Blame view
fvn_sparse/UMFPACK/Source/umfpack_get_numeric.c
26.7 KB
422234dc3
git-svn-id: https...
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 |
/* ========================================================================== */
/* === UMFPACK_get_numeric ================================================== */
/* ========================================================================== */
/* -------------------------------------------------------------------------- */
/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
/* -------------------------------------------------------------------------- */
/*
User-callable. Gets the LU factors and the permutation vectors held in the
Numeric object. L is returned in sparse row form with sorted rows, U is
returned in sparse column form with sorted columns, and P and Q are
returned as permutation vectors. See umfpack_get_numeric.h for a more
detailed description.
Returns TRUE if successful, FALSE if the Numeric object is invalid or
if out of memory.
Dynamic memory usage: calls UMF_malloc twice, for a total space of
2*n integers, and then frees all of it via UMF_free when done.
*/
#include "umf_internal.h"
#include "umf_valid_numeric.h"
#include "umf_malloc.h"
#include "umf_free.h"
#ifndef NDEBUG
PRIVATE Int init_count ;
#endif
PRIVATE void get_L
(
Int Lp [ ],
Int Lj [ ],
double Lx [ ],
#ifdef COMPLEX
double Lz [ ],
#endif
NumericType *Numeric,
Int Pattern [ ],
Int Wi [ ]
) ;
PRIVATE void get_U
(
Int Up [ ],
Int Ui [ ],
double Ux [ ],
#ifdef COMPLEX
double Uz [ ],
#endif
NumericType *Numeric,
Int Pattern [ ],
Int Wi [ ]
) ;
/* ========================================================================== */
/* === UMFPACK_get_numeric ================================================== */
/* ========================================================================== */
GLOBAL Int UMFPACK_get_numeric
(
Int Lp [ ],
Int Lj [ ],
double Lx [ ],
#ifdef COMPLEX
double Lz [ ],
#endif
Int Up [ ],
Int Ui [ ],
double Ux [ ],
#ifdef COMPLEX
double Uz [ ],
#endif
Int P [ ],
Int Q [ ],
double Dx [ ],
#ifdef COMPLEX
double Dz [ ],
#endif
Int *p_do_recip,
double Rs [ ],
void *NumericHandle
)
{
/* ---------------------------------------------------------------------- */
/* local variables */
/* ---------------------------------------------------------------------- */
NumericType *Numeric ;
Int getL, getU, *Rperm, *Cperm, k, nn, n_row, n_col, *Wi, *Pattern,
n_inner ;
double *Rs1 ;
Entry *D ;
#ifndef NDEBUG
init_count = UMF_malloc_count ;
#endif
Wi = (Int *) NULL ;
Pattern = (Int *) NULL ;
/* ---------------------------------------------------------------------- */
/* check input parameters */
/* ---------------------------------------------------------------------- */
Numeric = (NumericType *) NumericHandle ;
if (!UMF_valid_numeric (Numeric))
{
return (UMFPACK_ERROR_invalid_Numeric_object) ;
}
n_row = Numeric->n_row ;
n_col = Numeric->n_col ;
nn = MAX (n_row, n_col) ;
n_inner = MIN (n_row, n_col) ;
/* ---------------------------------------------------------------------- */
/* allocate workspace */
/* ---------------------------------------------------------------------- */
getL = Lp && Lj && Lx ;
getU = Up && Ui && Ux ;
if (getL || getU)
{
Wi = (Int *) UMF_malloc (nn, sizeof (Int)) ;
Pattern = (Int *) UMF_malloc (nn, sizeof (Int)) ;
if (!Wi || !Pattern)
{
(void) UMF_free ((void *) Wi) ;
(void) UMF_free ((void *) Pattern) ;
ASSERT (UMF_malloc_count == init_count) ;
DEBUGm4 (("out of memory: get numeric
")) ;
return (UMFPACK_ERROR_out_of_memory) ;
}
ASSERT (UMF_malloc_count == init_count + 2) ;
}
/* ---------------------------------------------------------------------- */
/* get contents of Numeric */
/* ---------------------------------------------------------------------- */
if (P != (Int *) NULL)
{
Rperm = Numeric->Rperm ;
for (k = 0 ; k < n_row ; k++)
{
P [k] = Rperm [k] ;
}
}
if (Q != (Int *) NULL)
{
Cperm = Numeric->Cperm ;
for (k = 0 ; k < n_col ; k++)
{
Q [k] = Cperm [k] ;
}
}
if (getL)
{
get_L (Lp, Lj, Lx,
#ifdef COMPLEX
Lz,
#endif
Numeric, Pattern, Wi) ;
}
if (getU)
{
get_U (Up, Ui, Ux,
#ifdef COMPLEX
Uz,
#endif
Numeric, Pattern, Wi) ;
}
if (Dx != (double *) NULL)
{
D = Numeric->D ;
#ifdef COMPLEX
if (SPLIT (Dz))
{
for (k = 0 ; k < n_inner ; k++)
{
Dx [k] = REAL_COMPONENT (D [k]) ;
Dz [k] = IMAG_COMPONENT (D [k]) ;
}
}
else
{
for (k = 0 ; k < n_inner ; k++)
{
Dx [2*k ] = REAL_COMPONENT (D [k]) ;
Dx [2*k+1] = IMAG_COMPONENT (D [k]) ;
}
}
#else
{
D = Numeric->D ;
for (k = 0 ; k < n_inner ; k++)
{
Dx [k] = D [k] ;
}
}
#endif
}
/* return the flag stating whether the scale factors are to be multiplied,
* or divided. If do_recip is TRUE, multiply. Otherwise, divided.
* If NRECIPROCAL is defined at compile time, the scale factors are always
* to be used by dividing.
*/
if (p_do_recip != (Int *) NULL)
{
#ifndef NRECIPROCAL
*p_do_recip = Numeric->do_recip ;
#else
*p_do_recip = FALSE ;
#endif
}
if (Rs != (double *) NULL)
{
Rs1 = Numeric->Rs ;
if (Rs1 == (double *) NULL)
{
/* R is the identity matrix. */
for (k = 0 ; k < n_row ; k++)
{
Rs [k] = 1.0 ;
}
}
else
{
for (k = 0 ; k < n_row ; k++)
{
Rs [k] = Rs1 [k] ;
}
}
}
/* ---------------------------------------------------------------------- */
/* free the workspace */
/* ---------------------------------------------------------------------- */
(void) UMF_free ((void *) Wi) ;
(void) UMF_free ((void *) Pattern) ;
ASSERT (UMF_malloc_count == init_count) ;
return (UMFPACK_OK) ;
}
/* ========================================================================== */
/* === get_L ================================================================ */
/* ========================================================================== */
/*
The matrix L is stored in the following arrays in the Numeric object:
Int Lpos [0..npiv]
Int Lip [0..npiv], index into Numeric->Memory
Int Lilen [0..npiv]
Unit *(Numeric->Memory), pointer to memory space holding row indices
and numerical values
where npiv is the number of pivot entries found. If A is n_row-by-n_col,
then npiv <= MIN (n_row,n_col).
Let L_k denote the pattern of entries in column k of L (excluding the
diagonal).
An Lchain is a sequence of columns of L whose nonzero patterns are related.
The start of an Lchain is denoted by a negative value of Lip [k].
To obtain L_k:
(1) If column k starts an Lchain, then L_k is stored in its entirety.
|Lip [k]| is an index into Numeric->Memory for the integer row indices
in L_k. The number of entries in the column is |L_k| = Lilen [k].
This defines the pattern of the "leading" column of this chain.
Lpos [k] is not used for the first column in the chain. Column zero
is always a leading column.
(2) If column k does not start an Lchain, then L_k is represented as a
superset of L_k-1. Define Lnew_k such that (L_k-1 - {k} union Lnew_k)
= L_k, where Lnew_k and (L_k-1)-{k} are disjoint. Lnew_k are the
entries in L_k that are not in L_k-1. Lpos [k] holds the position of
pivot row index k in the prior pattern L_k-1 (if it is present), so
that the set subtraction (L_k-1)-{k} can be computed quickly, when
computing the pattern of L_k from L_k-1. The number of new entries in
L_k is stored in Lilen [k] = |Lnew_k|.
Note that this means we must have the pattern L_k-1 to compute L_k.
In both cases (1) and (2), we obtain the pattern L_k.
The numerical values are stored in Numeric->Memory, starting at the index
|Lip [k]| + Lilen [k]. It is stored in the same order as the entries
in L_k, after L_k is obtained from cases (1) or (2), above.
The advantage of using this "packed" data structure is that it can
dramatically reduce the amount of storage needed for the pattern of L.
The disadvantage is that it can be difficult for the user to access,
and it does not match the sparse matrix data structure used in MATLAB.
Thus, this routine is provided to create a conventional sparse matrix
data structure for L, in sparse-row form. A row-form of L appears to
MATLAB to be a column-oriented from of the transpose of L. If you would
like a column-form of L, then use UMFPACK_transpose (an example of this
is in umfpackmex.c).
*/
/* ========================================================================== */
PRIVATE void get_L
(
Int Lp [ ], /* of size n_row+1 */
Int Lj [ ], /* of size lnz, where lnz = Lp [n_row] */
double Lx [ ], /* of size lnz */
#ifdef COMPLEX
double Lz [ ], /* of size lnz */
#endif
NumericType *Numeric,
Int Pattern [ ], /* workspace of size n_row */
Int Wi [ ] /* workspace of size n_row */
)
{
/* ---------------------------------------------------------------------- */
/* local variables */
/* ---------------------------------------------------------------------- */
Entry value ;
Entry *xp, *Lval ;
Int deg, *ip, j, row, n_row, n_col, n_inner, *Lpos, *Lilen, *Lip, p, llen,
lnz2, lp, newLchain, k, pos, npiv, *Li, n1 ;
#ifdef COMPLEX
Int split = SPLIT (Lz) ;
#endif
/* ---------------------------------------------------------------------- */
/* get parameters */
/* ---------------------------------------------------------------------- */
DEBUG4 (("get_L start:
")) ;
n_row = Numeric->n_row ;
n_col = Numeric->n_col ;
n_inner = MIN (n_row, n_col) ;
npiv = Numeric->npiv ;
n1 = Numeric->n1 ;
Lpos = Numeric->Lpos ;
Lilen = Numeric->Lilen ;
Lip = Numeric->Lip ;
deg = 0 ;
/* ---------------------------------------------------------------------- */
/* count the nonzeros in each row of L */
/* ---------------------------------------------------------------------- */
#pragma ivdep
for (row = 0 ; row < n_inner ; row++)
{
/* include the diagonal entry in the row counts */
Wi [row] = 1 ;
}
#pragma ivdep
for (row = n_inner ; row < n_row ; row++)
{
Wi [row] = 0 ;
}
/* singletons */
for (k = 0 ; k < n1 ; k++)
{
DEBUG4 (("Singleton k "ID"
", k)) ;
deg = Lilen [k] ;
if (deg > 0)
{
lp = Lip [k] ;
Li = (Int *) (Numeric->Memory + lp) ;
lp += UNITS (Int, deg) ;
Lval = (Entry *) (Numeric->Memory + lp) ;
for (j = 0 ; j < deg ; j++)
{
row = Li [j] ;
value = Lval [j] ;
DEBUG4 ((" row "ID" k "ID" value", row, k)) ;
EDEBUG4 (value) ;
DEBUG4 (("
")) ;
if (IS_NONZERO (value))
{
Wi [row]++ ;
}
}
}
}
/* non-singletons */
for (k = n1 ; k < npiv ; k++)
{
/* ------------------------------------------------------------------ */
/* make column of L in Pattern [0..deg-1] */
/* ------------------------------------------------------------------ */
lp = Lip [k] ;
newLchain = (lp < 0) ;
if (newLchain)
{
lp = -lp ;
deg = 0 ;
DEBUG4 (("start of chain for column of L
")) ;
}
/* remove pivot row */
pos = Lpos [k] ;
if (pos != EMPTY)
{
DEBUG4 ((" k "ID" removing row "ID" at position "ID"
",
k, Pattern [pos], pos)) ;
ASSERT (!newLchain) ;
ASSERT (deg > 0) ;
ASSERT (pos >= 0 && pos < deg) ;
ASSERT (Pattern [pos] == k) ;
Pattern [pos] = Pattern [--deg] ;
}
/* concatenate the pattern */
ip = (Int *) (Numeric->Memory + lp) ;
llen = Lilen [k] ;
for (j = 0 ; j < llen ; j++)
{
row = *ip++ ;
DEBUG4 ((" row "ID" k "ID"
", row, k)) ;
ASSERT (row > k && row < n_row) ;
Pattern [deg++] = row ;
}
xp = (Entry *) (Numeric->Memory + lp + UNITS (Int, llen)) ;
for (j = 0 ; j < deg ; j++)
{
DEBUG4 ((" row "ID" k "ID" value", Pattern [j], k)) ;
row = Pattern [j] ;
value = *xp++ ;
EDEBUG4 (value) ;
DEBUG4 (("
")) ;
if (IS_NONZERO (value))
{
Wi [row]++ ;
}
}
}
/* ---------------------------------------------------------------------- */
/* construct the final row form of L */
/* ---------------------------------------------------------------------- */
/* create the row pointers */
lnz2 = 0 ;
for (row = 0 ; row < n_row ; row++)
{
Lp [row] = lnz2 ;
lnz2 += Wi [row] ;
Wi [row] = Lp [row] ;
}
Lp [n_row] = lnz2 ;
ASSERT (Numeric->lnz + n_inner == lnz2) ;
/* add entries from the rows of L (singletons) */
for (k = 0 ; k < n1 ; k++)
{
DEBUG4 (("Singleton k "ID"
", k)) ;
deg = Lilen [k] ;
if (deg > 0)
{
lp = Lip [k] ;
Li = (Int *) (Numeric->Memory + lp) ;
lp += UNITS (Int, deg) ;
Lval = (Entry *) (Numeric->Memory + lp) ;
for (j = 0 ; j < deg ; j++)
{
row = Li [j] ;
value = Lval [j] ;
DEBUG4 ((" row "ID" k "ID" value", row, k)) ;
EDEBUG4 (value) ;
DEBUG4 (("
")) ;
if (IS_NONZERO (value))
{
p = Wi [row]++ ;
Lj [p] = k ;
#ifdef COMPLEX
if (split)
{
Lx [p] = REAL_COMPONENT (value) ;
Lz [p] = IMAG_COMPONENT (value) ;
}
else
{
Lx [2*p ] = REAL_COMPONENT (value) ;
Lx [2*p+1] = IMAG_COMPONENT (value) ;
}
#else
Lx [p] = value ;
#endif
}
}
}
}
/* add entries from the rows of L (non-singletons) */
for (k = n1 ; k < npiv ; k++)
{
/* ------------------------------------------------------------------ */
/* make column of L in Pattern [0..deg-1] */
/* ------------------------------------------------------------------ */
lp = Lip [k] ;
newLchain = (lp < 0) ;
if (newLchain)
{
lp = -lp ;
deg = 0 ;
DEBUG4 (("start of chain for column of L
")) ;
}
/* remove pivot row */
pos = Lpos [k] ;
if (pos != EMPTY)
{
DEBUG4 ((" k "ID" removing row "ID" at position "ID"
",
k, Pattern [pos], pos)) ;
ASSERT (!newLchain) ;
ASSERT (deg > 0) ;
ASSERT (pos >= 0 && pos < deg) ;
ASSERT (Pattern [pos] == k) ;
Pattern [pos] = Pattern [--deg] ;
}
/* concatenate the pattern */
ip = (Int *) (Numeric->Memory + lp) ;
llen = Lilen [k] ;
for (j = 0 ; j < llen ; j++)
{
row = *ip++ ;
DEBUG4 ((" row "ID" k "ID"
", row, k)) ;
ASSERT (row > k) ;
Pattern [deg++] = row ;
}
xp = (Entry *) (Numeric->Memory + lp + UNITS (Int, llen)) ;
for (j = 0 ; j < deg ; j++)
{
DEBUG4 ((" row "ID" k "ID" value", Pattern [j], k)) ;
row = Pattern [j] ;
value = *xp++ ;
EDEBUG4 (value) ;
DEBUG4 (("
")) ;
if (IS_NONZERO (value))
{
p = Wi [row]++ ;
Lj [p] = k ;
#ifdef COMPLEX
if (split)
{
Lx [p] = REAL_COMPONENT (value) ;
Lz [p] = IMAG_COMPONENT (value) ;
}
else
{
Lx [2*p ] = REAL_COMPONENT (value) ;
Lx [2*p+1] = IMAG_COMPONENT (value) ;
}
#else
Lx [p] = value ;
#endif
}
}
}
/* add all of the diagonal entries (L is unit diagonal) */
for (row = 0 ; row < n_inner ; row++)
{
p = Wi [row]++ ;
Lj [p] = row ;
#ifdef COMPLEX
if (split)
{
Lx [p] = 1. ;
Lz [p] = 0. ;
}
else
{
Lx [2*p ] = 1. ;
Lx [2*p+1] = 0. ;
}
#else
Lx [p] = 1. ;
#endif
ASSERT (Wi [row] == Lp [row+1]) ;
}
#ifndef NDEBUG
DEBUG6 (("L matrix (stored by rows):")) ;
UMF_dump_col_matrix (Lx,
#ifdef COMPLEX
Lz,
#endif
Lj, Lp, n_inner, n_row, Numeric->lnz+n_inner) ;
#endif
DEBUG4 (("get_L done:
")) ;
}
/* ========================================================================== */
/* === get_U ================================================================ */
/* ========================================================================== */
/*
The matrix U is stored in the following arrays in the Numeric object:
Int Upos [0..npiv]
Int Uip [0..npiv], index into Numeric->Memory
Int Uilen [0..npiv]
Unit *(Numeric->Memory), pointer to memory space holding column indices
and numerical values
where npiv is the number of pivot entries found. If A is n_row-by-n_col,
then npiv <= MIN (n_row,n_col).
Let U_k denote the pattern of entries in row k of U (excluding the
diagonal).
A Uchain is a sequence of columns of U whose nonzero patterns are related.
The start of a Uchain is denoted by a negative value of Uip [k].
To obtain U_k-1:
(1) If row k is the start of a Uchain then Uip [k] is negative and |Uip [k]|
is an index into Numeric->Memory for the integer column indices in
U_k-1. The number of entries in the row is |U_k-1| = Uilen [k]. This
defines the pattern of the "trailing" row of this chain that ends at
row k-1.
(2) If row k is not the start of a Uchain, then U_k-1 is a subset of U_k.
The indices in U_k are arranged so that last Uilen [k] entries of
U_k are those indices not in U_k-1. Next, the pivot column index k is
added if it appears in row U_k-1 (it never appears in U_k). Upos [k]
holds the position of pivot column index k in the pattern U_k-1 (if it
is present), so that the set union (U_k-1)+{k} can be computed quickly,
when computing the pattern of U_k-1 from U_k.
Note that this means we must have the pattern U_k to compute L_k-1.
In both cases (1) and (2), we obtain the pattern U_k.
The numerical values are stored in Numeric->Memory. If k is the start of a
Uchain, then the offset is |Uip [k]| plus the size of the space needed to
store the pattern U_k-1. Otherwise, Uip [k] is the offset itself of the
numerical values, since in this case no pattern is stored.
The numerical values are stored in the same order as the entries in U_k,
after U_k is obtained from cases (1) or (2), above.
The advantage of using this "packed" data structure is that it can
dramatically reduce the amount of storage needed for the pattern of U.
The disadvantage is that it can be difficult for the user to access,
and it does not match the sparse matrix data structure used in MATLAB.
Thus, this routine is provided to create a conventional sparse matrix
data structure for U, in sparse-column form.
*/
/* ========================================================================== */
PRIVATE void get_U
(
Int Up [ ], /* of size n_col+1 */
Int Ui [ ], /* of size unz, where unz = Up [n_col] */
double Ux [ ], /* of size unz */
#ifdef COMPLEX
double Uz [ ], /* of size unz */
#endif
NumericType *Numeric,
Int Pattern [ ], /* workspace of size n_col */
Int Wi [ ] /* workspace of size n_col */
)
{
/* ---------------------------------------------------------------------- */
/* local variables */
/* ---------------------------------------------------------------------- */
Entry value ;
Entry *xp, *D, *Uval ;
Int deg, j, *ip, col, *Upos, *Uilen, *Uip, n_col, ulen, *Usi,
unz2, p, k, up, newUchain, pos, npiv, n1 ;
#ifdef COMPLEX
Int split = SPLIT (Uz) ;
#endif
#ifndef NDEBUG
Int nnzpiv = 0 ;
#endif
/* ---------------------------------------------------------------------- */
/* get parameters */
/* ---------------------------------------------------------------------- */
DEBUG4 (("get_U start:
")) ;
n_col = Numeric->n_col ;
n1 = Numeric->n1 ;
npiv = Numeric->npiv ;
Upos = Numeric->Upos ;
Uilen = Numeric->Uilen ;
Uip = Numeric->Uip ;
D = Numeric->D ;
/* ---------------------------------------------------------------------- */
/* count the nonzeros in each column of U */
/* ---------------------------------------------------------------------- */
for (col = 0 ; col < npiv ; col++)
{
/* include the diagonal entry in the column counts */
DEBUG4 (("D ["ID"] = ", col)) ;
EDEBUG4 (D [col]) ;
Wi [col] = IS_NONZERO (D [col]) ;
DEBUG4 ((" is nonzero: "ID"
", Wi [col])) ;
#ifndef NDEBUG
nnzpiv += IS_NONZERO (D [col]) ;
#endif
}
DEBUG4 (("nnzpiv "ID" "ID"
", nnzpiv, Numeric->nnzpiv)) ;
ASSERT (nnzpiv == Numeric->nnzpiv) ;
for (col = npiv ; col < n_col ; col++)
{
/* diagonal entries are zero for structurally singular part */
Wi [col] = 0 ;
}
deg = Numeric->ulen ;
if (deg > 0)
{
/* make last pivot row of U (singular matrices only) */
DEBUG0 (("Last pivot row of U: ulen "ID"
", deg)) ;
for (j = 0 ; j < deg ; j++)
{
Pattern [j] = Numeric->Upattern [j] ;
DEBUG0 ((" column "ID"
", Pattern [j])) ;
}
}
/* non-singletons */
for (k = npiv-1 ; k >= n1 ; k--)
{
/* ------------------------------------------------------------------ */
/* use row k of U */
/* ------------------------------------------------------------------ */
up = Uip [k] ;
ulen = Uilen [k] ;
newUchain = (up < 0) ;
if (newUchain)
{
up = -up ;
xp = (Entry *) (Numeric->Memory + up + UNITS (Int, ulen)) ;
}
else
{
xp = (Entry *) (Numeric->Memory + up) ;
}
for (j = 0 ; j < deg ; j++)
{
DEBUG4 ((" k "ID" col "ID" value
", k, Pattern [j])) ;
col = Pattern [j] ;
ASSERT (col >= 0 && col < n_col) ;
value = *xp++ ;
EDEBUG4 (value) ;
DEBUG4 (("
")) ;
if (IS_NONZERO (value))
{
Wi [col]++ ;
}
}
/* ------------------------------------------------------------------ */
/* make row k-1 of U in Pattern [0..deg-1] */
/* ------------------------------------------------------------------ */
if (k == n1) break ;
if (newUchain)
{
/* next row is a new Uchain */
deg = ulen ;
DEBUG4 (("end of chain for row of U "ID" deg "ID"
", k-1, deg)) ;
ip = (Int *) (Numeric->Memory + up) ;
for (j = 0 ; j < deg ; j++)
{
col = *ip++ ;
DEBUG4 ((" k "ID" col "ID"
", k-1, col)) ;
ASSERT (k <= col) ;
Pattern [j] = col ;
}
}
else
{
deg -= ulen ;
DEBUG4 (("middle of chain for row of U "ID" deg "ID"
", k-1, deg));
ASSERT (deg >= 0) ;
pos = Upos [k] ;
if (pos != EMPTY)
{
/* add the pivot column */
DEBUG4 (("k "ID" add pivot entry at position "ID"
", k, pos)) ;
ASSERT (pos >= 0 && pos <= deg) ;
Pattern [deg++] = Pattern [pos] ;
Pattern [pos] = k ;
}
}
}
/* singletons */
for (k = n1 - 1 ; k >= 0 ; k--)
{
deg = Uilen [k] ;
DEBUG4 (("Singleton k "ID"
", k)) ;
if (deg > 0)
{
up = Uip [k] ;
Usi = (Int *) (Numeric->Memory + up) ;
up += UNITS (Int, deg) ;
Uval = (Entry *) (Numeric->Memory + up) ;
for (j = 0 ; j < deg ; j++)
{
col = Usi [j] ;
value = Uval [j] ;
DEBUG4 ((" k "ID" col "ID" value", k, col)) ;
EDEBUG4 (value) ;
DEBUG4 (("
")) ;
if (IS_NONZERO (value))
{
Wi [col]++ ;
}
}
}
}
/* ---------------------------------------------------------------------- */
/* construct the final column form of U */
/* ---------------------------------------------------------------------- */
/* create the column pointers */
unz2 = 0 ;
for (col = 0 ; col < n_col ; col++)
{
Up [col] = unz2 ;
unz2 += Wi [col] ;
}
Up [n_col] = unz2 ;
DEBUG1 (("Numeric->unz "ID" npiv "ID" nnzpiv "ID" unz2 "ID"
",
Numeric->unz, npiv, Numeric->nnzpiv, unz2)) ;
ASSERT (Numeric->unz + Numeric->nnzpiv == unz2) ;
for (col = 0 ; col < n_col ; col++)
{
Wi [col] = Up [col+1] ;
}
/* add all of the diagonal entries */
for (col = 0 ; col < npiv ; col++)
{
if (IS_NONZERO (D [col]))
{
p = --(Wi [col]) ;
Ui [p] = col ;
#ifdef COMPLEX
if (split)
{
Ux [p] = REAL_COMPONENT (D [col]) ;
Uz [p] = IMAG_COMPONENT (D [col]) ;
}
else
{
Ux [2*p ] = REAL_COMPONENT (D [col]) ;
Ux [2*p+1] = IMAG_COMPONENT (D [col]) ;
}
#else
Ux [p] = D [col] ;
#endif
}
}
/* add all the entries from the rows of U */
deg = Numeric->ulen ;
if (deg > 0)
{
/* make last pivot row of U (singular matrices only) */
for (j = 0 ; j < deg ; j++)
{
Pattern [j] = Numeric->Upattern [j] ;
}
}
/* non-singletons */
for (k = npiv-1 ; k >= n1 ; k--)
{
/* ------------------------------------------------------------------ */
/* use row k of U */
/* ------------------------------------------------------------------ */
up = Uip [k] ;
ulen = Uilen [k] ;
newUchain = (up < 0) ;
if (newUchain)
{
up = -up ;
xp = (Entry *) (Numeric->Memory + up + UNITS (Int, ulen)) ;
}
else
{
xp = (Entry *) (Numeric->Memory + up) ;
}
xp += deg ;
for (j = deg-1 ; j >= 0 ; j--)
{
DEBUG4 ((" k "ID" col "ID" value", k, Pattern [j])) ;
col = Pattern [j] ;
ASSERT (col >= 0 && col < n_col) ;
value = *(--xp) ;
EDEBUG4 (value) ;
DEBUG4 (("
")) ;
if (IS_NONZERO (value))
{
p = --(Wi [col]) ;
Ui [p] = k ;
#ifdef COMPLEX
if (split)
{
Ux [p] = REAL_COMPONENT (value) ;
Uz [p] = IMAG_COMPONENT (value) ;
}
else
{
Ux [2*p ] = REAL_COMPONENT (value) ;
Ux [2*p+1] = IMAG_COMPONENT (value) ;
}
#else
Ux [p] = value ;
#endif
}
}
/* ------------------------------------------------------------------ */
/* make row k-1 of U in Pattern [0..deg-1] */
/* ------------------------------------------------------------------ */
if (newUchain)
{
/* next row is a new Uchain */
deg = ulen ;
DEBUG4 (("end of chain for row of U "ID" deg "ID"
", k-1, deg)) ;
ip = (Int *) (Numeric->Memory + up) ;
for (j = 0 ; j < deg ; j++)
{
col = *ip++ ;
DEBUG4 ((" k "ID" col "ID"
", k-1, col)) ;
ASSERT (k <= col) ;
Pattern [j] = col ;
}
}
else
{
deg -= ulen ;
DEBUG4 (("middle of chain for row of U "ID" deg "ID"
", k-1, deg));
ASSERT (deg >= 0) ;
pos = Upos [k] ;
if (pos != EMPTY)
{
/* add the pivot column */
DEBUG4 (("k "ID" add pivot entry at position "ID"
", k, pos)) ;
ASSERT (pos >= 0 && pos <= deg) ;
Pattern [deg++] = Pattern [pos] ;
Pattern [pos] = k ;
}
}
}
/* singletons */
for (k = n1 - 1 ; k >= 0 ; k--)
{
deg = Uilen [k] ;
DEBUG4 (("Singleton k "ID"
", k)) ;
if (deg > 0)
{
up = Uip [k] ;
Usi = (Int *) (Numeric->Memory + up) ;
up += UNITS (Int, deg) ;
Uval = (Entry *) (Numeric->Memory + up) ;
for (j = 0 ; j < deg ; j++)
{
col = Usi [j] ;
value = Uval [j] ;
DEBUG4 ((" k "ID" col "ID" value", k, col)) ;
EDEBUG4 (value) ;
DEBUG4 (("
")) ;
if (IS_NONZERO (value))
{
p = --(Wi [col]) ;
Ui [p] = k ;
#ifdef COMPLEX
if (split)
{
Ux [p] = REAL_COMPONENT (value) ;
Uz [p] = IMAG_COMPONENT (value) ;
}
else
{
Ux [2*p ] = REAL_COMPONENT (value) ;
Ux [2*p+1] = IMAG_COMPONENT (value) ;
}
#else
Ux [p] = value ;
#endif
}
}
}
}
#ifndef NDEBUG
DEBUG6 (("U matrix:")) ;
UMF_dump_col_matrix (Ux,
#ifdef COMPLEX
Uz,
#endif
Ui, Up, Numeric->n_row, n_col, Numeric->unz + Numeric->nnzpiv) ;
#endif
}
|