Actual source code: ilut.c

  1: /*$Id: ilut.c,v 1.7 2001/08/06 21:15:14 bsmith Exp $*/
  2: /* ilut.f -- translated by f2c (version of 25 March 1992  12:58:56).

  4:      The Fortran version of this code was developed by Yousef Saad.
  5:   This code is copyrighted by Yousef Saad with the 

  7:                     GNU GENERAL PUBLIC LICENSE
  8:                        Version 2, June 1991

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345: Public License instead of this License.

347: */
348:  #include petsc.h

350: static int SPARSEKIT2qsplit(PetscScalar *a,int *ind,int *n,int *ncut)
351: {
352:     /* System generated locals */
353:     int i__1;
354:     PetscScalar d__1;

356:     /* Local variables */
357:     int last,itmp,j,first;
358:     PetscReal abskey;
359:     int mid;
360:     PetscScalar tmp;

362: /* -----------------------------------------------------------------------
363:  */
364: /*     does a quick-sort split of a real array. */
365: /*     on input a(1:n). is a real array */
366: /*     on output a(1:n) is permuted such that its elements satisfy: */

368: /*     abs(a(i)) .ge. abs(a(ncut)) for i .lt. ncut and */
369: /*     abs(a(i)) .le. abs(a(ncut)) for i .gt. ncut */

371: /*    ind(1:n) is an integer array which permuted in the same way as a(*).
372: */
373: /* -----------------------------------------------------------------------
374:  */
375: /* ----- */
376:     /* Parameter adjustments */
377:     --ind;
378:     --a;

380:     /* Function Body */
381:     first = 1;
382:     last = *n;
383:     if (*ncut < first || *ncut > last) {
384:         return 0;
385:     }

387: /*     outer loop -- while mid .ne. ncut do */

389: L1:
390:     mid = first;
391:     abskey = (d__1 = a[mid],PetscAbsScalar(d__1));
392:     i__1 = last;
393:     for (j = first + 1; j <= i__1; ++j) {
394:         if ((d__1 = a[j],PetscAbsScalar(d__1)) > abskey) {
395:             ++mid;
396: /*     interchange */
397:             tmp = a[mid];
398:             itmp = ind[mid];
399:             a[mid] = a[j];
400:             ind[mid] = ind[j];
401:             a[j] = tmp;
402:             ind[j] = itmp;
403:         }
404: /* L2: */
405:     }

407: /*     interchange */

409:     tmp = a[mid];
410:     a[mid] = a[first];
411:     a[first] = tmp;

413:     itmp = ind[mid];
414:     ind[mid] = ind[first];
415:     ind[first] = itmp;

417: /*     test for while loop */

419:     if (mid == *ncut) {
420:         return 0;
421:     }
422:     if (mid > *ncut) {
423:         last = mid - 1;
424:     } else {
425:         first = mid + 1;
426:     }
427:     goto L1;
428: /* ----------------end-of-qsplit------------------------------------------
429:  */
430: /* -----------------------------------------------------------------------
431:  */
432: } /* qsplit_ */


435: /* ---------------------------------------------------------------------- */
436: int SPARSEKIT2ilutp(int *n,PetscScalar *a,int *ja,int * ia,int *lfil,PetscReal droptol,PetscReal *permtol,int *mbloc,PetscScalar *alu,
437:         int *jlu,int *ju,int *iwk,PetscScalar *w,int *jw,  int *iperm,int *ierr)
438: {
439:     /* System generated locals */
440:     int i__1,i__2;
441:     PetscScalar d__1;

443:     /* Local variables */
444:     PetscScalar fact;
445:     int lenl,imax,lenu,icut,jpos;
446:     PetscReal xmax;
447:     int jrow;
448:     PetscReal xmax0;
449:     int i,j,k;
450:     PetscScalar s,t;
451:     int j_1,j2;
452:     PetscReal tnorm,t1;
453:     int ii,jj;
454:     int ju0,len;
455:     PetscScalar tmp;

457: /* -----------------------------------------------------------------------
458:  */
459: /*     implicit none */
460: /* ----------------------------------------------------------------------*
461:  */
462: /*       *** ILUTP preconditioner -- ILUT with pivoting  ***            * 
463: */
464: /*      incomplete LU factorization with dual truncation mechanism      * 
465: */
466: /* ----------------------------------------------------------------------*
467:  */
468: /* author Yousef Saad *Sep 8, 1993 -- Latest revision, August 1996.     * 
469: */
470: /* ----------------------------------------------------------------------*
471:  */
472: /* on entry: */
473: /* ========== */
474: /* n       = integer. The dimension of the matrix A. */

476: /* a,ja,ia = matrix stored in Compressed Sparse Row format. */
477: /*           ON RETURN THE COLUMNS OF A ARE PERMUTED. SEE BELOW FOR */
478: /*           DETAILS. */

480: /* lfil    = integer. The fill-in parameter. Each row of L and each row */

482: /*           of U will have a maximum of lfil elements (excluding the */
483: /*           diagonal element). lfil must be .ge. 0. */
484: /*           ** WARNING: THE MEANING OF LFIL HAS CHANGED WITH RESPECT TO 
485: */
486: /*           EARLIER VERSIONS. */

488: /* droptol = real*8. Sets the threshold for dropping small terms in the */

490: /*           factorization. See below for details on dropping strategy. */


493: /* lfil    = integer. The fill-in parameter. Each row of L and */
494: /*           each row of U will have a maximum of lfil elements. */
495: /*           WARNING: THE MEANING OF LFIL HAS CHANGED WITH RESPECT TO */
496: /*           EARLIER VERSIONS. */
497: /*           lfil must be .ge. 0. */

499: /* permtol = tolerance ratio used to  determne whether or not to permute 
500: */
501: /*           two columns.  At step i columns i and j are permuted when */

503: /*                     abs(a(i,j))*permtol .gt. abs(a(i,i)) */

505: /*           [0 --> never permute; good values 0.1 to 0.01] */

507: /* mbloc   = if desired, permuting can be done only within the diagonal */

509: /*           blocks of size mbloc. Useful for PDE problems with several */

511: /*           degrees of freedom.. If feature not wanted take mbloc=n. */


514: /* iwk     = integer. The lengths of arrays alu and jlu. If the arrays */
515: /*           are not big enough to store the ILU factorizations, ilut */
516: /*           will stop with an error message. */

518: /* On return: */
519: /* =========== */

521: /* alu,jlu = matrix stored in Modified Sparse Row (MSR) format containing 
522: */
523: /*           the L and U factors together. The diagonal (stored in */
524: /*           alu(1:n)) is inverted. Each i-th row of the alu,jlu matrix 
525: */
526: /*           contains the i-th row of L (excluding the diagonal entry=1) 
527: */
528: /*           followed by the i-th row of U. */

530: /* ju      = integer array of length n containing the pointers to */
531: /*           the beginning of each row of U in the matrix alu,jlu. */

533: /* iperm   = contains the permutation arrays. */
534: /*           iperm(1:n) = old numbers of unknowns */
535: /*           iperm(n+1:2*n) = reverse permutation = new unknowns. */

537: /* integer. Error message with the following meaning. */
538: /*           0    --> successful return. */
539: /*           ierr .gt. 0  --> zero pivot encountered at step number ierr. 
540: */
541: /*           -1   --> Error. input matrix may be wrong. */
542: /*                            (The elimination process has generated a */
543: /*                            row in L or U whose length is .gt.  n.) */
544: /*           -2   --> The matrix L overflows the array al. */
545: /*           -3   --> The matrix U overflows the array alu. */
546: /*           -4   --> Illegal value for lfil. */
547: /*           -5   --> zero row encountered. */

549: /* work arrays: */
550: /* ============= */
551: /* jw      = integer work array of length 2*n. */
552: /* w       = real work array of length n */

554: /* IMPORTANR NOTE: */
555: /* -------------- */
556: /* TO AVOID PERMUTING THE SOLUTION VECTORS ARRAYS FOR EACH LU-SOLVE, */
557: /* THE MATRIX A IS PERMUTED ON RETURN. [all column indices are */
558: /* changed]. SIMILARLY FOR THE U MATRIX. */
559: /* To permute the matrix back to its original state use the loop: */

561: /*      do k=ia(1), ia(n+1)-1 */
562: /*         ja(k) = iperm(ja(k)) */
563: /*      enddo */

565: /* -----------------------------------------------------------------------
566:  */
567: /*     local variables */


570:     /* Parameter adjustments */
571:     --iperm;
572:     --jw;
573:     --w;
574:     --ju;
575:     --jlu;
576:     --alu;
577:     --ia;
578:     --ja;
579:     --a;

581:     /* Function Body */
582:     if (*lfil < 0) {
583:         goto L998;
584:     }
585: /* -----------------------------------------------------------------------
586:  */
587: /*     initialize ju0 (points to next element to be added to alu,jlu) */
588: /*     and pointer array. */
589: /* -----------------------------------------------------------------------
590:  */
591:     ju0 = *n + 2;
592:     jlu[1] = ju0;

594: /*  integer PetscReal pointer array. */

596:     i__1 = *n;
597:     for (j = 1; j <= i__1; ++j) {
598:         jw[*n + j] = 0;
599:         iperm[j] = j;
600:         iperm[*n + j] = j;
601: /* L1: */
602:     }
603: /* -----------------------------------------------------------------------
604:  */
605: /*     beginning of main loop. */
606: /* -----------------------------------------------------------------------
607:  */
608:     i__1 = *n;
609:     for (ii = 1; ii <= i__1; ++ii) {
610:         j_1 = ia[ii];
611:         j2 = ia[ii + 1] - 1;
612:         tnorm = 0.;
613:         i__2 = j2;
614:         for (k = j_1; k <= i__2; ++k) {
615:             tnorm += (d__1 = a[k], PetscAbsScalar(d__1));
616: /* L501: */
617:         }
618:         if (tnorm == 0.) {
619:             goto L999;
620:         }
621:         tnorm /= j2 - j_1 + 1;

623: /*     unpack L-part and U-part of row of A in arrays  w  -- */

625:         lenu = 1;
626:         lenl = 0;
627:         jw[ii] = ii;
628:         w[ii] = (float)0.;
629:         jw[*n + ii] = ii;

631:         i__2 = j2;
632:         for (j = j_1; j <= i__2; ++j) {
633:             k = iperm[*n + ja[j]];
634:             t = a[j];
635:             if (k < ii) {
636:                 ++lenl;
637:                 jw[lenl] = k;
638:                 w[lenl] = t;
639:                 jw[*n + k] = lenl;
640:             } else if (k == ii) {
641:                 w[ii] = t;
642:             } else {
643:                 ++lenu;
644:                 jpos = ii + lenu - 1;
645:                 jw[jpos] = k;
646:                 w[jpos] = t;
647:                 jw[*n + k] = jpos;
648:             }
649: /* L170: */
650:         }
651:         jj = 0;
652:         len = 0;

654: /*     eliminate previous rows */

656: L150:
657:         ++jj;
658:         if (jj > lenl) {
659:             goto L160;
660:         }
661: /* ------------------------------------------------------------------
662: ----- */
663: /*     in order to do the elimination in the correct order we must sel
664: ect */
665: /*     the smallest column index among jw(k), k=jj+1, ..., lenl. */
666: /* ------------------------------------------------------------------
667: ----- */
668:         jrow = jw[jj];
669:         k = jj;

671: /*     determine smallest column index */

673:         i__2 = lenl;
674:         for (j = jj + 1; j <= i__2; ++j) {
675:             if (jw[j] < jrow) {
676:                 jrow = jw[j];
677:                 k = j;
678:             }
679: /* L151: */
680:         }

682:         if (k != jj) {
683: /*     exchange in jw */
684:             j = jw[jj];
685:             jw[jj] = jw[k];
686:             jw[k] = j;
687: /*     exchange in jr */
688:             jw[*n + jrow] = jj;
689:             jw[*n + j] = k;
690: /*     exchange in w */
691:             s = w[jj];
692:             w[jj] = w[k];
693:             w[k] = s;
694:         }

696: /*     zero out element in row by resetting jw(n+jrow) to zero. */

698:         jw[*n + jrow] = 0;

700: /*     get the multiplier for row to be eliminated: jrow */

702:         fact = w[jj] * alu[jrow];

704: /*     drop term if small */

706:         if (PetscAbsScalar(fact) <= droptol) {
707:             goto L150;
708:         }

710: /*     combine current row and row jrow */

712:         i__2 = jlu[jrow + 1] - 1;
713:         for (k = ju[jrow]; k <= i__2; ++k) {
714:             s = fact * alu[k];
715: /*     new column number */
716:             j = iperm[*n + jlu[k]];
717:             jpos = jw[*n + j];
718:             if (j >= ii) {

720: /*     dealing with upper part. */

722:                 if (jpos == 0) {

724: /*     this is a fill-in element */

726:                     ++lenu;
727:                     i = ii + lenu - 1;
728:                     if (lenu > *n) {
729:                         goto L995;
730:                     }
731:                     jw[i] = j;
732:                     jw[*n + j] = i;
733:                     w[i] = -s;
734:                 } else {
735: /*     no fill-in element -- */
736:                     w[jpos] -= s;
737:                 }
738:             } else {

740: /*     dealing with lower part. */

742:                 if (jpos == 0) {

744: /*     this is a fill-in element */

746:                     ++lenl;
747:                     if (lenl > *n) {
748:                         goto L995;
749:                     }
750:                     jw[lenl] = j;
751:                     jw[*n + j] = lenl;
752:                     w[lenl] = -s;
753:                 } else {

755: /*     this is not a fill-in element */

757:                     w[jpos] -= s;
758:                 }
759:             }
760: /* L203: */
761:         }

763: /*     store this pivot element -- (from left to right -- no danger of
764:  */
765: /*     overlap with the working elements in L (pivots). */

767:         ++len;
768:         w[len] = fact;
769:         jw[len] = jrow;
770:         goto L150;
771: L160:

773: /*     reset double-pointer to zero (U-part) */

775:         i__2 = lenu;
776:         for (k = 1; k <= i__2; ++k) {
777:             jw[*n + jw[ii + k - 1]] = 0;
778: /* L308: */
779:         }

781: /*     update L-matrix */

783:         lenl = len;
784:         len = PetscMin(lenl,*lfil);

786: /*     sort by quick-split */

788:         SPARSEKIT2qsplit(&w[1], &jw[1], &lenl, &len);

790: /*     store L-part -- in original coordinates .. */

792:         i__2 = len;
793:         for (k = 1; k <= i__2; ++k) {
794:             if (ju0 > *iwk) {
795:                 goto L996;
796:             }
797:             alu[ju0] = w[k];
798:             jlu[ju0] = iperm[jw[k]];
799:             ++ju0;
800: /* L204: */
801:         }

803: /*     save pointer to beginning of row ii of U */

805:         ju[ii] = ju0;

807: /*     update U-matrix -- first apply dropping strategy */

809:         len = 0;
810:         i__2 = lenu - 1;
811:         for (k = 1; k <= i__2; ++k) {
812:             if ((d__1 = w[ii + k], PetscAbsScalar(d__1)) > droptol * tnorm) {
813:                 ++len;
814:                 w[ii + len] = w[ii + k];
815:                 jw[ii + len] = jw[ii + k];
816:             }
817:         }
818:         lenu = len + 1;
819:         len = PetscMin(lenu,*lfil);
820:         i__2 = lenu - 1;
821:         SPARSEKIT2qsplit(&w[ii + 1], &jw[ii + 1], &i__2, &len);

823: /*     determine next pivot -- */

825:         imax = ii;
826:         xmax = (d__1 = w[imax], PetscAbsScalar(d__1));
827:         xmax0 = xmax;
828:         icut = ii - 1 + *mbloc - (ii - 1) % *mbloc;
829:         i__2 = ii + len - 1;
830:         for (k = ii + 1; k <= i__2; ++k) {
831:             t1 = (d__1 = w[k], PetscAbsScalar(d__1));
832:             if (t1 > xmax && t1 * *permtol > xmax0 && jw[k] <= icut) {
833:                 imax = k;
834:                 xmax = t1;
835:             }
836:         }

838: /*     exchange w's */

840:         tmp = w[ii];
841:         w[ii] = w[imax];
842:         w[imax] = tmp;

844: /*     update iperm and reverse iperm */

846:         j = jw[imax];
847:         i = iperm[ii];
848:         iperm[ii] = iperm[j];
849:         iperm[j] = i;

851: /*     reverse iperm */

853:         iperm[*n + iperm[ii]] = ii;
854:         iperm[*n + iperm[j]] = j;
855: /* ------------------------------------------------------------------
856: ----- */

858:         if (len + ju0 > *iwk) {
859:             goto L997;
860:         }

862: /*     copy U-part in original coordinates */

864:         i__2 = ii + len - 1;
865:         for (k = ii + 1; k <= i__2; ++k) {
866:             jlu[ju0] = iperm[jw[k]];
867:             alu[ju0] = w[k];
868:             ++ju0;
869: /* L302: */
870:         }

872: /*     store inverse of diagonal element of u */

874:         if (w[ii] == 0.) {
875:             w[ii] = (droptol + 1e-4) * tnorm;
876:         }
877:         alu[ii] = 1. / w[ii];

879: /*     update pointer to beginning of next row of U. */

881:         jlu[ii + 1] = ju0;
882: /* ------------------------------------------------------------------
883: ----- */
884: /*     end main loop */
885: /* ------------------------------------------------------------------
886: ----- */
887: /* L500: */
888:     }

890: /*     permute all column indices of LU ... */

892:     i__1 = jlu[*n + 1] - 1;
893:     for (k = jlu[1]; k <= i__1; ++k) {
894:         jlu[k] = iperm[*n + jlu[k]];
895:     }

897: /*     ...and of A */

899:     i__1 = ia[*n + 1] - 1;
900:     for (k = ia[1]; k <= i__1; ++k) {
901:         ja[k] = iperm[*n + ja[k]];
902:     }

904:     *0;
905:     return 0;

907: /*     incomprehensible error. Matrix must be wrong. */

909: L995:
910:     *-1;
911:     return 0;

913: /*     insufficient storage in L. */

915: L996:
916:     *-2;
917:     return 0;

919: /*     insufficient storage in U. */

921: L997:
922:     *-3;
923:     return 0;

925: /*     illegal lfil entered. */

927: L998:
928:     *-4;
929:     return 0;

931: /*     zero row encountered */

933: L999:
934:     *-5;
935:     return 0;
936: /* ----------------end-of-ilutp-------------------------------------------
937:  */
938: /* -----------------------------------------------------------------------
939:  */
940: } /* ilutp_ */