00909203
: error bounds for each singular value.
sval_numbers_for_bounds : 4
: index of singular value(s), for bounds.
norm_R_times_N : 0 : norm of (R*N), from spqr_ssi.
norm_R_transpose_times_NT : 0 : norm of (R'*NT), from spqr_ssi.
iters : 3 : iterations in spqr_ssi or spqr_ssp.
nsvals_large_found : 1 : number of large singular values found.
final_blocksize : 3 : final block size in spqr_ssi.
ssi_max_block_used : 4 : max block size for spqr_ssi.
ssi_min_block_used : 3 : initial block size for spqr_ssi.
time : 0.00448574 : total time taken (includes all timings below).
time_initialize : 0.00044112 : time to initialize.
time_svd : 0.000463685 : total time taken by svd.
time_iters : 0.0014619 : time for spqr_ssi iterations.
time_est_error_bounds : 0.000277138 : time taken to estimate error bounds in spqr_ssi.
stats_ssp_N : statistics from spqr_ssp (A,N).
flag : 1 : spqr_ssp did not converge with est. relative error <= opts_ssp.convergence_factor.
est_svals : 4.98489e-15
: estimated singular value(s) of A*N or A'*NT, from spqr_ssp.
est_error_bounds : 2.26877e-15
: error bounds for each singular value.
sval_numbers_for_bounds : 1
: index of singular value(s), for bounds.
iters : 10 : iterations in spqr_ssi or spqr_ssp.
time : 0.00891953 : total time taken (includes all timings below).
time_initialize : 0.000435418 : time to initialize.
time_svd : 0.000861395 : total time taken by svd.
time_iters : 0.00746511 : time for spqr_ssi iterations.
time_est_error_bounds : 2.9307e-05 : time taken to estimate error bounds in spqr_ssi.
results from spqr_basic with get_details = 1: err 2.22045e-16
flag : 0 : ok. stats.rank very likely to be correct.
rank : 4 : estimate of numerical rank.
rank_spqr : 4 : estimate of numerical rank from spqr.
This is normally an upper bound on the true rank.
tol : 1e-06 : numerical tolerance used.
est_sval_upper_bounds : 17.1615
: estimated upper bounds on singular value(s).
est_sval_lower_bounds : 3.60039
: estimated lower bounds on singular value(s).
sval_numbers_for_bounds : 4
: index of singular value(s), for bounds.
est_norm_A_transpose_times_NT : 0 : estimated norm(A'*NT).
est_err_bound_norm_A_transpose_times_NT : 0 : estimated error bound for norm(A'*NT).
time : 0.0116915 : total time taken (includes all timings below).
time_initialize : 0.000849542 : time to initialize.
time_svd : 0.000528542 : total time taken by svd.
time_basis : 0.000127805 : time to compute basis.
opts_used : options for the spqr_rank functions:
get_details : 1 : extensive statistics returned
tol : 1e-06
nsvals_large : 1 : # of large singular values to estimate.
nsvals_small : 1 : # of small singular values to estimate.
implicit_null_space_basis : true : N represented in Householder form.
start_with_A_transpose : false : spqr_cod computes qr(A).
ssi_tol : 1e-06
ssi_min_block : 3 : ssi initial block size.
ssi_max_block : 10 : spqr_ssi max block size.
ssi_min_iters : 3 : min # of iterations before checking convergence
ssi_max_iters : 100 : max # of iterations before stopping spqr_ssi iterations
ssi_nblock_increment : 5 : block size inc. if convergence not met.
ssi_convergence_factor : 0.1 : spqr_ssi termination criterion.
k : ssp_min_iters : 4 : min # of iterations before checking convergence
ssp_max_iters : 10 : max # of ssp iterations before stopping iterations
ssp_convergence_factor : 0.1 ssp terminates when relative error drops below this value.
repeatable : true : internal random stream used to guarantee repeatability
info_spqr1 : statistics from first QR factorization.
nnzR_upper_bound: 14
nnzH_upper_bound: 6
number_of_frontal_matrices: 1
number_of_TBB_tasks: 1
rank_A_estimate: 4
number_of_column_singletons: 0
number_of_singleton_rows: 0
ordering: 'colamd'
memory_usage_in_bytes: 2645
flops_upper_bound: 150
tol: 1.0000e-06
number_of_TBB_threads: 'default'
norm_E_fro: 0
spqr_compiled_with_TBB: 'no'
spqr_compiled_with_METIS: 'yes'
time: 4.1654e-04
stats_ssi : statistics from spqr_ssi.
flag : 0 : ok. stats.rank very likely to be correct.
rank : 4 : estimate of numerical rank.
tol : 1e-06 : numerical tolerance used.
est_svals_of_R : 3.6005
: estimated singular value(s) of triangular matrix R.
est_error_bounds : 0.000103967
: error bounds for each singular value.
sval_numbers_for_bounds : 4
: index of singular value(s), for bounds.
norm_R_times_N : 0 : norm of (R*N), from spqr_ssi.
norm_R_transpose_times_NT : 0 : norm of (R'*NT), from spqr_ssi.
iters : 3 : iterations in spqr_ssi or spqr_ssp.
nsvals_large_found : 1 : number of large singular values found.
final_blocksize : 3 : final block size in spqr_ssi.
ssi_max_block_used : 4 : max block size for spqr_ssi.
ssi_min_block_used : 3 : initial block size for spqr_ssi.
time : 0.00464281 : total time taken (includes all timings below).
time_initialize : 0.000448914 : time to initialize.
time_svd : 0.000473298 : total time taken by svd.
time_iters : 0.00149702 : time for spqr_ssi iterations.
time_est_error_bounds : 0.000288067 : time taken to estimate error bounds in spqr_ssi.
stats_ssp_NT : statistics from spqr_ssp (A',NT).
flag : 0 : ok. spqr_ssp converged with est. relative error <= opts_ssp.convergence_factor.
est_svals : 0
: estimated singular value(s) of A*N or A'*NT, from spqr_ssp.
est_error_bounds : 0
: error bounds for each singular value.
sval_numbers_for_bounds : 0
: index of singular value(s), for bounds.
iters : 0 : iterations in spqr_ssi or spqr_ssp.
time : 0 : total time taken (includes all timings below).
time_initialize : 0.000433066 : time to initialize.
time_svd : 0 : total time taken by svd.
time_iters : 0 : time for spqr_ssi iterations.
time_est_error_bounds : 0 : time taken to estimate error bounds in spqr_ssi.
stats_ssp_NT.opts_used.k : 1 : number of singular values to compute in spqr_ssp(A',NT).
opts for spqr_cod with get_details = 2:
options for the spqr_rank functions:
get_details : 2 : basic statistics and a few additional statisticsreturned
tol : 1e-06
nsvals_large : 1 : # of large singular values to estimate.
nsvals_small : 1 : # of small singular values to estimate.
implicit_null_space_basis : true : N represented in Householder form.
start_with_A_transpose : false : spqr_cod computes qr(A).
ssi_tol : default : same as tol.
ssi_min_block : 3 : ssi initial block size.
ssi_max_block : 10 : spqr_ssi max block size.
ssi_min_iters : 3 : min # of iterations before checking convergence
ssi_max_iters : 100 : max # of iterations before stopping spqr_ssi iterations
ssi_nblock_increment : 5 : block size inc. if convergence not met.
ssi_convergence_factor : 0.1 : spqr_ssi termination criterion.
k : ssp_min_iters : 4 : min # of iterations before checking convergence
ssp_max_iters : 10 : max # of ssp iterations before stopping iterations
ssp_convergence_factor : 0.1 ssp terminates when relative error drops below this value.
repeatable : true : internal random stream used to guarantee repeatability
results from spqr_cod with get_details = 2: err 2.1528e-15
flag : 0 : ok. stats.rank very likely to be correct.
rank : 4 : estimate of numerical rank.
rank_spqr : 4 : estimate of numerical rank from spqr.
This is normally an upper bound on the true rank.
tol : 1e-06 : numerical tolerance used.
est_sval_upper_bounds : 13.135
: estimated upper bounds on singular value(s).
est_sval_lower_bounds : 13.0823
: estimated lower bounds on singular value(s).
sval_numbers_for_bounds : 4
: index of singular value(s), for bounds.
stats_ssi : statistics from spqr_ssi.
flag : 0 : ok. stats.rank very likely to be correct.
rank : 4 : estimate of numerical rank.
tol : 1e-06 : numerical tolerance used.
est_svals_of_R : 13.1087
: estimated singular value(s) of triangular matrix R.
est_error_bounds : 0.0263153
: error bounds for each singular value.
sval_numbers_for_bounds : 4
: index of singular value(s), for bounds.
ssi_max_block_used : 4 : max block size for spqr_ssi.
ssi_min_block_used : 3 : initial block size for spqr_ssi.
results from spqr_pinv with get_details = 2: err 1.40433e-15
flag : 0 : ok. stats.rank very likely to be correct.
rank : 4 : estimate of numerical rank.
rank_spqr : 4 : estimate of numerical rank from spqr.
This is normally an upper bound on the true rank.
tol : 1e-06 : numerical tolerance used.
est_sval_upper_bounds : 17.1615
: estimated upper bounds on singular value(s).
est_sval_lower_bounds : 3.60039
: estimated lower bounds on singular value(s).
sval_numbers_for_bounds : 4
: index of singular value(s), for bounds.
est_norm_A_times_N : 4.98489e-15 : estimated norm(A*N).
est_norm_A_transpose_times_NT : 0 : estimated norm(A'*NT).
results from spqr_basic with get_details = 2: err 2.22045e-16
flag : 0 : ok. stats.rank very likely to be correct.
rank : 4 : estimate of numerical rank.
rank_spqr : 4 : estimate of numerical rank from spqr.
This is normally an upper bound on the true rank.
tol : 1e-06 : numerical tolerance used.
est_sval_upper_bounds : 17.1615
: estimated upper bounds on singular value(s).
est_sval_lower_bounds : 3.60039
: estimated lower bounds on singular value(s).
sval_numbers_for_bounds : 4
: index of singular value(s), for bounds.
est_norm_A_transpose_times_NT : 0 : estimated norm(A'*NT).
stats_ssi : statistics from spqr_ssi.
flag : 0 : ok. stats.rank very likely to be correct.
rank : 4 : estimate of numerical rank.
tol : 1e-06 : numerical tolerance used.
est_svals_of_R : 3.6005
: estimated singular value(s) of triangular matrix R.
est_error_bounds : 0.000103967
: error bounds for each singular value.
sval_numbers_for_bounds : 4
: index of singular value(s), for bounds.
ssi_max_block_used : 4 : max block size for spqr_ssi.
ssi_min_block_used : 3 : initial block size for spqr_ssi.
opts for spqr_null with explicit basis N:
options for the spqr_rank functions:
get_details : 1 : extensive statistics returned
tol : default : max(m,n)*eps(normest(A,0.01))
nsvals_large : 1 : # of large singular values to estimate.
nsvals_small : 1 : # of small singular values to estimate.
implicit_null_space_basis : false : N represented as an explicit matrix.
start_with_A_transpose : true : spqr_cod computes qr(A').
ssi_tol : 1e-06
ssi_min_block : 3 : ssi initial block size.
ssi_max_block : 10 : spqr_ssi max block size.
ssi_min_iters : 3 : min # of iterations before checking convergence
ssi_max_iters : 100 : max # of iterations before stopping spqr_ssi iterations
ssi_nblock_increment : 5 : block size inc. if convergence not met.
ssi_convergence_factor : 0.1 : spqr_ssi termination criterion.
k : ssp_min_iters : 4 : min # of iterations before checking convergence
ssp_max_iters : 10 : max # of ssp iterations before stopping iterations
ssp_convergence_factor : 0.1 ssp terminates when relative error drops below this value.
repeatable : false : use whatever current random stream is in effect.
Expected error caught: unrecognized method
Expected error caught: unrecognized method
Expected error caught: unrecognized N struct
Expected error caught: unrecognized N struct
Expected error caught: unrecognized N struct
Expected error caught: unrecognized N struct
detailed stats from spqr_cod:
flag : 0 : ok. stats.rank very likely to be correct.
rank : 3 : estimate of numerical rank.
rank_spqr : 3 : estimate of numerical rank from spqr.
This is normally an upper bound on the true rank.
tol : 5.68434e-14 : numerical tolerance used.
est_sval_upper_bounds : 1.77763 4.44089e-15
: estimated upper bounds on singular value(s).
est_sval_lower_bounds : 1.77763 0
: estimated lower bounds on singular value(s).
sval_numbers_for_bounds : 3 4
: index of singular value(s), for bounds.
est_norm_A_times_N : 4.18953e-15 : estimated norm(A*N).
est_norm_A_transpose_times_NT : 9.67173e-15 : estimated norm(A'*NT).
stats_ssi : statistics from spqr_ssi.
flag : 0 : ok. stats.rank very likely to be correct.
rank : 3 : estimate of numerical rank.
tol : 1e-06 : numerical tolerance used.
est_svals_of_R : 1.77763
: estimated singular value(s) of triangular matrix R.
est_error_bounds : 5.44614e-15
: error bounds for each singular value.
sval_numbers_for_bounds : 3
: index of singular value(s), for bounds.
ssi_max_block_used : 3 : max block size for spqr_ssi.
ssi_min_block_used : 3 : initial block size for spqr_ssi.
default options for the spqr_rank functions:
get_details : 0 : basic statistics returned
tol : default : max(m,n)*eps(normest(A,0.01))
nsvals_large : 1 : # of large singular values to estimate.
nsvals_small : 1 : # of small singular values to estimate.
implicit_null_space_basis : true : N represented in Householder form.
start_with_A_transpose : false : spqr_cod computes qr(A).
ssi_tol : default : same as tol.
ssi_min_block : 3 : ssi initial block size.
ssi_max_block : 10 : spqr_ssi max block size.
ssi_min_iters : 3 : min # of iterations before checking convergence
ssi_max_iters : 100 : max # of iterations before stopping spqr_ssi iterations
ssi_nblock_increment : 5 : block size inc. if convergence not met.
ssi_convergence_factor : 0.1 : spqr_ssi termination criterion.
k : ssp_min_iters : 4 : min # of iterations before checking convergence
ssp_max_iters : 10 : max # of ssp iterations before stopping iterations
ssp_convergence_factor : 0.1 ssp terminates when relative error drops below this value.
repeatable : true : internal random stream used to guarantee repeatability
(default for spqr_ssp): options for the spqr_rank functions:
get_details : 0 : basic statistics returned
tol : default : max(m,n)*eps(normest(A,0.01))
nsvals_large : 1 : # of large singular values to estimate.
nsvals_small : 1 : # of small singular values to estimate.
implicit_null_space_basis : true : N represented in Householder form.
start_with_A_transpose : false : spqr_cod computes qr(A).
ssi_tol : default : same as tol.
ssi_min_block : 3 : ssi initial block size.
ssi_max_block : 10 : spqr_ssi max block size.
ssi_min_iters : 3 : min # of iterations before checking convergence
ssi_max_iters : 100 : max # of iterations before stopping spqr_ssi iterations
ssi_nblock_increment : 5 : block size inc. if convergence not met.
ssi_convergence_factor : 0.1 : spqr_ssi termination criterion.
k : ssp_min_iters : 4 : min # of iterations before checking convergence
ssp_max_iters : 10 : max # of ssp iterations before stopping iterations
ssp_convergence_factor : 0.1 ssp terminates when relative error drops below this value.
repeatable : true : internal random stream used to guarantee repeatability
description of statistics:
Description of basic stats returned by spqr_basic, spqr_null, spqr_pinv
or spqr_cod:
stats.flag (for all routines except spqr_ssp) --
if stats.flag is 0 if it is likely, although not
guaranteed, that stats.rank is the correct numerical rank for
tolerance stats.tol (i.e. agrees with the numerical rank
determined by the singular values of R).
stats.flag is 1 if the calculated numerical rank stats.rank may
be correct for the tolerance stats.tol but the estimated error
bounds are too large to confirm this. However stats.rank appears
to be correct for an alternate tolerance stats.tol_alt. More
generally stats.rank appears to be correct for any tolerance
between stats.est_sval_lower_bounds(nsvals_large) and
stats.est_sval_upper_bounds(nsvals_large+1).
stats.flag is 2 if the calculated numerical rank stats.numerical
may be correct but estimated error bounds are too large to confirm
this. The conditions for stats.flag to be 0 or 1 are not
satisfied.
stats.flag is 3 if is likely that the numerical rank returned,
stats.rank, is too large.
stats.flag is 4 if overflow occurred during the inverse power
method. The method fails in this case, and all parameters other
stats are returned as empty ([ ]).
stats.flag is 5 if a catastrophic failure occurred.
stats.rank -- the estimated numerical rank when stats.flag is
0, 1 or 2. stats.rank is typically an upper bound on the
numerical rank when stats.flag is 3. Note that stats.rank is a
correction to the rank returned by spqr (stats.rank_spqr) in the
case that the calculations in the routine inidicate that the rank
returned by spqr not correct.
stats.tol -- the tolerance used to define the numerical rank.
stat.tol_alt -- an alternate tolerance that corresponds to the
calculated numerical rank when stats.flag is 1.
stats.est_sval_upper_bounds -- stats.est_sval_upper_bounds(i) is an
estimate of an upper bound on singular value number
stats.sval_numbers_for_bounds(i) of A.
stats.est_sval_lower_bounds -- stats.est_sval_lower_bounds(i) is an
estimate of an lower bound on singular value number
stats.sval_numbers_for_bounds(i) of A.
Note that stats.est_sval_upper_bounds(i) is a rigorous upper bound
on some singular value of (A+E) where where E is O(norm(A)*eps)
Also stats.est_sval_lower_bounds(i) is a rigorous lower bound on
some singular value of (A+E). In both cases the singular value is
normally singular value number sval_numbers_for_bounds(i) of A,
but the singular value number is not guaranteed. For i such that
sval_numbers_for_bounds(i) = stats.rank (that is for estimates
of singular value stats.rank) if stats.est_sval_upper_bounds(i)
is a large multiple of stats.est_sval_lower_bounds(i) then
solution vectors x produced by spqr_basic may be inferior (i.e.
be significanty larger) than solutions produced by spqr_pinv or
spqr_cod.
stats.sval_numbers_for_bounds -- component i in the error bounds is an estimated
error bound for singular value number sval_numbers_for_bounds(i).
stats.est_norm_A_transpose_times_NT -- an estimate of norm(A'*NT).
stats.est_norm_A_times_N -- an estimate of norm(A*N).
Description of basic stats returned by spqr_ssi:
stats.flag (for all routines except spqr_ssp) --
if stats.flag is 0 if it is likely, although not
guaranteed, that stats.rank is the correct numerical rank for
tolerance stats.tol (i.e. agrees with the numerical rank
determined by the singular values of R).
stats.flag is 1 if the calculated numerical rank stats.rank may
be correct for the tolerance stats.tol but the estimated error
bounds are too large to confirm this. However stats.rank appears
to be correct for an alternate tolerance stats.tol_alt. More
generally stats.rank appears to be correct for any tolerance
between stats.est_sval_lower_bounds(nsvals_large) and
stats.est_sval_upper_bounds(nsvals_large+1).
stats.flag is 2 if the calculated numerical rank stats.numerical
may be correct but estimated error bounds are too large to confirm
this. The conditions for stats.flag to be 0 or 1 are not
satisfied.
stats.flag is 3 if is likely that the numerical rank returned,
stats.rank, is too large.
stats.flag is 4 if overflow occurred during the inverse power
method. The method fails in this case, and all parameters other
stats are returned as empty ([ ]).
stats.flag is 5 if a catastrophic failure occurred.
stats.rank -- the estimated numerical rank when stats.flag is
0, 1 or 2. stats.rank is typically an upper bound on the
numerical rank when stats.flag is 3. Note that stats.rank is a
correction to the rank returned by spqr (stats.rank_spqr) in the
case that the calculations in the routine inidicate that the rank
returned by spqr not correct.
stats.tol -- the tolerance used to define the numerical rank.
stats.est_svals_of_R -- computed by spqr_ssi.
stats.est_svals_of_R contains estimates of the smallest singular
of R.
stats.est_error_bounds -- computed by spqr_ssi and spqr_ssp.
stats.est_error_bounds(i) is an estimated bound on the absolute
error in singular value number stats.sval_numbers_for_bounds(i).
of R (for spqr_ssi) or of A or A*N (for spqr_ssp). It is also a
rigorous bound on abs (s(i) - some true singular value of (B+E)),
where E is O(norm(B)*eps) and B = R (for spqr_ssi) and B =
A or A*N (for spqr_ssp).
stats.sval_numbers_for_bounds -- component i in the error bounds is an estimated
error bound for singular value number sval_numbers_for_bounds(i).
Description of basic stats returned by spqr_ssp:
stats.flag -- (for spqr_ssp)
stats.flag is 0 if spqr_ssp converged with estimated relative
error in singular value opts.k of A (or of A*N) <=
opts_ssp.convergence_factor. stats.flag is 1 if this is not true.
stats.est_svals -- computed by spqr_ssp.
stats.est_svals(i) is an estimate of the ith largest singular of
A or of A*N. Also for i = 1:nsval, stats.est_svals(i) is a lower
bound on the ith largest singular value of A (or A*N).
stats.est_error_bounds -- computed by spqr_ssi and spqr_ssp.
stats.est_error_bounds(i) is an estimated bound on the absolute
error in singular value number stats.sval_numbers_for_bounds(i).
of R (for spqr_ssi) or of A or A*N (for spqr_ssp). It is also a
rigorous bound on abs (s(i) - some true singular value of (B+E)),
where E is O(norm(B)*eps) and B = R (for spqr_ssi) and B =
A or A*N (for spqr_ssp).
stats.sval_numbers_for_bounds -- component i in the error bounds is an estimated
error bound for singular value number sval_numbers_for_bounds(i).
Description of basic stats returned by spqr_basic, spqr_null, spqr_pinv
or spqr_cod:
stats.flag (for all routines except spqr_ssp) --
if stats.flag is 0 if it is likely, although not
guaranteed, that stats.rank is the correct numerical rank for
tolerance stats.tol (i.e. agrees with the numerical rank
determined by the singular values of R).
stats.flag is 1 if the calculated numerical rank stats.rank may
be correct for the tolerance stats.tol but the estimated error
bounds are too large to confirm this. However stats.rank appears
to be correct for an alternate tolerance stats.tol_alt. More
generally stats.rank appears to be correct for any tolerance
between stats.est_sval_lower_bounds(nsvals_large) and
stats.est_sval_upper_bounds(nsvals_large+1).
stats.flag is 2 if the calculated numerical rank stats.numerical
may be correct but estimated error bounds are too large to confirm
this. The conditions for stats.flag to be 0 or 1 are not
satisfied.
stats.flag is 3 if is likely that the numerical rank returned,
stats.rank, is too large.
stats.flag is 4 if overflow occurred during the inverse power
method. The method fails in this case, and all parameters other
stats are returned as empty ([ ]).
stats.flag is 5 if a catastrophic failure occurred.
stats.rank -- the estimated numerical rank when stats.flag is
0, 1 or 2. stats.rank is typically an upper bound on the
numerical rank when stats.flag is 3. Note that stats.rank is a
correction to the rank returned by spqr (stats.rank_spqr) in the
case that the calculations in the routine inidicate that the rank
returned by spqr not correct.
stats.tol -- the tolerance used to define the numerical rank.
stat.tol_alt -- an alternate tolerance that corresponds to the
calculated numerical rank when stats.flag is 1.
stats.est_sval_upper_bounds -- stats.est_sval_upper_bounds(i) is an
estimate of an upper bound on singular value number
stats.sval_numbers_for_bounds(i) of A.
stats.est_sval_lower_bounds -- stats.est_sval_lower_bounds(i) is an
estimate of an lower bound on singular value number
stats.sval_numbers_for_bounds(i) of A.
Note that stats.est_sval_upper_bounds(i) is a rigorous upper bound
on some singular value of (A+E) where where E is O(norm(A)*eps)
Also stats.est_sval_lower_bounds(i) is a rigorous lower bound on
some singular value of (A+E). In both cases the singular value is
normally singular value number sval_numbers_for_bounds(i) of A,
but the singular value number is not guaranteed. For i such that
sval_numbers_for_bounds(i) = stats.rank (that is for estimates
of singular value stats.rank) if stats.est_sval_upper_bounds(i)
is a large multiple of stats.est_sval_lower_bounds(i) then
solution vectors x produced by spqr_basic may be inferior (i.e.
be significanty larger) than solutions produced by spqr_pinv or
spqr_cod.
stats.sval_numbers_for_bounds -- component i in the error bounds is an estimated
error bound for singular value number sval_numbers_for_bounds(i).
stats.est_norm_A_transpose_times_NT -- an estimate of norm(A'*NT).
stats.est_norm_A_times_N -- an estimate of norm(A*N).
Description of basic stats returned by all spqr_functions:
stats.flag (for all routines except spqr_ssp) --
if stats.flag is 0 if it is likely, although not
guaranteed, that stats.rank is the correct numerical rank for
tolerance stats.tol (i.e. agrees with the numerical rank
determined by the singular values of R).
stats.flag is 1 if the calculated numerical rank stats.rank may
be correct for the tolerance stats.tol but the estimated error
bounds are too large to confirm this. However stats.rank appears
to be correct for an alternate tolerance stats.tol_alt. More
generally stats.rank appears to be correct for any tolerance
between stats.est_sval_lower_bounds(nsvals_large) and
stats.est_sval_upper_bounds(nsvals_large+1).
stats.flag is 2 if the calculated numerical rank stats.numerical
may be correct but estimated error bounds are too large to confirm
this. The conditions for stats.flag to be 0 or 1 are not
satisfied.
stats.flag is 3 if is likely that the numerical rank returned,
stats.rank, is too large.
stats.flag is 4 if overflow occurred during the inverse power
method. The method fails in this case, and all parameters other
stats are returned as empty ([ ]).
stats.flag is 5 if a catastrophic failure occurred.
stats.flag -- (for spqr_ssp)
stats.flag is 0 if spqr_ssp converged with estimated relative
error in singular value opts.k of A (or of A*N) <=
opts_ssp.convergence_factor. stats.flag is 1 if this is not true.
stats.rank -- the estimated numerical rank when stats.flag is
0, 1 or 2. stats.rank is typically an upper bound on the
numerical rank when stats.flag is 3. Note that stats.rank is a
correction to the rank returned by spqr (stats.rank_spqr) in the
case that the calculations in the routine inidicate that the rank
returned by spqr not correct.
stats.tol -- the tolerance used to define the numerical rank.
stat.tol_alt -- an alternate tolerance that corresponds to the
calculated numerical rank when stats.flag is 1.
stats.est_sval_upper_bounds -- stats.est_sval_upper_bounds(i) is an
estimate of an upper bound on singular value number
stats.sval_numbers_for_bounds(i) of A.
stats.est_sval_lower_bounds -- stats.est_sval_lower_bounds(i) is an
estimate of an lower bound on singular value number
stats.sval_numbers_for_bounds(i) of A.
Note that stats.est_sval_upper_bounds(i) is a rigorous upper bound
on some singular value of (A+E) where where E is O(norm(A)*eps)
Also stats.est_sval_lower_bounds(i) is a rigorous lower bound on
some singular value of (A+E). In both cases the singular value is
normally singular value number sval_numbers_for_bounds(i) of A,
but the singular value number is not guaranteed. For i such that
sval_numbers_for_bounds(i) = stats.rank (that is for estimates
of singular value stats.rank) if stats.est_sval_upper_bounds(i)
is a large multiple of stats.est_sval_lower_bounds(i) then
solution vectors x produced by spqr_basic may be inferior (i.e.
be significanty larger) than solutions produced by spqr_pinv or
spqr_cod.
stats.est_svals_of_R -- computed by spqr_ssi.
stats.est_svals_of_R contains estimates of the smallest singular
of R.
stats.est_svals -- computed by spqr_ssp.
stats.est_svals(i) is an estimate of the ith largest singular of
A or of A*N. Also for i = 1:nsval, stats.est_svals(i) is a lower
bound on the ith largest singular value of A (or A*N).
stats.est_error_bounds -- computed by spqr_ssi and spqr_ssp.
stats.est_error_bounds(i) is an estimated bound on the absolute
error in singular value number stats.sval_numbers_for_bounds(i).
of R (for spqr_ssi) or of A or A*N (for spqr_ssp). It is also a
rigorous bound on abs (s(i) - some true singular value of (B+E)),
where E is O(norm(B)*eps) and B = R (for spqr_ssi) and B =
A or A*N (for spqr_ssp).
stats.sval_numbers_for_bounds -- component i in the error bounds is an estimated
error bound for singular value number sval_numbers_for_bounds(i).
stats.est_norm_A_transpose_times_NT -- an estimate of norm(A'*NT).
stats.est_norm_A_times_N -- an estimate of norm(A*N).
***** Additional statistics when opts.get_details is 2: *****
stats.rank_spqr -- the rough estimate of the numerical rank
computed by spqr. This is typically correct if the numerical
rank is well-defined.
stats.stats_ssi -- statistics returned by spqr_ssi.
stats_ssi.ssi_max_block_used -- the maximum block size used by spqr_ssi.
stats_ssi.ssi_min_block_used -- the initial block size used by spqr_ssi.
***** Additions statistics when opts.get_details is 1: *****
stats.normest_A -- an estimate of the Euclidean norm of A. Calculated using
normest(A,0.01).
stats.normest_R -- an estimate of the Euclidean norm of R. Calculated for spqr_ssi
using normest(R,0.01).
stats.est_err_bound_norm_A_times_N -- an estimate of an
error bound on stats.est_norm_A_times_N. It is also a
rigorous bound on abs (stats.est_norm_A_times_N - s)
where s is some singular value of (A+E)*N and where E is
O(norm(A)*eps). Usually the singular value is the first singular
value but this is not guaranteed.
stats.est_err_bound_norm_A_transpose_times_NT -- an estimate of an
error bound on stats.est_norm_A_transpose_times_NT. It is also a
rigorous bound on abs (stats.est_norm_A_transpose_times_NT - s)
where s is some singular value of (A+E)'*NT and where E is
O(norm(A)*eps). Usually the singular value is the first singular
value but this is not guaranteed.
stats_ssi.norm_R_times_N -- Euclidean norm of (R*N), from spqr_ssi.
stats_ssi.norm_R_transpose_times_NT -- Eucliean norm of (R'*NT), from spqr_ssi.
stats_ssi.iters or stats_ssp_N.iters or stats_ssp_NT.iters -- number of
iterations for subspace iteration in spqr_ssi or spqr_ssp.
stats_ssi.nsvals_large_found -- the number of 'large' (larger than tol) singular
values found, from spqr_ssi.
stats_ssi.final_blocksize -- final block size for subspace iteration in
spqr_ssi.
stats.stats_spqr_basic -- statistics returned when spqr_basic is called by spqr_pinv.
stats.stats_spqr_null -- statistics returned when spqr_null is called by spqr_pinv.
stats.info_spqr1 -- statistics from spqr for the first QR factorization.
See 'help spqr' for details.
stats.info_spqr2 -- statistics from spqr for the second QR factorization, if
required. See 'help spqr' for details.
stats.stats_ssp_N -- statistics from spqr_ssp when calculating the basis
N for the null space of A.
stats.stats_ssp_NT -- statistics from spqr_ssp when calculating the basis
NT for the null space of A transpose.
stats.opts_used, stats_ssi.opts_used, or stats_ssp.opts_used -- values of
options used. These can be different from values in opts since, for example,
the size of A can restrict some values in opts.
stats.time, stats_ssi.time, etc. -- the total time of the routine including
the times described below.
stats.time_initialize, stats_ssi.time_initialize, etc. -- the time to
set default values of opts, including calculating normest(A,0.01),
or normest(R,0.01) if needed.
stats.time_basis -- the time to compute the basis for the numerical null space
following any calls to spqr and spqr_ssi. This will be small
if the null space basis is returned in implicit form but can, in some cases,
be significant if the null space basis is returned as an explicit matrix.
stats_ssi.time_iters, stats_ssp_N.time_iters, etc. -- the time for the
subspace iterations in spqr_ssi or spqr_ssp. Excludes time for initialization,
error flag calculation, etc..
stats_ssi.time_est_error_bounds, stats_ssp_N.time_est_error_bounds, etc. -- the time
for estimating the singular value error bounds in spqr_ssi or spqr_ssp.
stats.time_svd, stats_ssi.time_svd, etc. -- the total time for calls to MATLAB's SVD
in the current routine and its subroutines.
Description of basic stats returned by all spqr_functions:
stats.flag (for all routines except spqr_ssp) --
if stats.flag is 0 if it is likely, although not
guaranteed, that stats.rank is the correct numerical rank for
tolerance stats.tol (i.e. agrees with the numerical rank
determined by the singular values of R).
stats.flag is 1 if the calculated numerical rank stats.rank may
be correct for the tolerance stats.tol but the estimated error
bounds are too large to confirm this. However stats.rank appears
to be correct for an alternate tolerance stats.tol_alt. More
generally stats.rank appears to be correct for any tolerance
between stats.est_sval_lower_bounds(nsvals_large) and
stats.est_sval_upper_bounds(nsvals_large+1).
stats.flag is 2 if the calculated numerical rank stats.numerical
may be correct but estimated error bounds are too large to confirm
this. The conditions for stats.flag to be 0 or 1 are not
satisfied.
stats.flag is 3 if is likely that the numerical rank returned,
stats.rank, is too large.
stats.flag is 4 if overflow occurred during the inverse power
method. The method fails in this case, and all parameters other
stats are returned as empty ([ ]).
stats.flag is 5 if a catastrophic failure occurred.
stats.flag -- (for spqr_ssp)
stats.flag is 0 if spqr_ssp converged with estimated relative
error in singular value opts.k of A (or of A*N) <=
opts_ssp.convergence_factor. stats.flag is 1 if this is not true.
stats.rank -- the estimated numerical rank when stats.flag is
0, 1 or 2. stats.rank is typically an upper bound on the
numerical rank when stats.flag is 3. Note that stats.rank is a
correction to the rank returned by spqr (stats.rank_spqr) in the
case that the calculations in the routine inidicate that the rank
returned by spqr not correct.
stats.tol -- the tolerance used to define the numerical rank.
stat.tol_alt -- an alternate tolerance that corresponds to the
calculated numerical rank when stats.flag is 1.
stats.est_sval_upper_bounds -- stats.est_sval_upper_bounds(i) is an
estimate of an upper bound on singular value number
stats.sval_numbers_for_bounds(i) of A.
stats.est_sval_lower_bounds -- stats.est_sval_lower_bounds(i) is an
estimate of an lower bound on singular value number
stats.sval_numbers_for_bounds(i) of A.
Note that stats.est_sval_upper_bounds(i) is a rigorous upper bound
on some singular value of (A+E) where where E is O(norm(A)*eps)
Also stats.est_sval_lower_bounds(i) is a rigorous lower bound on
some singular value of (A+E). In both cases the singular value is
normally singular value number sval_numbers_for_bounds(i) of A,
but the singular value number is not guaranteed. For i such that
sval_numbers_for_bounds(i) = stats.rank (that is for estimates
of singular value stats.rank) if stats.est_sval_upper_bounds(i)
is a large multiple of stats.est_sval_lower_bounds(i) then
solution vectors x produced by spqr_basic may be inferior (i.e.
be significanty larger) than solutions produced by spqr_pinv or
spqr_cod.
stats.est_svals_of_R -- computed by spqr_ssi.
stats.est_svals_of_R contains estimates of the smallest singular
of R.
stats.est_svals -- computed by spqr_ssp.
stats.est_svals(i) is an estimate of the ith largest singular of
A or of A*N. Also for i = 1:nsval, stats.est_svals(i) is a lower
bound on the ith largest singular value of A (or A*N).
stats.est_error_bounds -- computed by spqr_ssi and spqr_ssp.
stats.est_error_bounds(i) is an estimated bound on the absolute
error in singular value number stats.sval_numbers_for_bounds(i).
of R (for spqr_ssi) or of A or A*N (for spqr_ssp). It is also a
rigorous bound on abs (s(i) - some true singular value of (B+E)),
where E is O(norm(B)*eps) and B = R (for spqr_ssi) and B =
A or A*N (for spqr_ssp).
stats.sval_numbers_for_bounds -- component i in the error bounds is an estimated
error bound for singular value number sval_numbers_for_bounds(i).
stats.est_norm_A_transpose_times_NT -- an estimate of norm(A'*NT).
stats.est_norm_A_times_N -- an estimate of norm(A*N).
***** Additional statistics when opts.get_details is 2: *****
stats.rank_spqr -- the rough estimate of the numerical rank
computed by spqr. This is typically correct if the numerical
rank is well-defined.
stats.stats_ssi -- statistics returned by spqr_ssi.
stats_ssi.ssi_max_block_used -- the maximum block size used by spqr_ssi.
stats_ssi.ssi_min_block_used -- the initial block size used by spqr_ssi.
---------------------------------------------------------------
test that illustrates the rare case of a miscalculated rank:
downloading http://www.math.sjsu.edu/singular/matrices/mat/Sandia/oscil_dcop_33.mat
to /Users/davis/sparse/MyPapers/Foster/spqr_rank/SJget/mat/Sandia/oscil_dcop_33.mat
Problem =
name: 'Sandia/oscil_dcop_33'
title: 'Sandia/oscil_dcop_33 circuit simulation matrix. Sandia National Lab.'
A: [430x430 double]
b: [430x1 double]
SJid: 182
UFid: 1144
kind: 'subsequent circuit simulation problem'
notes: 'next: Sandia/oscil_dcop_34 first: Sandia/oscil_dcop_01'
date: '2003'
author: 'R. Hoekstra'
ed: 'T. Davis'
svals: [430x1 double]
sval_info: 'Routine svd from Matlab 7.6.0.324 (R2008a) used to calculate the singular values.'
flag : 0 : ok. stats.rank very likely to be correct.
rank : 423 : estimate of numerical rank.
rank_spqr : 425 : estimate of numerical rank from spqr.
This is normally an upper bound on the true rank.
tol : 1.00117e-07 : numerical tolerance used.
est_sval_upper_bounds : 2.13431e-07 7.15797e-08
: estimated upper bounds on singular value(s).
est_sval_lower_bounds : 1.26859e-07 3.33239e-08
: estimated lower bounds on singular value(s).
sval_numbers_for_bounds : 423 424
: index of singular value(s), for bounds.
est_norm_A_times_N : 7.155e-08 : estimated norm(A*N).
est_err_bound_norm_A_times_N : 2.96843e-11 : estimated error bound for norm(A*N).
time : 0.0411242 : total time taken (includes all timings below).
time_initialize : 0.000724137 : time to initialize.
time_svd : 0.00166625 : total time taken by svd.
time_basis : 0.000198297 : time to compute basis.
opts_used : options for the spqr_rank functions:
get_details : 1 : extensive statistics returned
tol : 1.00117e-07
nsvals_large : 1 : # of large singular values to estimate.
nsvals_small : 1 : # of small singular values to estimate.
implicit_null_space_basis : true : N represented in Householder form.
start_with_A_transpose : false : spqr_cod computes qr(A).
ssi_tol : 1.00117e-07
ssi_min_block : 3 : ssi initial block size.
ssi_max_block : 10 : spqr_ssi max block size.
ssi_min_iters : 3 : min # of iterations before checking convergence
ssi_max_iters : 100 : max # of iterations before stopping spqr_ssi iterations
ssi_nblock_increment : 5 : block size inc. if convergence not met.
ssi_convergence_factor : 0.1 : spqr_ssi termination criterion.
k : ssp_min_iters : 4 : min # of iterations before checking convergence
ssp_max_iters : 10 : max # of ssp iterations before stopping iterations
ssp_convergence_factor : 0.1 ssp terminates when relative error drops below this value.
repeatable : true : internal random stream used to guarantee repeatability
info_spqr1 : statistics from first QR factorization.
nnzR_upper_bound: 6338
nnzH_upper_bound: 3664
number_of_frontal_matrices: 50
number_of_TBB_tasks: 1
rank_A_estimate: 425
number_of_column_singletons: 8
number_of_singleton_rows: 8
ordering: 'colamd'
memory_usage_in_bytes: 274334
flops_upper_bound: 197791
tol: 1.0012e-07
number_of_TBB_threads: 'default'
norm_E_fro: 8.3997e-08
spqr_compiled_with_TBB: 'no'
spqr_compiled_with_METIS: 'yes'
time: 0.0016
stats_ssi : statistics from spqr_ssi.
flag : 0 : ok. stats.rank very likely to be correct.
rank : 423 : estimate of numerical rank.
tol : 1.00117e-07 : numerical tolerance used.
est_svals_of_R : 1.29434e-07 3.33299e-08 1.96839e-08
: estimated singular value(s) of triangular matrix R.
est_error_bounds : 2.57485e-09 5.97769e-12 1.72923e-13
: error bounds for each singular value.
sval_numbers_for_bounds : 423 424 425
: index of singular value(s), for bounds.
norm_R_times_N : 3.33299e-08 : norm of (R*N), from spqr_ssi.
norm_R_transpose_times_NT : 3.33299e-08 : norm of (R'*NT), from spqr_ssi.
iters : 5 : iterations in spqr_ssi or spqr_ssp.
nsvals_large_found : 1 : number of large singular values found.
final_blocksize : 3 : final block size in spqr_ssi.
ssi_max_block_used : 10 : max block size for spqr_ssi.
ssi_min_block_used : 3 : initial block size for spqr_ssi.
time : 0.017417 : total time taken (includes all timings below).
time_initialize : 0.000412213 : time to initialize.
time_svd : 0.00111743 : total time taken by svd.
time_iters : 0.00362718 : time for spqr_ssi iterations.
time_est_error_bounds : 0.000383958 : time taken to estimate error bounds in spqr_ssi.
stats_ssp_N : statistics from spqr_ssp (A,N).
flag : 0 : ok. spqr_ssp converged with est. relative error <= opts_ssp.convergence_factor.
est_svals : 7.155e-08
: estimated singular value(s) of A*N or A'*NT, from spqr_ssp.
est_error_bounds : 2.96843e-11
: error bounds for each singular value.
sval_numbers_for_bounds : 1
: index of singular value(s), for bounds.
iters : 4 : iterations in spqr_ssi or spqr_ssp.
time : 0.0117262 : total time taken (includes all timings below).
time_initialize : 0.000420176 : time to initialize.
time_svd : 0.000410698 : total time taken by svd.
time_iters : 0.00978757 : time for spqr_ssi iterations.
time_est_error_bounds : 2.8997e-05 : time taken to estimate error bounds in spqr_ssi.
stats_ssp_N.opts_used.k : 1 : number of singular values to compute in spqr_ssp(A,N).
expected rank mismatch 423 422
---------------------------------------------------------------
another rare case:
downloading http://www.math.sjsu.edu/singular/matrices/mat/Regtools/gravity_1000.mat
to /Users/davis/sparse/MyPapers/Foster/spqr_rank/SJget/mat/Regtools/gravity_1000.mat
Problem =
title: 'GRAVITY 1000x1000 Test problem: 1-D gravity surveying model problem'
A: [1000x1000 double]
b: [1000x1 double]
x: [1000x1 double]
SJid: 240
UFid: -1
name: 'Regtools/gravity_1000'
date: '2002'
author: 'Hansen'
ed: 'Per Christian Hansen'
kind: 'ill-posed problem'
notes: [29x73 char]
svals: [1000x1 double]
sval_info: 'Routine svd from Matlab 7.6.0.324 (R2008a) used to calculate the singular values.'
flag : 2 : stats.rank may be correct for tolerance stats.tol,
but error bounds are too high to confirm this.
rank : 96 : estimate of numerical rank.
rank_spqr : 105 : estimate of numerical rank from spqr.
This is normally an upper bound on the true rank.
tol : 8.88178e-13 : numerical tolerance used.
normest_A : 6.45915 : estimate of Euclidean norm of A.
est_sval_upper_bounds : 1.12062e-11 1.04414e-12
: estimated upper bounds on singular value(s).
est_sval_lower_bounds : 0 0
: estimated lower bounds on singular value(s).
sval_numbers_for_bounds : 96 97
: index of singular value(s), for bounds.
est_norm_A_times_N : 9.53893e-13 : estimated norm(A*N).
est_err_bound_norm_A_times_N : 9.02516e-14 : estimated error bound for norm(A*N).
time : 0.916144 : total time taken (includes all timings below).
time_initialize : 0.0294718 : time to initialize including estimating the norm of A or R.
time_svd : 0.0392797 : total time taken by svd.
time_basis : 0.00807209 : time to compute basis.
opts_used : options for the spqr_rank functions:
get_details : 1 : extensive statistics returned
tol : 8.88178e-13
nsvals_large : 1 : # of large singular values to estimate.
nsvals_small : 1 : # of small singular values to estimate.
implicit_null_space_basis : true : N represented in Householder form.
start_with_A_transpose : false : spqr_cod computes qr(A).
ssi_tol : 8.88178e-13
ssi_min_block : 3 : ssi initial block size.
ssi_max_block : 10 : spqr_ssi max block size.
ssi_min_iters : 3 : min # of iterations before checking convergence
ssi_max_iters : 100 : max # of iterations before stopping spqr_ssi iterations
ssi_nblock_increment : 5 : block size inc. if convergence not met.
ssi_convergence_factor : 0.1 : spqr_ssi termination criterion.
k : ssp_min_iters : 4 : min # of iterations before checking convergence
ssp_max_iters : 10 : max # of ssp iterations before stopping iterations
ssp_convergence_factor : 0.1 ssp terminates when relative error drops below this value.
repeatable : true : internal random stream used to guarantee repeatability
info_spqr1 : statistics from first QR factorization.
nnzR_upper_bound: 501500
nnzH_upper_bound: 499500
number_of_frontal_matrices: 1
number_of_TBB_tasks: 1
rank_A_estimate: 105
number_of_column_singletons: 0
number_of_singleton_rows: 0
ordering: 'colamd'
memory_usage_in_bytes: 32184856
flops_upper_bound: 1.3368e+09
tol: 8.8818e-13
number_of_TBB_threads: 'default'
norm_E_fro: 1.0304e-11
spqr_compiled_with_TBB: 'no'
spqr_compiled_with_METIS: 'yes'
time: 0.6314
info_spqr2 : statistics from second QR factorization.
nnzR_upper_bound: 5565
nnzH_upper_bound: 93047
number_of_frontal_matrices: 1
number_of_TBB_tasks: 1
rank_A_estimate: 105
number_of_column_singletons: 0
number_of_singleton_rows: 0
ordering: 'colamd'
memory_usage_in_bytes: 2900145
flops_upper_bound: 18787808
tol: 0
number_of_TBB_threads: 'default'
norm_E_fro: 0
spqr_compiled_with_TBB: 'no'
spqr_compiled_with_METIS: 'yes'
time: 0.0279
stats_ssi : statistics from spqr_ssi.
flag : 2 : stats.rank may be correct for tolerance stats.tol,
but error bounds are too high to confirm this.
rank : 96 : estimate of numerical rank.
tol : 8.88178e-13 : numerical tolerance used.
est_svals_of_R : 8.90935e-13 8.86406e-13 8.83128e-13 8.76611e-13 8.52567e-13 8.33851e-13 7.9034e-13 7.87582e-13 7.7819e-13 7.65881e-13
: estimated singular value(s) of triangular matrix R.
est_error_bounds : 1.11465e-14 1.18174e-14 4.12246e-15 7.32091e-15 4.85468e-17 5.12503e-17 2.04029e-17 1.17029e-16 2.89358e-16 1.31374e-16
: error bounds for each singular value.
sval_numbers_for_bounds : 96 97 98 99 100 101 102 103 104 105
: index of singular value(s), for bounds.
norm_R_times_N : 8.86564e-13 : norm of (R*N), from spqr_ssi.
norm_R_transpose_times_NT : 8.86406e-13 : norm of (R'*NT), from spqr_ssi.
iters : 100 : iterations in spqr_ssi or spqr_ssp.
nsvals_large_found : 1 : number of large singular values found.
final_blocksize : 10 : final block size in spqr_ssi.
ssi_max_block_used : 10 : max block size for spqr_ssi.
ssi_min_block_used : 3 : initial block size for spqr_ssi.
time : 0.102325 : total time taken (includes all timings below).
time_initialize : 0.000494758 : time to initialize.
time_svd : 0.0345215 : total time taken by svd.
time_iters : 0.0981155 : time for spqr_ssi iterations.
time_est_error_bounds : 0.00048222 : time taken to estimate error bounds in spqr_ssi.
stats_ssp_N : statistics from spqr_ssp (A,N).
flag : 0 : ok. spqr_ssp converged with est. relative error <= opts_ssp.convergence_factor.
est_svals : 9.53893e-13
: estimated singular value(s) of A*N or A'*NT, from spqr_ssp.
est_error_bounds : 9.02516e-14
: error bounds for each singular value.
sval_numbers_for_bounds : 1
: index of singular value(s), for bounds.
iters : 6 : iterations in spqr_ssi or spqr_ssp.
time : 0.0786006 : total time taken (includes all timings below).
time_initialize : 0.000449645 : time to initialize.
time_svd : 0.00475822 : total time taken by svd.
time_iters : 0.0765276 : time for spqr_ssi iterations.
time_est_error_bounds : 3.1375e-05 : time taken to estimate error bounds in spqr_ssi.
stats_ssp_N.opts_used.k : 1 : number of singular values to compute in spqr_ssp(A,N).
---------------------------------------------------------------
another rare case:
downloading http://www.math.sjsu.edu/singular/matrices/mat/Regtools/heat_200.mat
to /Users/davis/sparse/MyPapers/Foster/spqr_rank/SJget/mat/Regtools/heat_200.mat
Problem =
title: 'HEAT 200x200 Test problem: inverse heat equation.'
A: [200x200 double]
b: [200x1 double]
x: [200x1 double]
SJid: 242
UFid: -1
name: 'Regtools/heat_200'
date: '1982'
author: 'Carasso, Elden'
ed: 'Per Christian Hansen'
kind: 'ill-posed problem'
notes: [17x73 char]
svals: [200x1 double]
sval_info: 'Routine svd from Matlab 7.6.0.324 (R2008a) used to calculate the singular values.'
flag : 4 : failure. Overflow during inverse power method.
rank : -1 : estimate of numerical rank.
rank_spqr : 198 : estimate of numerical rank from spqr.
This is normally an upper bound on the true rank.
tol : 1.11022e-14 : numerical tolerance used.
tol_alt : -1 : alternate numerical tolerance used.
normest_A : 0.355517 : estimate of Euclidean norm of A.
est_sval_upper_bounds : -1
: estimated upper bounds on singular value(s).
est_sval_lower_bounds : -1
: estimated lower bounds on singular value(s).
sval_numbers_for_bounds : -1
: index of singular value(s), for bounds.
est_norm_A_times_N : -1 : estimated norm(A*N).
time : 0.0405573 : total time taken (includes all timings below).
time_initialize : 0.0107148 : time to initialize including estimating the norm of A or R.
time_svd : 0 : total time taken by svd.
time_basis : 0 : time to compute basis.
opts_used : options for the spqr_rank functions:
get_details : 1 : extensive statistics returned
tol : 1.11022e-14
nsvals_large : 1 : # of large singular values to estimate.
nsvals_small : 1 : # of small singular values to estimate.
implicit_null_space_basis : true : N represented in Householder form.
start_with_A_transpose : false : spqr_cod computes qr(A).
ssi_tol : 1.11022e-14
ssi_min_block : 3 : ssi initial block size.
ssi_max_block : 10 : spqr_ssi max block size.
ssi_min_iters : 3 : min # of iterations before checking convergence
ssi_max_iters : 100 : max # of iterations before stopping spqr_ssi iterations
ssi_nblock_increment : 5 : block size inc. if convergence not met.
ssi_convergence_factor : 0.1 : spqr_ssi termination criterion.
k : ssp_min_iters : 4 : min # of iterations before checking convergence
ssp_max_iters : 10 : max # of ssp iterations before stopping iterations
ssp_convergence_factor : 0.1 ssp terminates when relative error drops below this value.
repeatable : true : internal random stream used to guarantee repeatability
info_spqr1 : statistics from first QR factorization.
nnzR_upper_bound: 20100
nnzH_upper_bound: 0
number_of_frontal_matrices: 1
number_of_TBB_tasks: 1
rank_A_estimate: 198
number_of_column_singletons: 0
number_of_singleton_rows: 0
ordering: 'colamd'
memory_usage_in_bytes: 727512
flops_upper_bound: 80200
tol: 1.1102e-14
number_of_TBB_threads: 'default'
norm_E_fro: 7.2492e-15
spqr_compiled_with_TBB: 'no'
spqr_compiled_with_METIS: 'yes'
time: 0.0097
stats_ssi : statistics from spqr_ssi.
flag : 4 : failure. Overflow during inverse power method.
rank : : estimate of numerical rank.
tol : 1.11022e-14 : numerical tolerance used.
tol_alt : -1 : alternate numerical tolerance used.
est_svals_of_R : 0
: estimated singular value(s) of triangular matrix R.
est_error_bounds : -1
: error bounds for each singular value.
sval_numbers_for_bounds : -1
: index of singular value(s), for bounds.
norm_R_times_N : -1 : norm of (R*N), from spqr_ssi.
norm_R_transpose_times_NT : -1 : norm of (R'*NT), from spqr_ssi.
iters : 1 : iterations in spqr_ssi or spqr_ssp.
nsvals_large_found : 0 : number of large singular values found.
final_blocksize : 3 : final block size in spqr_ssi.
ssi_max_block_used : 10 : max block size for spqr_ssi.
ssi_min_block_used : 3 : initial block size for spqr_ssi.
time : 0.00625787 : total time taken (includes all timings below).
time_initialize : 0.000474455 : time to initialize.
time_svd : 0 : total time taken by svd.
time_iters : 0.00088613 : time for spqr_ssi iterations.
time_est_error_bounds : 0 : time taken to estimate error bounds in spqr_ssi.
flag : 4 : failure. Overflow during inverse power method.
rank : : estimate of numerical rank.
tol : 1e-14 : numerical tolerance used.
tol_alt : -1 : alternate numerical tolerance used.
est_svals_of_R : 0
: estimated singular value(s) of triangular matrix R.
est_error_bounds : -1
: error bounds for each singular value.
sval_numbers_for_bounds : -1
: index of singular value(s), for bounds.
norm_R_times_N : -1 : norm of (R*N), from spqr_ssi.
norm_R_transpose_times_NT : -1 : norm of (R'*NT), from spqr_ssi.
iters : 1 : iterations in spqr_ssi or spqr_ssp.
nsvals_large_found : 0 : number of large singular values found.
final_blocksize : 3 : final block size in spqr_ssi.
ssi_max_block_used : 10 : max block size for spqr_ssi.
ssi_min_block_used : 3 : initial block size for spqr_ssi.
time : 0.0162294 : total time taken (includes all timings below).
time_initialize : 0.000768599 : time to initialize.
time_svd : 0 : total time taken by svd.
time_iters : 0.00321402 : time for spqr_ssi iterations.
time_est_error_bounds : 0 : time taken to estimate error bounds in spqr_ssi.
opts_used : options for the spqr_rank functions:
get_details : 1 : extensive statistics returned
tol : 1e-14
nsvals_large : 1 : # of large singular values to estimate.
nsvals_small : 1 : # of small singular values to estimate.
implicit_null_space_basis : true : N represented in Householder form.
start_with_A_transpose : false : spqr_cod computes qr(A).
ssi_tol : 1e-14
ssi_min_block : 3 : ssi initial block size.
ssi_max_block : 10 : spqr_ssi max block size.
ssi_min_iters : 3 : min # of iterations before checking convergence
ssi_max_iters : 100 : max # of iterations before stopping spqr_ssi iterations
ssi_nblock_increment : 5 : block size inc. if convergence not met.
ssi_convergence_factor : 0.1 : spqr_ssi termination criterion.
k : ssp_min_iters : 4 : min # of iterations before checking convergence
ssp_max_iters : 10 : max # of ssp iterations before stopping iterations
ssp_convergence_factor : 0.1 ssp terminates when relative error drops below this value.
repeatable : true : internal random stream used to guarantee repeatability
---------------------------------------------------------------
Near-overflow in spqr_ssi, 2nd test:
downloading http://www.math.sjsu.edu/singular/matrices/mat/GHS_indef/laser.mat
to /Users/davis/sparse/MyPapers/Foster/spqr_rank/SJget/mat/GHS_indef/laser.mat
Problem =
name: 'GHS_indef/laser'
title: 'Gould, Hu, & Scott:'
A: [3002x3002 double]
SJid: 137
UFid: 1239
date: '2004'
author: ''
ed: 'N. Gould, Y. Hu, J. Scott'
kind: 'materials problem'
svals: [3002x1 double]
sval_info: 'Routine svd from Matlab 7.6.0.324 (R2008a) used to calculate the singular values.'
flag : 3 : poor results. stats.rank is likely too high.
rank : 2990 : estimate of numerical rank.
tol : 2.66454e-12 : numerical tolerance used.
normest_R : 4.24912 : estimate of Euclidean norm of R (calculated for spqr_ssi).
est_svals_of_R : 1.98996e-252 8.38236e-253 6.11455e-253 3.17976e-253 1.10908e-253 4.70703e-254 5.73529e-255 2.30014e-256 5.15646e-287 4.69716e-287
: estimated singular value(s) of triangular matrix R.
est_error_bounds : 0.644895 0.619061 0.782134 0.644269 0.776826 0.707497 0.921243 0.966076 6.96139e-16 3.66017e-17
: error bounds for each singular value.
sval_numbers_for_bounds : 2991 2992 2993 2994 2995 2996 2997 2998 2999 3000
: index of singular value(s), for bounds.
norm_R_times_N : 0.935774 : norm of (R*N), from spqr_ssi.
norm_R_transpose_times_NT : 1.2243 : norm of (R'*NT), from spqr_ssi.
iters : 3 : iterations in spqr_ssi or spqr_ssp.
nsvals_large_found : 0 : number of large singular values found.
final_blocksize : 10 : final block size in spqr_ssi.
ssi_max_block_used : 10 : max block size for spqr_ssi.
ssi_min_block_used : 3 : initial block size for spqr_ssi.
time : 0.116426 : total time taken (includes all timings below).
time_initialize : 0.00408767 : time to initialize including estimating the norm of A or R.
time_svd : 0.0533761 : total time taken by svd.
time_iters : 0.0743084 : time for spqr_ssi iterations.
time_est_error_bounds : 0.0113516 : time taken to estimate error bounds in spqr_ssi.
opts_used : options for the spqr_rank functions:
get_details : 1 : extensive statistics returned
tol : 2.66454e-12
nsvals_large : 1 : # of large singular values to estimate.
nsvals_small : 1 : # of small singular values to estimate.
implicit_null_space_basis : true : N represented in Householder form.
start_with_A_transpose : false : spqr_cod computes qr(A).
ssi_tol : 2.66454e-12
ssi_min_block : 3 : ssi initial block size.
ssi_max_block : 10 : spqr_ssi max block size.
ssi_min_iters : 3 : min # of iterations before checking convergence
ssi_max_iters : 100 : max # of iterations before stopping spqr_ssi iterations
ssi_nblock_increment : 5 : block size inc. if convergence not met.
ssi_convergence_factor : 0.1 : spqr_ssi termination criterion.
k : ssp_min_iters : 4 : min # of iterations before checking convergence
ssp_max_iters : 10 : max # of ssp iterations before stopping iterations
ssp_convergence_factor : 0.1 ssp terminates when relative error drops below this value.
repeatable : true : internal random stream used to guarantee repeatability
flag : 3 : poor results. stats.rank is likely too high.
rank : 2990 : estimate of numerical rank.
tol : 2.66454e-12 : numerical tolerance used.
normest_R : 4.24912 : estimate of Euclidean norm of R (calculated for spqr_ssi).
est_svals_of_R : 1.98996e-252 8.38236e-253 6.11455e-253 3.17976e-253 1.10908e-253 4.70703e-254 5.73529e-255 2.30014e-256 5.15646e-287 4.69716e-287
: estimated singular value(s) of triangular matrix R.
est_error_bounds : 0.644895 0.619061 0.782134 0.644269 0.776826 0.707497 0.921243 0.966076 6.96139e-16 3.66017e-17
: error bounds for each singular value.
sval_numbers_for_bounds : 2991 2992 2993 2994 2995 2996 2997 2998 2999 3000
: index of singular value(s), for bounds.
norm_R_times_N : 0.935774 : norm of (R*N), from spqr_ssi.
norm_R_transpose_times_NT : 1.2243 : norm of (R'*NT), from spqr_ssi.
iters : 3 : iterations in spqr_ssi or spqr_ssp.
nsvals_large_found : 0 : number of large singular values found.
final_blocksize : 10 : final block size in spqr_ssi.
ssi_max_block_used : 10 : max block size for spqr_ssi.
ssi_min_block_used : 3 : initial block size for spqr_ssi.
time : 0.0834376 : total time taken (includes all timings below).
time_initialize : 0.0033231 : time to initialize including estimating the norm of A or R.
time_svd : 0.058933 : total time taken by svd.
time_iters : 0.0558443 : time for spqr_ssi iterations.
time_est_error_bounds : 0.0087643 : time taken to estimate error bounds in spqr_ssi.
opts_used : options for the spqr_rank functions:
get_details : 1 : extensive statistics returned
tol : 2.66454e-12
nsvals_large : 1 : # of large singular values to estimate.
nsvals_small : 1 : # of small singular values to estimate.
implicit_null_space_basis : true : N represented in Householder form.
start_with_A_transpose : false : spqr_cod computes qr(A).
ssi_tol : 2.66454e-12
ssi_min_block : 3 : ssi initial block size.
ssi_max_block : 10 : spqr_ssi max block size.
ssi_min_iters : 3 : min # of iterations before checking convergence
ssi_max_iters : 100 : max # of iterations before stopping spqr_ssi iterations
ssi_nblock_increment : 5 : block size inc. if convergence not met.
ssi_convergence_factor : 0.1 : spqr_ssi termination criterion.
k : ssp_min_iters : 4 : min # of iterations before checking convergence
ssp_max_iters : 10 : max # of ssp iterations before stopping iterations
ssp_convergence_factor : 0.1 ssp terminates when relative error drops below this value.
repeatable : true : internal random stream used to guarantee repeatability
flag : 3 : poor results. stats.rank is likely too high.
rank : 2990 : estimate of numerical rank.
tol : 2.66454e-12 : numerical tolerance used.
normest_R : 4.24912 : estimate of Euclidean norm of R (calculated for spqr_ssi).
est_svals_of_R : 1.98996e-252 8.38236e-253 6.11455e-253 3.17976e-253 1.10908e-253 4.70703e-254 5.73529e-255 2.30014e-256 5.15646e-287 4.69716e-287
: estimated singular value(s) of triangular matrix R.
est_error_bounds : 0.644895 0.619061 0.782134 0.644269 0.776826 0.707497 0.921243 0.966076 6.96139e-16 3.66017e-17
: error bounds for each singular value.
sval_numbers_for_bounds : 2991 2992 2993 2994 2995 2996 2997 2998 2999 3000
: index of singular value(s), for bounds.
norm_R_times_N : 0.935774 : norm of (R*N), from spqr_ssi.
norm_R_transpose_times_NT : 1.2243 : norm of (R'*NT), from spqr_ssi.
iters : 3 : iterations in spqr_ssi or spqr_ssp.
nsvals_large_found : 0 : number of large singular values found.
final_blocksize : 10 : final block size in spqr_ssi.
ssi_max_block_used : 10 : max block size for spqr_ssi.
ssi_min_block_used : 3 : initial block size for spqr_ssi.
time : 0.080309 : total time taken (includes all timings below).
time_initialize : 0.00337819 : time to initialize including estimating the norm of A or R.
time_svd : 0.0375243 : total time taken by svd.
time_iters : 0.0526907 : time for spqr_ssi iterations.
time_est_error_bounds : 0.00869351 : time taken to estimate error bounds in spqr_ssi.
opts_used : options for the spqr_rank functions:
get_details : 1 : extensive statistics returned
tol : 2.66454e-12
nsvals_large : 1 : # of large singular values to estimate.
nsvals_small : 1 : # of small singular values to estimate.
implicit_null_space_basis : true : N represented in Householder form.
start_with_A_transpose : false : spqr_cod computes qr(A).
ssi_tol : 2.66454e-12
ssi_min_block : 3 : ssi initial block size.
ssi_max_block : 10 : spqr_ssi max block size.
ssi_min_iters : 3 : min # of iterations before checking convergence
ssi_max_iters : 100 : max # of iterations before stopping spqr_ssi iterations
ssi_nblock_increment : 5 : block size inc. if convergence not met.
ssi_convergence_factor : 0.1 : spqr_ssi termination criterion.
k : ssp_min_iters : 4 : min # of iterations before checking convergence
ssp_max_iters : 10 : max # of ssp iterations before stopping iterations
ssp_convergence_factor : 0.1 ssp terminates when relative error drops below this value.
repeatable : true : internal random stream used to guarantee repeatability
flag : 3 : poor results. stats.rank is likely too high.
rank : 2990 : estimate of numerical rank.
tol : 2.66454e-12 : numerical tolerance used.
normest_R : 4.24912 : estimate of Euclidean norm of R (calculated for spqr_ssi).
est_svals_of_R : 1.98996e-252 8.38236e-253 6.11455e-253 3.17976e-253 1.10908e-253 4.70703e-254 5.73529e-255 2.30014e-256 5.15646e-287 4.69716e-287
: estimated singular value(s) of triangular matrix R.
est_error_bounds : 0.644895 0.619061 0.782134 0.644269 0.776826 0.707497 0.921243 0.966076 6.96139e-16 3.66017e-17
: error bounds for each singular value.
sval_numbers_for_bounds : 2991 2992 2993 2994 2995 2996 2997 2998 2999 3000
: index of singular value(s), for bounds.
norm_R_times_N : 0.935774 : norm of (R*N), from spqr_ssi.
norm_R_transpose_times_NT : 1.2243 : norm of (R'*NT), from spqr_ssi.
iters : 3 : iterations in spqr_ssi or spqr_ssp.
nsvals_large_found : 0 : number of large singular values found.
final_blocksize : 10 : final block size in spqr_ssi.
ssi_max_block_used : 10 : max block size for spqr_ssi.
ssi_min_block_used : 3 : initial block size for spqr_ssi.
time : 0.0908939 : total time taken (includes all timings below).
time_initialize : 0.00313181 : time to initialize including estimating the norm of A or R.
time_svd : 0.0562253 : total time taken by svd.
time_iters : 0.0635849 : time for spqr_ssi iterations.
time_est_error_bounds : 0.00869098 : time taken to estimate error bounds in spqr_ssi.
opts_used : options for the spqr_rank functions:
get_details : 1 : extensive statistics returned
tol : 2.66454e-12
nsvals_large : 1 : # of large singular values to estimate.
nsvals_small : 1 : # of small singular values to estimate.
implicit_null_space_basis : true : N represented in Householder form.
start_with_A_transpose : false : spqr_cod computes qr(A).
ssi_tol : 2.66454e-12
ssi_min_block : 3 : ssi initial block size.
ssi_max_block : 10 : spqr_ssi max block size.
ssi_min_iters : 3 : min # of iterations before checking convergence
ssi_max_iters : 100 : max # of iterations before stopping spqr_ssi iterations
ssi_nblock_increment : 5 : block size inc. if convergence not met.
ssi_convergence_factor : 0.1 : spqr_ssi termination criterion.
k : ssp_min_iters : 4 : min # of iterations before checking convergence
ssp_max_iters : 10 : max # of ssp iterations before stopping iterations
ssp_convergence_factor : 0.1 ssp terminates when relative error drops below this value.
repeatable : true : internal random stream used to guarantee repeatability
---------------------------------------------------------------
case where rank appears correct but with alternate tolerance:
downloading http://www.math.sjsu.edu/singular/matrices/mat/Sandia/oscil_dcop_34.mat
to /Users/davis/sparse/MyPapers/Foster/spqr_rank/SJget/mat/Sandia/oscil_dcop_34.mat
Problem =
name: 'Sandia/oscil_dcop_34'
title: 'Sandia/oscil_dcop_34 circuit simulation matrix. Sandia National Lab.'
A: [430x430 double]
b: [430x1 double]
SJid: 183
UFid: 1145
kind: 'subsequent circuit simulation problem'
notes: 'next: Sandia/oscil_dcop_35 first: Sandia/oscil_dcop_01'
date: '2003'
author: 'R. Hoekstra'
ed: 'T. Davis'
svals: [430x1 double]
sval_info: 'Routine svd from Matlab 7.6.0.324 (R2008a) used to calculate the singular values.'
flag : 2 : stats.rank may be correct for tolerance stats.tol,
but error bounds are too high to confirm this.
rank : 420 : estimate of numerical rank.
rank_spqr : 422 : estimate of numerical rank from spqr.
This is normally an upper bound on the true rank.
tol : 1.00117e-07 : numerical tolerance used.
normest_A : 2.001e+06 : estimate of Euclidean norm of A.
est_sval_upper_bounds : 2.38962e-07 1.00766e-07
: estimated upper bounds on singular value(s).
est_sval_lower_bounds : 2.03094e-08 0
: estimated lower bounds on singular value(s).
sval_numbers_for_bounds : 420 421
: index of singular value(s), for bounds.
est_norm_A_times_N : 9.99216e-08 : estimated norm(A*N).
est_err_bound_norm_A_times_N : 8.44851e-10 : estimated error bound for norm(A*N).
time : 0.0505359 : total time taken (includes all timings below).
time_initialize : 0.00408757 : time to initialize including estimating the norm of A or R.
time_svd : 0.0017679 : total time taken by svd.
time_basis : 0.000282482 : time to compute basis.
opts_used : options for the spqr_rank functions:
get_details : 1 : extensive statistics returned
tol : 1.00117e-07
nsvals_large : 1 : # of large singular values to estimate.
nsvals_small : 1 : # of small singular values to estimate.
implicit_null_space_basis : true : N represented in Householder form.
start_with_A_transpose : false : spqr_cod computes qr(A).
ssi_tol : 1.00117e-07
ssi_min_block : 3 : ssi initial block size.
ssi_max_block : 10 : spqr_ssi max block size.
ssi_min_iters : 3 : min # of iterations before checking convergence
ssi_max_iters : 100 : max # of iterations before stopping spqr_ssi iterations
ssi_nblock_increment : 5 : block size inc. if convergence not met.
ssi_convergence_factor : 0.1 : spqr_ssi termination criterion.
k : ssp_min_iters : 4 : min # of iterations before checking convergence
ssp_max_iters : 10 : max # of ssp iterations before stopping iterations
ssp_convergence_factor : 0.1 ssp terminates when relative error drops below this value.
repeatable : true : internal random stream used to guarantee repeatability
info_spqr1 : statistics from first QR factorization.
nnzR_upper_bound: 6559
nnzH_upper_bound: 3129
number_of_frontal_matrices: 47
number_of_TBB_tasks: 1
rank_A_estimate: 422
number_of_column_singletons: 20
number_of_singleton_rows: 20
ordering: 'colamd'
memory_usage_in_bytes: 199859
flops_upper_bound: 177357
tol: 1.0012e-07
number_of_TBB_threads: 'default'
norm_E_fro: 1.0836e-07
spqr_compiled_with_TBB: 'no'
spqr_compiled_with_METIS: 'yes'
time: 0.0018
info_spqr2 : statistics from second QR factorization.
nnzR_upper_bound: 16363
nnzH_upper_bound: 11663
number_of_frontal_matrices: 33
number_of_TBB_tasks: 1
rank_A_estimate: 422
number_of_column_singletons: 6
number_of_singleton_rows: 6
ordering: 'colamd'
memory_usage_in_bytes: 645040
flops_upper_bound: 1490925
tol: 0
number_of_TBB_threads: 'default'
norm_E_fro: 0
spqr_compiled_with_TBB: 'no'
spqr_compiled_with_METIS: 'yes'
time: 0.0034
stats_ssi : statistics from spqr_ssi.
flag : 1 : stats.rank may be correct for tolerance stats.tol,
but error bounds are too high to confirm this.
However, stats.rank appears to be correct for tolerance stats.tol_alt.
rank : 420 : estimate of numerical rank.
tol : 1.00117e-07 : numerical tolerance used.
tol_alt : 1.28674e-07 : alternate numerical tolerance used.
est_svals_of_R : 1.29636e-07 9.98811e-08 6.10815e-08
: estimated singular value(s) of triangular matrix R.
est_error_bounds : 9.61685e-10 1.05907e-08 3.36933e-11
: error bounds for each singular value.
sval_numbers_for_bounds : 420 421 422
: index of singular value(s), for bounds.
norm_R_times_N : 1.00998e-07 : norm of (R*N), from spqr_ssi.
norm_R_transpose_times_NT : 9.98811e-08 : norm of (R'*NT), from spqr_ssi.
iters : 6 : iterations in spqr_ssi or spqr_ssp.
nsvals_large_found : 1 : number of large singular values found.
final_blocksize : 3 : final block size in spqr_ssi.
ssi_max_block_used : 10 : max block size for spqr_ssi.
ssi_min_block_used : 3 : initial block size for spqr_ssi.
time : 0.00941014 : total time taken (includes all timings below).
time_initialize : 0.000496846 : time to initialize.
time_svd : 0.00134638 : total time taken by svd.
time_iters : 0.00568262 : time for spqr_ssi iterations.
time_est_error_bounds : 0.000479269 : time taken to estimate error bounds in spqr_ssi.
stats_ssp_N : statistics from spqr_ssp (A,N).
flag : 0 : ok. spqr_ssp converged with est. relative error <= opts_ssp.convergence_factor.
est_svals : 9.99216e-08
: estimated singular value(s) of A*N or A'*NT, from spqr_ssp.
est_error_bounds : 8.44851e-10
: error bounds for each singular value.
sval_numbers_for_bounds : 1
: index of singular value(s), for bounds.
iters : 4 : iterations in spqr_ssi or spqr_ssp.
time : 0.0149239 : total time taken (includes all timings below).
time_initialize : 0.000427153 : time to initialize.
time_svd : 0.000421518 : total time taken by svd.
time_iters : 0.012899 : time for spqr_ssi iterations.
time_est_error_bounds : 2.9054e-05 : time taken to estimate error bounds in spqr_ssi.
stats_ssp_N.opts_used.k : 1 : number of singular values to compute in spqr_ssp(A,N).
Please wait ...
1 of 10 : id: 215 HB/rgg010
downloading http://www.math.sjsu.edu/singular/matrices/mat/HB/rgg010.mat
to /Users/davis/sparse/MyPapers/Foster/spqr_rank/SJget/mat/HB/rgg010.mat
2 of 10 : id: 229 Regtools/foxgood_100
downloading http://www.math.sjsu.edu/singular/matrices/mat/Regtools/foxgood_100.mat
to /Users/davis/sparse/MyPapers/Foster/spqr_rank/SJget/mat/Regtools/foxgood_100.mat
3 of 10 : id: 241 Regtools/heat_100
downloading http://www.math.sjsu.edu/singular/matrices/mat/Regtools/heat_100.mat
to /Users/davis/sparse/MyPapers/Foster/spqr_rank/SJget/mat/Regtools/heat_100.mat
4 of 10 : id: 245 Regtools/i_laplace_100
downloading http://www.math.sjsu.edu/singular/matrices/mat/Regtools/i_laplace_100.mat
to /Users/davis/sparse/MyPapers/Foster/spqr_rank/SJget/mat/Regtools/i_laplace_100.mat
5 of 10 : id: 249 Regtools/parallax_100
downloading http://www.math.sjsu.edu/singular/matrices/mat/Regtools/parallax_100.mat
to /Users/davis/sparse/MyPapers/Foster/spqr_rank/SJget/mat/Regtools/parallax_100.mat
6 of 10 : id: 242 Regtools/heat_200
7 of 10 : id: 173 Sandia/oscil_dcop_24
downloading http://www.math.sjsu.edu/singular/matrices/mat/Sandia/oscil_dcop_24.mat
to /Users/davis/sparse/MyPapers/Foster/spqr_rank/SJget/mat/Sandia/oscil_dcop_24.mat
8 of 10 : id: 183 Sandia/oscil_dcop_34
9 of 10 : id: 263 Regtools/wing_500
downloading http://www.math.sjsu.edu/singular/matrices/mat/Regtools/wing_500.mat
to /Users/davis/sparse/MyPapers/Foster/spqr_rank/SJget/mat/Regtools/wing_500.mat
10 of 10 : id: 134 HB/jgl009
downloading http://www.math.sjsu.edu/singular/matrices/mat/HB/jgl009.mat
to /Users/davis/sparse/MyPapers/Foster/spqr_rank/SJget/mat/HB/jgl009.mat
All tests passed.
diary off
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