Actual source code: ilut.c

  1: #define PETSCMAT_DLL

 3:  #include petsc.h
  4: #if !defined(PETSC_AVOID_GNUCOPYRIGHT_CODE)

  6: /* ilut.f -- translated by f2c (version of 25 March 1992  12:58:56).

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

 11:                     GNU GENERAL PUBLIC LICENSE
 12:                        Version 2, June 1991

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303:     <one line to give the program's name and a brief idea of what it does.>
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348: library.  If this is what you want to do, use the GNU Library General
349: Public License instead of this License.

351: */

353: static PetscErrorCode SPARSEKIT2qsplit(PetscScalar *a,PetscInt *ind,PetscInt *n,PetscInt *ncut)
354: {
355:     /* System generated locals */
356:     PetscInt i__1;
357:     PetscScalar d__1;

359:     /* Local variables */
360:     PetscInt last,itmp,j,first;
361:     PetscReal abskey;
362:     PetscInt mid;
363:     PetscScalar tmp;

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

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

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

383:     /* Function Body */
384:     first = 1;
385:     last = *n;
386:     if (*ncut < first || *ncut > last) {
387:         return 0;
388:     }

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

392: L1:
393:     mid = first;
394:     abskey = (d__1 = a[mid],PetscAbsScalar(d__1));
395:     i__1 = last;
396:     for (j = first + 1; j <= i__1; ++j) {
397:         if ((d__1 = a[j],PetscAbsScalar(d__1)) > abskey) {
398:             ++mid;
399: /*     interchange */
400:             tmp = a[mid];
401:             itmp = ind[mid];
402:             a[mid] = a[j];
403:             ind[mid] = ind[j];
404:             a[j] = tmp;
405:             ind[j] = itmp;
406:         }
407: /* L2: */
408:     }

410: /*     interchange */

412:     tmp = a[mid];
413:     a[mid] = a[first];
414:     a[first] = tmp;

416:     itmp = ind[mid];
417:     ind[mid] = ind[first];
418:     ind[first] = itmp;

420: /*     test for while loop */

422:     if (mid == *ncut) {
423:         return 0;
424:     }
425:     if (mid > *ncut) {
426:         last = mid - 1;
427:     } else {
428:         first = mid + 1;
429:     }
430:     goto L1;
431: /* ----------------end-of-qsplit------------------------------------------
432:  */
433: /* -----------------------------------------------------------------------
434:  */
435: } /* qsplit_ */


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

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

460: /* -----------------------------------------------------------------------
461:  */
462: /*     implicit none */
463: /* ----------------------------------------------------------------------*
464:  */
465: /*       *** ILUTP preconditioner -- ILUT with pivoting  ***            * 
466: */
467: /*      incomplete LU factorization with dual truncation mechanism      * 
468: */
469: /* ----------------------------------------------------------------------*
470:  */
471: /* author Yousef Saad *Sep 8, 1993 -- Latest revision, August 1996.     * 
472: */
473: /* ----------------------------------------------------------------------*
474:  */
475: /* on entry: */
476: /* ========== */
477: /* n       = integer. The dimension of the matrix A. */

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

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

485: /*           of U will have a maximum of lfil elements (excluding the */
486: /*           diagonal element). lfil must be .ge. 0. */
487: /*           ** WARNING: THE MEANING OF LFIL HAS CHANGED WITH RESPECT TO 
488: */
489: /*           EARLIER VERSIONS. */

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

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


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

502: /* permtol = tolerance ratio used to  determne whether or not to permute 
503: */
504: /*           two columns.  At step i columns i and j are permuted when */

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

508: /*           [0 --> never permute; good values 0.1 to 0.01] */

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

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

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


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

521: /* On return: */
522: /* =========== */

524: /* alu,jlu = matrix stored in Modified Sparse Row (MSR) format containing 
525: */
526: /*           the L and U factors together. The diagonal (stored in */
527: /*           alu(1:n)) is inverted. Each i-th row of the alu,jlu matrix 
528: */
529: /*           contains the i-th row of L (excluding the diagonal entry=1) 
530: */
531: /*           followed by the i-th row of U. */

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

536: /* iperm   = contains the permutation arrays. */
537: /*           iperm(1:n) = old numbers of unknowns */
538: /*           iperm(n+1:2*n) = reverse permutation = new unknowns. */

540: /* integer. Error message with the following meaning. */
541: /*           0    --> successful return. */
542: /*           ierr .gt. 0  --> zero pivot encountered at step number ierr. 
543: */
544: /*           -1   --> Error. input matrix may be wrong. */
545: /*                            (The elimination process has generated a */
546: /*                            row in L or U whose length is .gt.  n.) */
547: /*           -2   --> The matrix L overflows the array al. */
548: /*           -3   --> The matrix U overflows the array alu. */
549: /*           -4   --> Illegal value for lfil. */
550: /*           -5   --> zero row encountered. */

552: /* work arrays: */
553: /* ============= */
554: /* jw      = integer work array of length 2*n. */
555: /* w       = real work array of length n */

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

564: /*      do k=ia(1), ia(n+1)-1 */
565: /*         ja(k) = iperm(ja(k)) */
566: /*      enddo */

568: /* -----------------------------------------------------------------------
569:  */
570: /*     local variables */


573:     /* Parameter adjustments */
574:     --iperm;
575:     --jw;
576:     --w;
577:     --ju;
578:     --jlu;
579:     --alu;
580:     --ia;
581:     --ja;
582:     --a;

584:     /* Function Body */
585:     if (*lfil < 0) {
586:         goto L998;
587:     }
588: /* -----------------------------------------------------------------------
589:  */
590: /*     initialize ju0 (points to next element to be added to alu,jlu) */
591: /*     and pointer array. */
592: /* -----------------------------------------------------------------------
593:  */
594:     ju0 = *n + 2;
595:     jlu[1] = ju0;

597: /*  integer PetscReal pointer array. */

599:     i__1 = *n;
600:     for (j = 1; j <= i__1; ++j) {
601:         jw[*n + j] = 0;
602:         iperm[j] = j;
603:         iperm[*n + j] = j;
604: /* L1: */
605:     }
606: /* -----------------------------------------------------------------------
607:  */
608: /*     beginning of main loop. */
609: /* -----------------------------------------------------------------------
610:  */
611:     i__1 = *n;
612:     for (ii = 1; ii <= i__1; ++ii) {
613:         j_1 = ia[ii];
614:         j2 = ia[ii + 1] - 1;
615:         tnorm = 0.;
616:         i__2 = j2;
617:         for (k = j_1; k <= i__2; ++k) {
618:             tnorm += (d__1 = a[k], PetscAbsScalar(d__1));
619: /* L501: */
620:         }
621:         if (!tnorm) {
622:             goto L999;
623:         }
624:         tnorm /= j2 - j_1 + 1;

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

628:         lenu = 1;
629:         lenl = 0;
630:         jw[ii] = ii;
631:         w[ii] = (float)0.;
632:         jw[*n + ii] = ii;

634:         i__2 = j2;
635:         for (j = j_1; j <= i__2; ++j) {
636:             k = iperm[*n + ja[j]];
637:             t = a[j];
638:             if (k < ii) {
639:                 ++lenl;
640:                 jw[lenl] = k;
641:                 w[lenl] = t;
642:                 jw[*n + k] = lenl;
643:             } else if (k == ii) {
644:                 w[ii] = t;
645:             } else {
646:                 ++lenu;
647:                 jpos = ii + lenu - 1;
648:                 jw[jpos] = k;
649:                 w[jpos] = t;
650:                 jw[*n + k] = jpos;
651:             }
652: /* L170: */
653:         }
654:         jj = 0;
655:         len = 0;

657: /*     eliminate previous rows */

659: L150:
660:         ++jj;
661:         if (jj > lenl) {
662:             goto L160;
663:         }
664: /* ------------------------------------------------------------------
665: ----- */
666: /*     in order to do the elimination in the correct order we must sel
667: ect */
668: /*     the smallest column index among jw(k), k=jj+1, ..., lenl. */
669: /* ------------------------------------------------------------------
670: ----- */
671:         jrow = jw[jj];
672:         k = jj;

674: /*     determine smallest column index */

676:         i__2 = lenl;
677:         for (j = jj + 1; j <= i__2; ++j) {
678:             if (jw[j] < jrow) {
679:                 jrow = jw[j];
680:                 k = j;
681:             }
682: /* L151: */
683:         }

685:         if (k != jj) {
686: /*     exchange in jw */
687:             j = jw[jj];
688:             jw[jj] = jw[k];
689:             jw[k] = j;
690: /*     exchange in jr */
691:             jw[*n + jrow] = jj;
692:             jw[*n + j] = k;
693: /*     exchange in w */
694:             s = w[jj];
695:             w[jj] = w[k];
696:             w[k] = s;
697:         }

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

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

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

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

707: /*     drop term if small */

709:         if (PetscAbsScalar(fact) <= droptol) {
710:             goto L150;
711:         }

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

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

723: /*     dealing with upper part. */

725:                 if (!jpos) {

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

729:                     ++lenu;
730:                     i = ii + lenu - 1;
731:                     if (lenu > *n) {
732:                         goto L995;
733:                     }
734:                     jw[i] = j;
735:                     jw[*n + j] = i;
736:                     w[i] = -s;
737:                 } else {
738: /*     no fill-in element -- */
739:                     w[jpos] -= s;
740:                 }
741:             } else {

743: /*     dealing with lower part. */

745:                 if (!jpos) {

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

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

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

760:                     w[jpos] -= s;
761:                 }
762:             }
763: /* L203: */
764:         }

766: /*     store this pivot element -- (from left to right -- no danger of
767:  */
768: /*     overlap with the working elements in L (pivots). */

770:         ++len;
771:         w[len] = fact;
772:         jw[len] = jrow;
773:         goto L150;
774: L160:

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

778:         i__2 = lenu;
779:         for (k = 1; k <= i__2; ++k) {
780:             jw[*n + jw[ii + k - 1]] = 0;
781: /* L308: */
782:         }

784: /*     update L-matrix */

786:         lenl = len;
787:         len = PetscMin(lenl,*lfil);

789: /*     sort by quick-split */

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

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

795:         i__2 = len;
796:         for (k = 1; k <= i__2; ++k) {
797:             if (ju0 > *iwk) {
798:                 goto L996;
799:             }
800:             alu[ju0] = w[k];
801:             jlu[ju0] = iperm[jw[k]];
802:             ++ju0;
803: /* L204: */
804:         }

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

808:         ju[ii] = ju0;

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

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

826: /*     determine next pivot -- */

828:         imax = ii;
829:         xmax = (d__1 = w[imax], PetscAbsScalar(d__1));
830:         xmax0 = xmax;
831:         icut = ii - 1 + *mbloc - (ii - 1) % *mbloc;
832:         i__2 = ii + len - 1;
833:         for (k = ii + 1; k <= i__2; ++k) {
834:             t1 = (d__1 = w[k], PetscAbsScalar(d__1));
835:             if (t1 > xmax && t1 * *permtol > xmax0 && jw[k] <= icut) {
836:                 imax = k;
837:                 xmax = t1;
838:             }
839:         }

841: /*     exchange w's */

843:         tmp = w[ii];
844:         w[ii] = w[imax];
845:         w[imax] = tmp;

847: /*     update iperm and reverse iperm */

849:         j = jw[imax];
850:         i = iperm[ii];
851:         iperm[ii] = iperm[j];
852:         iperm[j] = i;

854: /*     reverse iperm */

856:         iperm[*n + iperm[ii]] = ii;
857:         iperm[*n + iperm[j]] = j;
858: /* ------------------------------------------------------------------
859: ----- */

861:         if (len + ju0 > *iwk) {
862:             goto L997;
863:         }

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

867:         i__2 = ii + len - 1;
868:         for (k = ii + 1; k <= i__2; ++k) {
869:             jlu[ju0] = iperm[jw[k]];
870:             alu[ju0] = w[k];
871:             ++ju0;
872: /* L302: */
873:         }

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

877:         if (w[ii] == 0.0) {
878:             w[ii] = (droptol + 1e-4) * tnorm;
879:         }
880:         alu[ii] = 1. / w[ii];

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

884:         jlu[ii + 1] = ju0;
885: /* ------------------------------------------------------------------
886: ----- */
887: /*     end main loop */
888: /* ------------------------------------------------------------------
889: ----- */
890: /* L500: */
891:     }

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

895:     i__1 = jlu[*n + 1] - 1;
896:     for (k = jlu[1]; k <= i__1; ++k) {
897:         jlu[k] = iperm[*n + jlu[k]];
898:     }

900: /*     ...and of A */

902:     i__1 = ia[*n + 1] - 1;
903:     for (k = ia[1]; k <= i__1; ++k) {
904:         ja[k] = iperm[*n + ja[k]];
905:     }

907:     *0;
908:     return 0;

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

912: L995:
913:     *-1;
914:     return 0;

916: /*     insufficient storage in L. */

918: L996:
919:     *-2;
920:     return 0;

922: /*     insufficient storage in U. */

924: L997:
925:     *-3;
926:     return 0;

928: /*     illegal lfil entered. */

930: L998:
931:     *-4;
932:     return 0;

934: /*     zero row encountered */

936: L999:
937:     *-5;
938:     return 0;
939: /* ----------------end-of-ilutp-------------------------------------------
940:  */
941: /* -----------------------------------------------------------------------
942:  */
943: } /* ilutp_ */
944: #endif