1 2 3-------------------------------------------------------- 4Input file: ../Matrix/A01 5name: Dense/0 n: 0 entries: 0 6-------------------------------------------------------- 7 8 9AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 10 dense row parameter: 10 11 (rows with more than max (10 * sqrt (n), 16) entries are 12 considered "dense", and placed last in output permutation) 13 aggressive absorption: yes 14 size of AMD integer: 8 15 16 17AMD version 2.4.6, May 4, 2016, results: 18 status: OK 19 n, dimension of A: 0 20 21 The following approximate statistics are for a subsequent 22 factorization of A(P,P) + A(P,P)'. They are slight upper 23 bounds if there are no dense rows/columns in A+A', and become 24 looser if dense rows/columns exist. 25 26Factorize PAP'=LDL' and solve Ax=b 27Nz in L: 0 Flop count: 0 28relative maxnorm of residual: 0 29Factorize A=LDL' and solve Ax=b 30Nz in L: 0 Flop count: 0 31relative maxnorm of residual: 0 32 33 34-------------------------------------------------------- 35Input file: ../Matrix/A02 36name: Dense/0 n: 0 entries: 0 (jumbled version) 37-------------------------------------------------------- 38 39 40AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 41 dense row parameter: 10 42 (rows with more than max (10 * sqrt (n), 16) entries are 43 considered "dense", and placed last in output permutation) 44 aggressive absorption: yes 45 size of AMD integer: 8 46 47 48AMD version 2.4.6, May 4, 2016, results: 49 status: OK 50 n, dimension of A: 0 51 52 The following approximate statistics are for a subsequent 53 factorization of A(P,P) + A(P,P)'. They are slight upper 54 bounds if there are no dense rows/columns in A+A', and become 55 looser if dense rows/columns exist. 56 57Factorize PAP'=LDL' and solve Ax=b 58Nz in L: 0 Flop count: 0 59relative maxnorm of residual: 0 60Factorize A=LDL' and solve Ax=b 61Nz in L: 0 Flop count: 0 62relative maxnorm of residual: 0 63 64 65-------------------------------------------------------- 66Input file: ../Matrix/A03 67name: Dense/1 n: 1 entries: 1 68-------------------------------------------------------- 69 70 71AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 72 dense row parameter: 10 73 (rows with more than max (10 * sqrt (n), 16) entries are 74 considered "dense", and placed last in output permutation) 75 aggressive absorption: yes 76 size of AMD integer: 8 77 78 79AMD version 2.4.6, May 4, 2016, results: 80 status: OK 81 n, dimension of A: 1 82 nz, number of nonzeros in A: 1 83 symmetry of A: 1.0000 84 number of nonzeros on diagonal: 1 85 nonzeros in pattern of A+A' (excl. diagonal): 0 86 # dense rows/columns of A+A': 0 87 memory used, in bytes: 72 88 # of memory compactions: 0 89 90 The following approximate statistics are for a subsequent 91 factorization of A(P,P) + A(P,P)'. They are slight upper 92 bounds if there are no dense rows/columns in A+A', and become 93 looser if dense rows/columns exist. 94 95 nonzeros in L (excluding diagonal): 0 96 nonzeros in L (including diagonal): 1 97 # divide operations for LDL' or LU: 0 98 # multiply-subtract operations for LDL': 0 99 # multiply-subtract operations for LU: 0 100 max nz. in any column of L (incl. diagonal): 1 101 102 chol flop count for real A, sqrt counted as 1 flop: 1 103 LDL' flop count for real A: 0 104 LDL' flop count for complex A: 0 105 LU flop count for real A (with no pivoting): 0 106 LU flop count for complex A (with no pivoting): 0 107 108Factorize PAP'=LDL' and solve Ax=b 109Nz in L: 0 Flop count: 0 110relative maxnorm of residual: 0 111Factorize A=LDL' and solve Ax=b 112Nz in L: 0 Flop count: 0 113relative maxnorm of residual: 0 114 115 116-------------------------------------------------------- 117Input file: ../Matrix/A04 118name: Dense/1 n: 1 entries: 2 (jumbled version) 119-------------------------------------------------------- 120 121 122AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 123 dense row parameter: 10 124 (rows with more than max (10 * sqrt (n), 16) entries are 125 considered "dense", and placed last in output permutation) 126 aggressive absorption: yes 127 size of AMD integer: 8 128 129 130AMD version 2.4.6, May 4, 2016, results: 131 status: OK, but jumbled 132 n, dimension of A: 1 133 nz, number of nonzeros in A: 1 134 symmetry of A: 1.0000 135 number of nonzeros on diagonal: 1 136 nonzeros in pattern of A+A' (excl. diagonal): 0 137 # dense rows/columns of A+A': 0 138 memory used, in bytes: 104 139 # of memory compactions: 0 140 141 The following approximate statistics are for a subsequent 142 factorization of A(P,P) + A(P,P)'. They are slight upper 143 bounds if there are no dense rows/columns in A+A', and become 144 looser if dense rows/columns exist. 145 146 nonzeros in L (excluding diagonal): 0 147 nonzeros in L (including diagonal): 1 148 # divide operations for LDL' or LU: 0 149 # multiply-subtract operations for LDL': 0 150 # multiply-subtract operations for LU: 0 151 max nz. in any column of L (incl. diagonal): 1 152 153 chol flop count for real A, sqrt counted as 1 flop: 1 154 LDL' flop count for real A: 0 155 LDL' flop count for complex A: 0 156 LU flop count for real A (with no pivoting): 0 157 LU flop count for complex A (with no pivoting): 0 158 159Factorize PAP'=LDL' and solve Ax=b 160Nz in L: 0 Flop count: 0 161relative maxnorm of residual: 8.32667e-17 162Factorize A=LDL' and solve Ax=b 163Nz in L: 0 Flop count: 0 164relative maxnorm of residual: 8.32667e-17 165 166 167-------------------------------------------------------- 168Input file: ../Matrix/A05 169name: Dense/2 n: 2 entries: 4 170-------------------------------------------------------- 171 172 173AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 174 dense row parameter: 10 175 (rows with more than max (10 * sqrt (n), 16) entries are 176 considered "dense", and placed last in output permutation) 177 aggressive absorption: yes 178 size of AMD integer: 8 179 180 181AMD version 2.4.6, May 4, 2016, results: 182 status: OK 183 n, dimension of A: 2 184 nz, number of nonzeros in A: 4 185 symmetry of A: 1.0000 186 number of nonzeros on diagonal: 2 187 nonzeros in pattern of A+A' (excl. diagonal): 2 188 # dense rows/columns of A+A': 0 189 memory used, in bytes: 160 190 # of memory compactions: 0 191 192 The following approximate statistics are for a subsequent 193 factorization of A(P,P) + A(P,P)'. They are slight upper 194 bounds if there are no dense rows/columns in A+A', and become 195 looser if dense rows/columns exist. 196 197 nonzeros in L (excluding diagonal): 1 198 nonzeros in L (including diagonal): 3 199 # divide operations for LDL' or LU: 1 200 # multiply-subtract operations for LDL': 1 201 # multiply-subtract operations for LU: 1 202 max nz. in any column of L (incl. diagonal): 2 203 204 chol flop count for real A, sqrt counted as 1 flop: 5 205 LDL' flop count for real A: 3 206 LDL' flop count for complex A: 17 207 LU flop count for real A (with no pivoting): 3 208 LU flop count for complex A (with no pivoting): 17 209 210Factorize PAP'=LDL' and solve Ax=b 211Nz in L: 1 Flop count: 3 212relative maxnorm of residual: 5.55112e-17 213Factorize A=LDL' and solve Ax=b 214Nz in L: 1 Flop count: 3 215relative maxnorm of residual: 5.55112e-17 216 217 218-------------------------------------------------------- 219Input file: ../Matrix/A06 220name: Dense/2 n: 2 entries: 5 (jumbled version) 221-------------------------------------------------------- 222 223 224AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 225 dense row parameter: 10 226 (rows with more than max (10 * sqrt (n), 16) entries are 227 considered "dense", and placed last in output permutation) 228 aggressive absorption: yes 229 size of AMD integer: 8 230 231 232AMD version 2.4.6, May 4, 2016, results: 233 status: OK, but jumbled 234 n, dimension of A: 2 235 nz, number of nonzeros in A: 4 236 symmetry of A: 1.0000 237 number of nonzeros on diagonal: 2 238 nonzeros in pattern of A+A' (excl. diagonal): 2 239 # dense rows/columns of A+A': 0 240 memory used, in bytes: 224 241 # of memory compactions: 0 242 243 The following approximate statistics are for a subsequent 244 factorization of A(P,P) + A(P,P)'. They are slight upper 245 bounds if there are no dense rows/columns in A+A', and become 246 looser if dense rows/columns exist. 247 248 nonzeros in L (excluding diagonal): 1 249 nonzeros in L (including diagonal): 3 250 # divide operations for LDL' or LU: 1 251 # multiply-subtract operations for LDL': 1 252 # multiply-subtract operations for LU: 1 253 max nz. in any column of L (incl. diagonal): 2 254 255 chol flop count for real A, sqrt counted as 1 flop: 5 256 LDL' flop count for real A: 3 257 LDL' flop count for complex A: 17 258 LU flop count for real A (with no pivoting): 3 259 LU flop count for complex A (with no pivoting): 17 260 261Factorize PAP'=LDL' and solve Ax=b 262Nz in L: 1 Flop count: 3 263relative maxnorm of residual: 1.11022e-16 264Factorize A=LDL' and solve Ax=b 265Nz in L: 1 Flop count: 3 266relative maxnorm of residual: 1.11022e-16 267 268 269-------------------------------------------------------- 270Input file: ../Matrix/A07 271name: Dense/3 n: 3 entries: 9 272-------------------------------------------------------- 273 274 275AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 276 dense row parameter: 10 277 (rows with more than max (10 * sqrt (n), 16) entries are 278 considered "dense", and placed last in output permutation) 279 aggressive absorption: yes 280 size of AMD integer: 8 281 282 283AMD version 2.4.6, May 4, 2016, results: 284 status: OK 285 n, dimension of A: 3 286 nz, number of nonzeros in A: 9 287 symmetry of A: 1.0000 288 number of nonzeros on diagonal: 3 289 nonzeros in pattern of A+A' (excl. diagonal): 6 290 # dense rows/columns of A+A': 0 291 memory used, in bytes: 272 292 # of memory compactions: 0 293 294 The following approximate statistics are for a subsequent 295 factorization of A(P,P) + A(P,P)'. They are slight upper 296 bounds if there are no dense rows/columns in A+A', and become 297 looser if dense rows/columns exist. 298 299 nonzeros in L (excluding diagonal): 3 300 nonzeros in L (including diagonal): 6 301 # divide operations for LDL' or LU: 3 302 # multiply-subtract operations for LDL': 4 303 # multiply-subtract operations for LU: 5 304 max nz. in any column of L (incl. diagonal): 3 305 306 chol flop count for real A, sqrt counted as 1 flop: 14 307 LDL' flop count for real A: 11 308 LDL' flop count for complex A: 59 309 LU flop count for real A (with no pivoting): 13 310 LU flop count for complex A (with no pivoting): 67 311 312Factorize PAP'=LDL' and solve Ax=b 313Nz in L: 3 Flop count: 11 314relative maxnorm of residual: 1.11022e-16 315Factorize A=LDL' and solve Ax=b 316Nz in L: 3 Flop count: 11 317relative maxnorm of residual: 1.11022e-16 318 319 320-------------------------------------------------------- 321Input file: ../Matrix/A08 322name: Dense/3 n: 3 entries: 11 (jumbled version) 323-------------------------------------------------------- 324 325 326AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 327 dense row parameter: 10 328 (rows with more than max (10 * sqrt (n), 16) entries are 329 considered "dense", and placed last in output permutation) 330 aggressive absorption: yes 331 size of AMD integer: 8 332 333 334AMD version 2.4.6, May 4, 2016, results: 335 status: OK, but jumbled 336 n, dimension of A: 3 337 nz, number of nonzeros in A: 9 338 symmetry of A: 1.0000 339 number of nonzeros on diagonal: 3 340 nonzeros in pattern of A+A' (excl. diagonal): 6 341 # dense rows/columns of A+A': 0 342 memory used, in bytes: 392 343 # of memory compactions: 0 344 345 The following approximate statistics are for a subsequent 346 factorization of A(P,P) + A(P,P)'. They are slight upper 347 bounds if there are no dense rows/columns in A+A', and become 348 looser if dense rows/columns exist. 349 350 nonzeros in L (excluding diagonal): 3 351 nonzeros in L (including diagonal): 6 352 # divide operations for LDL' or LU: 3 353 # multiply-subtract operations for LDL': 4 354 # multiply-subtract operations for LU: 5 355 max nz. in any column of L (incl. diagonal): 3 356 357 chol flop count for real A, sqrt counted as 1 flop: 14 358 LDL' flop count for real A: 11 359 LDL' flop count for complex A: 59 360 LU flop count for real A (with no pivoting): 13 361 LU flop count for complex A (with no pivoting): 67 362 363Factorize PAP'=LDL' and solve Ax=b 364Nz in L: 3 Flop count: 11 365relative maxnorm of residual: 1.38778e-16 366Factorize A=LDL' and solve Ax=b 367Nz in L: 3 Flop count: 11 368relative maxnorm of residual: 1.38778e-16 369 370 371-------------------------------------------------------- 372Input file: ../Matrix/A09 373name: HB/can_24 n: 24 entries: 160 374-------------------------------------------------------- 375 376 377AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 378 dense row parameter: 10 379 (rows with more than max (10 * sqrt (n), 16) entries are 380 considered "dense", and placed last in output permutation) 381 aggressive absorption: yes 382 size of AMD integer: 8 383 384 385AMD version 2.4.6, May 4, 2016, results: 386 status: OK 387 n, dimension of A: 24 388 nz, number of nonzeros in A: 160 389 symmetry of A: 1.0000 390 number of nonzeros on diagonal: 24 391 nonzeros in pattern of A+A' (excl. diagonal): 136 392 # dense rows/columns of A+A': 0 393 memory used, in bytes: 3032 394 # of memory compactions: 0 395 396 The following approximate statistics are for a subsequent 397 factorization of A(P,P) + A(P,P)'. They are slight upper 398 bounds if there are no dense rows/columns in A+A', and become 399 looser if dense rows/columns exist. 400 401 nonzeros in L (excluding diagonal): 97 402 nonzeros in L (including diagonal): 121 403 # divide operations for LDL' or LU: 97 404 # multiply-subtract operations for LDL': 275 405 # multiply-subtract operations for LU: 453 406 max nz. in any column of L (incl. diagonal): 8 407 408 chol flop count for real A, sqrt counted as 1 flop: 671 409 LDL' flop count for real A: 647 410 LDL' flop count for complex A: 3073 411 LU flop count for real A (with no pivoting): 1003 412 LU flop count for complex A (with no pivoting): 4497 413 414Factorize PAP'=LDL' and solve Ax=b 415Nz in L: 96 Flop count: 632 416Ax=b not solved since D(1,1) is zero. 417Factorize A=LDL' and solve Ax=b 418Nz in L: 146 Flop count: 1360 419Ax=b not solved since D(5,5) is zero. 420 421 422-------------------------------------------------------- 423Input file: ../Matrix/A10 424name: HB/can_24 n: 24 entries: 188 (jumbled version) 425-------------------------------------------------------- 426 427 428AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 429 dense row parameter: 10 430 (rows with more than max (10 * sqrt (n), 16) entries are 431 considered "dense", and placed last in output permutation) 432 aggressive absorption: yes 433 size of AMD integer: 8 434 435 436AMD version 2.4.6, May 4, 2016, results: 437 status: OK, but jumbled 438 n, dimension of A: 24 439 nz, number of nonzeros in A: 160 440 symmetry of A: 1.0000 441 number of nonzeros on diagonal: 24 442 nonzeros in pattern of A+A' (excl. diagonal): 136 443 # dense rows/columns of A+A': 0 444 memory used, in bytes: 4736 445 # of memory compactions: 0 446 447 The following approximate statistics are for a subsequent 448 factorization of A(P,P) + A(P,P)'. They are slight upper 449 bounds if there are no dense rows/columns in A+A', and become 450 looser if dense rows/columns exist. 451 452 nonzeros in L (excluding diagonal): 97 453 nonzeros in L (including diagonal): 121 454 # divide operations for LDL' or LU: 97 455 # multiply-subtract operations for LDL': 275 456 # multiply-subtract operations for LU: 453 457 max nz. in any column of L (incl. diagonal): 8 458 459 chol flop count for real A, sqrt counted as 1 flop: 671 460 LDL' flop count for real A: 647 461 LDL' flop count for complex A: 3073 462 LU flop count for real A (with no pivoting): 1003 463 LU flop count for complex A (with no pivoting): 4497 464 465Factorize PAP'=LDL' and solve Ax=b 466Nz in L: 96 Flop count: 632 467Ax=b not solved since D(1,1) is zero. 468Factorize A=LDL' and solve Ax=b 469Nz in L: 146 Flop count: 1360 470Ax=b not solved since D(5,5) is zero. 471 472 473-------------------------------------------------------- 474Input file: ../Matrix/A11 475name: FIDAP/ex5 n: 27 entries: 279 476-------------------------------------------------------- 477 478 479AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 480 dense row parameter: 10 481 (rows with more than max (10 * sqrt (n), 16) entries are 482 considered "dense", and placed last in output permutation) 483 aggressive absorption: yes 484 size of AMD integer: 8 485 486 487AMD version 2.4.6, May 4, 2016, results: 488 status: OK 489 n, dimension of A: 27 490 nz, number of nonzeros in A: 279 491 symmetry of A: 1.0000 492 number of nonzeros on diagonal: 27 493 nonzeros in pattern of A+A' (excl. diagonal): 252 494 # dense rows/columns of A+A': 0 495 memory used, in bytes: 4360 496 # of memory compactions: 0 497 498 The following approximate statistics are for a subsequent 499 factorization of A(P,P) + A(P,P)'. They are slight upper 500 bounds if there are no dense rows/columns in A+A', and become 501 looser if dense rows/columns exist. 502 503 nonzeros in L (excluding diagonal): 126 504 nonzeros in L (including diagonal): 153 505 # divide operations for LDL' or LU: 126 506 # multiply-subtract operations for LDL': 414 507 # multiply-subtract operations for LU: 702 508 max nz. in any column of L (incl. diagonal): 9 509 510 chol flop count for real A, sqrt counted as 1 flop: 981 511 LDL' flop count for real A: 954 512 LDL' flop count for complex A: 4446 513 LU flop count for real A (with no pivoting): 1530 514 LU flop count for complex A (with no pivoting): 6750 515 516Factorize PAP'=LDL' and solve Ax=b 517Nz in L: 126 Flop count: 954 518relative maxnorm of residual: 2.59625e-10 519Factorize A=LDL' and solve Ax=b 520Nz in L: 276 Flop count: 4206 521relative maxnorm of residual: 2.72848e-10 522 523 524-------------------------------------------------------- 525Input file: ../Matrix/A12 526name: FIDAP/ex5 n: 27 entries: 325 (jumbled version) 527-------------------------------------------------------- 528 529 530AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 531 dense row parameter: 10 532 (rows with more than max (10 * sqrt (n), 16) entries are 533 considered "dense", and placed last in output permutation) 534 aggressive absorption: yes 535 size of AMD integer: 8 536 537 538AMD version 2.4.6, May 4, 2016, results: 539 status: OK, but jumbled 540 n, dimension of A: 27 541 nz, number of nonzeros in A: 279 542 symmetry of A: 1.0000 543 number of nonzeros on diagonal: 27 544 nonzeros in pattern of A+A' (excl. diagonal): 252 545 # dense rows/columns of A+A': 0 546 memory used, in bytes: 7184 547 # of memory compactions: 0 548 549 The following approximate statistics are for a subsequent 550 factorization of A(P,P) + A(P,P)'. They are slight upper 551 bounds if there are no dense rows/columns in A+A', and become 552 looser if dense rows/columns exist. 553 554 nonzeros in L (excluding diagonal): 126 555 nonzeros in L (including diagonal): 153 556 # divide operations for LDL' or LU: 126 557 # multiply-subtract operations for LDL': 414 558 # multiply-subtract operations for LU: 702 559 max nz. in any column of L (incl. diagonal): 9 560 561 chol flop count for real A, sqrt counted as 1 flop: 981 562 LDL' flop count for real A: 954 563 LDL' flop count for complex A: 4446 564 LU flop count for real A (with no pivoting): 1530 565 LU flop count for complex A (with no pivoting): 6750 566 567Factorize PAP'=LDL' and solve Ax=b 568Nz in L: 126 Flop count: 954 569relative maxnorm of residual: 3.27418e-10 570Factorize A=LDL' and solve Ax=b 571Nz in L: 276 Flop count: 4206 572relative maxnorm of residual: 2.32376e-10 573 574 575-------------------------------------------------------- 576Input file: ../Matrix/A13 577name: HB/bcsstk01 n: 48 entries: 400 578-------------------------------------------------------- 579 580 581AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 582 dense row parameter: 10 583 (rows with more than max (10 * sqrt (n), 16) entries are 584 considered "dense", and placed last in output permutation) 585 aggressive absorption: yes 586 size of AMD integer: 8 587 588 589AMD version 2.4.6, May 4, 2016, results: 590 status: OK 591 n, dimension of A: 48 592 nz, number of nonzeros in A: 400 593 symmetry of A: 1.0000 594 number of nonzeros on diagonal: 48 595 nonzeros in pattern of A+A' (excl. diagonal): 352 596 # dense rows/columns of A+A': 0 597 memory used, in bytes: 6832 598 # of memory compactions: 0 599 600 The following approximate statistics are for a subsequent 601 factorization of A(P,P) + A(P,P)'. They are slight upper 602 bounds if there are no dense rows/columns in A+A', and become 603 looser if dense rows/columns exist. 604 605 nonzeros in L (excluding diagonal): 441 606 nonzeros in L (including diagonal): 489 607 # divide operations for LDL' or LU: 441 608 # multiply-subtract operations for LDL': 2760 609 # multiply-subtract operations for LU: 5079 610 max nz. in any column of L (incl. diagonal): 20 611 612 chol flop count for real A, sqrt counted as 1 flop: 6009 613 LDL' flop count for real A: 5961 614 LDL' flop count for complex A: 26049 615 LU flop count for real A (with no pivoting): 10599 616 LU flop count for complex A (with no pivoting): 44601 617 618Factorize PAP'=LDL' and solve Ax=b 619Nz in L: 441 Flop count: 5961 620relative maxnorm of residual: 2.38712e-13 621Factorize A=LDL' and solve Ax=b 622Nz in L: 829 Flop count: 20103 623relative maxnorm of residual: 2.27374e-13 624 625 626-------------------------------------------------------- 627Input file: ../Matrix/A14 628name: HB/bcsstk01 n: 48 entries: 472 (jumbled version) 629-------------------------------------------------------- 630 631 632AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 633 dense row parameter: 10 634 (rows with more than max (10 * sqrt (n), 16) entries are 635 considered "dense", and placed last in output permutation) 636 aggressive absorption: yes 637 size of AMD integer: 8 638 639 640AMD version 2.4.6, May 4, 2016, results: 641 status: OK, but jumbled 642 n, dimension of A: 48 643 nz, number of nonzeros in A: 400 644 symmetry of A: 1.0000 645 number of nonzeros on diagonal: 48 646 nonzeros in pattern of A+A' (excl. diagonal): 352 647 # dense rows/columns of A+A': 0 648 memory used, in bytes: 11000 649 # of memory compactions: 0 650 651 The following approximate statistics are for a subsequent 652 factorization of A(P,P) + A(P,P)'. They are slight upper 653 bounds if there are no dense rows/columns in A+A', and become 654 looser if dense rows/columns exist. 655 656 nonzeros in L (excluding diagonal): 441 657 nonzeros in L (including diagonal): 489 658 # divide operations for LDL' or LU: 441 659 # multiply-subtract operations for LDL': 2760 660 # multiply-subtract operations for LU: 5079 661 max nz. in any column of L (incl. diagonal): 20 662 663 chol flop count for real A, sqrt counted as 1 flop: 6009 664 LDL' flop count for real A: 5961 665 LDL' flop count for complex A: 26049 666 LU flop count for real A (with no pivoting): 10599 667 LU flop count for complex A (with no pivoting): 44601 668 669Factorize PAP'=LDL' and solve Ax=b 670Nz in L: 441 Flop count: 5961 671relative maxnorm of residual: 2.27374e-13 672Factorize A=LDL' and solve Ax=b 673Nz in L: 829 Flop count: 20103 674relative maxnorm of residual: 3.83693e-13 675 676 677-------------------------------------------------------- 678Input file: ../Matrix/A15 679name: HB/bcsstm01 n: 48 entries: 24 680-------------------------------------------------------- 681 682 683AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 684 dense row parameter: 10 685 (rows with more than max (10 * sqrt (n), 16) entries are 686 considered "dense", and placed last in output permutation) 687 aggressive absorption: yes 688 size of AMD integer: 8 689 690 691AMD version 2.4.6, May 4, 2016, results: 692 status: OK 693 n, dimension of A: 48 694 nz, number of nonzeros in A: 24 695 symmetry of A: 1.0000 696 number of nonzeros on diagonal: 24 697 nonzeros in pattern of A+A' (excl. diagonal): 0 698 # dense rows/columns of A+A': 0 699 memory used, in bytes: 3456 700 # of memory compactions: 0 701 702 The following approximate statistics are for a subsequent 703 factorization of A(P,P) + A(P,P)'. They are slight upper 704 bounds if there are no dense rows/columns in A+A', and become 705 looser if dense rows/columns exist. 706 707 nonzeros in L (excluding diagonal): 0 708 nonzeros in L (including diagonal): 48 709 # divide operations for LDL' or LU: 0 710 # multiply-subtract operations for LDL': 0 711 # multiply-subtract operations for LU: 0 712 max nz. in any column of L (incl. diagonal): 1 713 714 chol flop count for real A, sqrt counted as 1 flop: 48 715 LDL' flop count for real A: 0 716 LDL' flop count for complex A: 0 717 LU flop count for real A (with no pivoting): 0 718 LU flop count for complex A (with no pivoting): 0 719 720Factorize PAP'=LDL' and solve Ax=b 721Nz in L: 0 Flop count: 0 722Ax=b not solved since D(3,3) is zero. 723Factorize A=LDL' and solve Ax=b 724Nz in L: 0 Flop count: 0 725Ax=b not solved since D(3,3) is zero. 726 727 728-------------------------------------------------------- 729Input file: ../Matrix/A16 730name: HB/bcsstm01 n: 48 entries: 26 (jumbled version) 731-------------------------------------------------------- 732 733 734AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 735 dense row parameter: 10 736 (rows with more than max (10 * sqrt (n), 16) entries are 737 considered "dense", and placed last in output permutation) 738 aggressive absorption: yes 739 size of AMD integer: 8 740 741 742AMD version 2.4.6, May 4, 2016, results: 743 status: OK, but jumbled 744 n, dimension of A: 48 745 nz, number of nonzeros in A: 24 746 symmetry of A: 1.0000 747 number of nonzeros on diagonal: 24 748 nonzeros in pattern of A+A' (excl. diagonal): 0 749 # dense rows/columns of A+A': 0 750 memory used, in bytes: 4056 751 # of memory compactions: 0 752 753 The following approximate statistics are for a subsequent 754 factorization of A(P,P) + A(P,P)'. They are slight upper 755 bounds if there are no dense rows/columns in A+A', and become 756 looser if dense rows/columns exist. 757 758 nonzeros in L (excluding diagonal): 0 759 nonzeros in L (including diagonal): 48 760 # divide operations for LDL' or LU: 0 761 # multiply-subtract operations for LDL': 0 762 # multiply-subtract operations for LU: 0 763 max nz. in any column of L (incl. diagonal): 1 764 765 chol flop count for real A, sqrt counted as 1 flop: 48 766 LDL' flop count for real A: 0 767 LDL' flop count for complex A: 0 768 LU flop count for real A (with no pivoting): 0 769 LU flop count for complex A (with no pivoting): 0 770 771Factorize PAP'=LDL' and solve Ax=b 772Nz in L: 0 Flop count: 0 773Ax=b not solved since D(3,3) is zero. 774Factorize A=LDL' and solve Ax=b 775Nz in L: 0 Flop count: 0 776Ax=b not solved since D(3,3) is zero. 777 778 779-------------------------------------------------------- 780Input file: ../Matrix/A17 781name: Pothen/mesh1e1 n: 48 entries: 306 782-------------------------------------------------------- 783 784 785AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 786 dense row parameter: 10 787 (rows with more than max (10 * sqrt (n), 16) entries are 788 considered "dense", and placed last in output permutation) 789 aggressive absorption: yes 790 size of AMD integer: 8 791 792 793AMD version 2.4.6, May 4, 2016, results: 794 status: OK 795 n, dimension of A: 48 796 nz, number of nonzeros in A: 306 797 symmetry of A: 1.0000 798 number of nonzeros on diagonal: 48 799 nonzeros in pattern of A+A' (excl. diagonal): 258 800 # dense rows/columns of A+A': 0 801 memory used, in bytes: 5928 802 # of memory compactions: 1 803 804 The following approximate statistics are for a subsequent 805 factorization of A(P,P) + A(P,P)'. They are slight upper 806 bounds if there are no dense rows/columns in A+A', and become 807 looser if dense rows/columns exist. 808 809 nonzeros in L (excluding diagonal): 288 810 nonzeros in L (including diagonal): 336 811 # divide operations for LDL' or LU: 288 812 # multiply-subtract operations for LDL': 1171 813 # multiply-subtract operations for LU: 2054 814 max nz. in any column of L (incl. diagonal): 13 815 816 chol flop count for real A, sqrt counted as 1 flop: 2678 817 LDL' flop count for real A: 2630 818 LDL' flop count for complex A: 11960 819 LU flop count for real A (with no pivoting): 4396 820 LU flop count for complex A (with no pivoting): 19024 821 822Factorize PAP'=LDL' and solve Ax=b 823Nz in L: 288 Flop count: 2630 824relative maxnorm of residual: 5.96745e-16 825Factorize A=LDL' and solve Ax=b 826Nz in L: 511 Flop count: 7383 827relative maxnorm of residual: 6.93889e-16 828 829 830-------------------------------------------------------- 831Input file: ../Matrix/A18 832name: Pothen/mesh1e1 n: 48 entries: 359 (jumbled version) 833-------------------------------------------------------- 834 835 836AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 837 dense row parameter: 10 838 (rows with more than max (10 * sqrt (n), 16) entries are 839 considered "dense", and placed last in output permutation) 840 aggressive absorption: yes 841 size of AMD integer: 8 842 843 844AMD version 2.4.6, May 4, 2016, results: 845 status: OK, but jumbled 846 n, dimension of A: 48 847 nz, number of nonzeros in A: 306 848 symmetry of A: 1.0000 849 number of nonzeros on diagonal: 48 850 nonzeros in pattern of A+A' (excl. diagonal): 258 851 # dense rows/columns of A+A': 0 852 memory used, in bytes: 9192 853 # of memory compactions: 1 854 855 The following approximate statistics are for a subsequent 856 factorization of A(P,P) + A(P,P)'. They are slight upper 857 bounds if there are no dense rows/columns in A+A', and become 858 looser if dense rows/columns exist. 859 860 nonzeros in L (excluding diagonal): 288 861 nonzeros in L (including diagonal): 336 862 # divide operations for LDL' or LU: 288 863 # multiply-subtract operations for LDL': 1171 864 # multiply-subtract operations for LU: 2054 865 max nz. in any column of L (incl. diagonal): 13 866 867 chol flop count for real A, sqrt counted as 1 flop: 2678 868 LDL' flop count for real A: 2630 869 LDL' flop count for complex A: 11960 870 LU flop count for real A (with no pivoting): 4396 871 LU flop count for complex A (with no pivoting): 19024 872 873Factorize PAP'=LDL' and solve Ax=b 874Nz in L: 288 Flop count: 2630 875relative maxnorm of residual: 5.55112e-16 876Factorize A=LDL' and solve Ax=b 877Nz in L: 511 Flop count: 7383 878relative maxnorm of residual: 5.55112e-16 879 880 881-------------------------------------------------------- 882Input file: ../Matrix/A19 883name: Bai/bfwb62 n: 62 entries: 342 884-------------------------------------------------------- 885 886 887AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 888 dense row parameter: 10 889 (rows with more than max (10 * sqrt (n), 16) entries are 890 considered "dense", and placed last in output permutation) 891 aggressive absorption: yes 892 size of AMD integer: 8 893 894 895AMD version 2.4.6, May 4, 2016, results: 896 status: OK 897 n, dimension of A: 62 898 nz, number of nonzeros in A: 342 899 symmetry of A: 1.0000 900 number of nonzeros on diagonal: 62 901 nonzeros in pattern of A+A' (excl. diagonal): 280 902 # dense rows/columns of A+A': 0 903 memory used, in bytes: 7152 904 # of memory compactions: 0 905 906 The following approximate statistics are for a subsequent 907 factorization of A(P,P) + A(P,P)'. They are slight upper 908 bounds if there are no dense rows/columns in A+A', and become 909 looser if dense rows/columns exist. 910 911 nonzeros in L (excluding diagonal): 226 912 nonzeros in L (including diagonal): 288 913 # divide operations for LDL' or LU: 226 914 # multiply-subtract operations for LDL': 623 915 # multiply-subtract operations for LU: 1020 916 max nz. in any column of L (incl. diagonal): 9 917 918 chol flop count for real A, sqrt counted as 1 flop: 1534 919 LDL' flop count for real A: 1472 920 LDL' flop count for complex A: 7018 921 LU flop count for real A (with no pivoting): 2266 922 LU flop count for complex A (with no pivoting): 10194 923 924Factorize PAP'=LDL' and solve Ax=b 925Nz in L: 226 Flop count: 1472 926relative maxnorm of residual: 5.55112e-16 927Factorize A=LDL' and solve Ax=b 928Nz in L: 662 Flop count: 11350 929relative maxnorm of residual: 1.11022e-15 930 931 932-------------------------------------------------------- 933Input file: ../Matrix/A20 934name: Bai/bfwb62 n: 62 entries: 407 (jumbled version) 935-------------------------------------------------------- 936 937 938AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 939 dense row parameter: 10 940 (rows with more than max (10 * sqrt (n), 16) entries are 941 considered "dense", and placed last in output permutation) 942 aggressive absorption: yes 943 size of AMD integer: 8 944 945 946AMD version 2.4.6, May 4, 2016, results: 947 status: OK, but jumbled 948 n, dimension of A: 62 949 nz, number of nonzeros in A: 342 950 symmetry of A: 1.0000 951 number of nonzeros on diagonal: 62 952 nonzeros in pattern of A+A' (excl. diagonal): 280 953 # dense rows/columns of A+A': 0 954 memory used, in bytes: 10912 955 # of memory compactions: 0 956 957 The following approximate statistics are for a subsequent 958 factorization of A(P,P) + A(P,P)'. They are slight upper 959 bounds if there are no dense rows/columns in A+A', and become 960 looser if dense rows/columns exist. 961 962 nonzeros in L (excluding diagonal): 226 963 nonzeros in L (including diagonal): 288 964 # divide operations for LDL' or LU: 226 965 # multiply-subtract operations for LDL': 623 966 # multiply-subtract operations for LU: 1020 967 max nz. in any column of L (incl. diagonal): 9 968 969 chol flop count for real A, sqrt counted as 1 flop: 1534 970 LDL' flop count for real A: 1472 971 LDL' flop count for complex A: 7018 972 LU flop count for real A (with no pivoting): 2266 973 LU flop count for complex A (with no pivoting): 10194 974 975Factorize PAP'=LDL' and solve Ax=b 976Nz in L: 226 Flop count: 1472 977relative maxnorm of residual: 5.68434e-14 978Factorize A=LDL' and solve Ax=b 979Nz in L: 662 Flop count: 11350 980relative maxnorm of residual: 2.15827e-12 981 982 983-------------------------------------------------------- 984Input file: ../Matrix/A21 985name: HB/bcsstk02 n: 66 entries: 4356 986-------------------------------------------------------- 987 988 989AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 990 dense row parameter: 10 991 (rows with more than max (10 * sqrt (n), 16) entries are 992 considered "dense", and placed last in output permutation) 993 aggressive absorption: yes 994 size of AMD integer: 8 995 996 997AMD version 2.4.6, May 4, 2016, results: 998 status: OK 999 n, dimension of A: 66 1000 nz, number of nonzeros in A: 4356 1001 symmetry of A: 1.0000 1002 number of nonzeros on diagonal: 66 1003 nonzeros in pattern of A+A' (excl. diagonal): 4290 1004 # dense rows/columns of A+A': 0 1005 memory used, in bytes: 45936 1006 # of memory compactions: 0 1007 1008 The following approximate statistics are for a subsequent 1009 factorization of A(P,P) + A(P,P)'. They are slight upper 1010 bounds if there are no dense rows/columns in A+A', and become 1011 looser if dense rows/columns exist. 1012 1013 nonzeros in L (excluding diagonal): 2145 1014 nonzeros in L (including diagonal): 2211 1015 # divide operations for LDL' or LU: 2145 1016 # multiply-subtract operations for LDL': 47905 1017 # multiply-subtract operations for LU: 93665 1018 max nz. in any column of L (incl. diagonal): 66 1019 1020 chol flop count for real A, sqrt counted as 1 flop: 98021 1021 LDL' flop count for real A: 97955 1022 LDL' flop count for complex A: 402545 1023 LU flop count for real A (with no pivoting): 189475 1024 LU flop count for complex A (with no pivoting): 768625 1025 1026Factorize PAP'=LDL' and solve Ax=b 1027Nz in L: 2145 Flop count: 97955 1028relative maxnorm of residual: 7.50219e-13 1029Factorize A=LDL' and solve Ax=b 1030Nz in L: 2145 Flop count: 97955 1031relative maxnorm of residual: 7.50219e-13 1032 1033 1034-------------------------------------------------------- 1035Input file: ../Matrix/A22 1036name: HB/bcsstk02 n: 66 entries: 5175 (jumbled version) 1037-------------------------------------------------------- 1038 1039 1040AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 1041 dense row parameter: 10 1042 (rows with more than max (10 * sqrt (n), 16) entries are 1043 considered "dense", and placed last in output permutation) 1044 aggressive absorption: yes 1045 size of AMD integer: 8 1046 1047 1048AMD version 2.4.6, May 4, 2016, results: 1049 status: OK, but jumbled 1050 n, dimension of A: 66 1051 nz, number of nonzeros in A: 4356 1052 symmetry of A: 1.0000 1053 number of nonzeros on diagonal: 66 1054 nonzeros in pattern of A+A' (excl. diagonal): 4290 1055 # dense rows/columns of A+A': 0 1056 memory used, in bytes: 87872 1057 # of memory compactions: 0 1058 1059 The following approximate statistics are for a subsequent 1060 factorization of A(P,P) + A(P,P)'. They are slight upper 1061 bounds if there are no dense rows/columns in A+A', and become 1062 looser if dense rows/columns exist. 1063 1064 nonzeros in L (excluding diagonal): 2145 1065 nonzeros in L (including diagonal): 2211 1066 # divide operations for LDL' or LU: 2145 1067 # multiply-subtract operations for LDL': 47905 1068 # multiply-subtract operations for LU: 93665 1069 max nz. in any column of L (incl. diagonal): 66 1070 1071 chol flop count for real A, sqrt counted as 1 flop: 98021 1072 LDL' flop count for real A: 97955 1073 LDL' flop count for complex A: 402545 1074 LU flop count for real A (with no pivoting): 189475 1075 LU flop count for complex A (with no pivoting): 768625 1076 1077Factorize PAP'=LDL' and solve Ax=b 1078Nz in L: 2145 Flop count: 97955 1079relative maxnorm of residual: 8.59759e-13 1080Factorize A=LDL' and solve Ax=b 1081Nz in L: 2145 Flop count: 97955 1082relative maxnorm of residual: 8.59759e-13 1083 1084 1085-------------------------------------------------------- 1086Input file: ../Matrix/A23 1087name: HB/bcsstm02 n: 66 entries: 66 1088-------------------------------------------------------- 1089 1090 1091AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 1092 dense row parameter: 10 1093 (rows with more than max (10 * sqrt (n), 16) entries are 1094 considered "dense", and placed last in output permutation) 1095 aggressive absorption: yes 1096 size of AMD integer: 8 1097 1098 1099AMD version 2.4.6, May 4, 2016, results: 1100 status: OK 1101 n, dimension of A: 66 1102 nz, number of nonzeros in A: 66 1103 symmetry of A: 1.0000 1104 number of nonzeros on diagonal: 66 1105 nonzeros in pattern of A+A' (excl. diagonal): 0 1106 # dense rows/columns of A+A': 0 1107 memory used, in bytes: 4752 1108 # of memory compactions: 0 1109 1110 The following approximate statistics are for a subsequent 1111 factorization of A(P,P) + A(P,P)'. They are slight upper 1112 bounds if there are no dense rows/columns in A+A', and become 1113 looser if dense rows/columns exist. 1114 1115 nonzeros in L (excluding diagonal): 0 1116 nonzeros in L (including diagonal): 66 1117 # divide operations for LDL' or LU: 0 1118 # multiply-subtract operations for LDL': 0 1119 # multiply-subtract operations for LU: 0 1120 max nz. in any column of L (incl. diagonal): 1 1121 1122 chol flop count for real A, sqrt counted as 1 flop: 66 1123 LDL' flop count for real A: 0 1124 LDL' flop count for complex A: 0 1125 LU flop count for real A (with no pivoting): 0 1126 LU flop count for complex A (with no pivoting): 0 1127 1128Factorize PAP'=LDL' and solve Ax=b 1129Nz in L: 0 Flop count: 0 1130relative maxnorm of residual: 2.22045e-16 1131Factorize A=LDL' and solve Ax=b 1132Nz in L: 0 Flop count: 0 1133relative maxnorm of residual: 2.22045e-16 1134 1135 1136-------------------------------------------------------- 1137Input file: ../Matrix/A24 1138name: HB/bcsstm02 n: 66 entries: 72 (jumbled version) 1139-------------------------------------------------------- 1140 1141 1142AMD version 2.4.6, May 4, 2016: approximate minimum degree ordering 1143 dense row parameter: 10 1144 (rows with more than max (10 * sqrt (n), 16) entries are 1145 considered "dense", and placed last in output permutation) 1146 aggressive absorption: yes 1147 size of AMD integer: 8 1148 1149 1150AMD version 2.4.6, May 4, 2016, results: 1151 status: OK, but jumbled 1152 n, dimension of A: 66 1153 nz, number of nonzeros in A: 66 1154 symmetry of A: 1.0000 1155 number of nonzeros on diagonal: 66 1156 nonzeros in pattern of A+A' (excl. diagonal): 0 1157 # dense rows/columns of A+A': 0 1158 memory used, in bytes: 5864 1159 # of memory compactions: 0 1160 1161 The following approximate statistics are for a subsequent 1162 factorization of A(P,P) + A(P,P)'. They are slight upper 1163 bounds if there are no dense rows/columns in A+A', and become 1164 looser if dense rows/columns exist. 1165 1166 nonzeros in L (excluding diagonal): 0 1167 nonzeros in L (including diagonal): 66 1168 # divide operations for LDL' or LU: 0 1169 # multiply-subtract operations for LDL': 0 1170 # multiply-subtract operations for LU: 0 1171 max nz. in any column of L (incl. diagonal): 1 1172 1173 chol flop count for real A, sqrt counted as 1 flop: 66 1174 LDL' flop count for real A: 0 1175 LDL' flop count for complex A: 0 1176 LU flop count for real A (with no pivoting): 0 1177 LU flop count for complex A (with no pivoting): 0 1178 1179Factorize PAP'=LDL' and solve Ax=b 1180Nz in L: 0 Flop count: 0 1181relative maxnorm of residual: 2.22045e-16 1182Factorize A=LDL' and solve Ax=b 1183Nz in L: 0 Flop count: 0 1184relative maxnorm of residual: 2.22045e-16 1185 1186 1187-------------------------------------------------------- 1188Input file: ../Matrix/A25 1189name: Dense/0 n: 0 entries: 0 (invalid matrix, Ap [0] = 1) 1190-------------------------------------------------------- 1191 1192ldlamd: invalid matrix and/or permutation 1193 1194 1195-------------------------------------------------------- 1196Input file: ../Matrix/A26 1197name: Dense/2 n: 2 entries: 4 (invalid perm, P[1]=99) 1198-------------------------------------------------------- 1199 1200ldlamd: invalid matrix and/or permutation 1201 1202 1203-------------------------------------------------------- 1204Input file: ../Matrix/A27 1205name: Dense/3 n: 3 entries: 9 (invalid perm) 1206-------------------------------------------------------- 1207 1208ldlamd: invalid matrix and/or permutation 1209 1210 1211-------------------------------------------------------- 1212Input file: ../Matrix/A28 1213name: Dense/3 n: 3 entries: 9 (invalid Ap) 1214-------------------------------------------------------- 1215 1216ldlamd: invalid matrix and/or permutation 1217 1218 1219-------------------------------------------------------- 1220Input file: ../Matrix/A29 1221name: Dense/3 n: 3 entries: 9 (invalid Ai) 1222-------------------------------------------------------- 1223 1224ldlamd: invalid matrix and/or permutation 1225 1226 1227-------------------------------------------------------- 1228Input file: ../Matrix/A30 1229name: Dense/3 n: 3 entries: 9 (invalid Ai) 1230-------------------------------------------------------- 1231 1232ldlamd: invalid matrix and/or permutation 1233 1234Largest residual during all tests: 3.27418e-10 1235 1236ldlamd: all tests passed 1237