Actual source code: ido.c

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

      3: #include <../src/mat/graphops/color/impls/minpack/color.h>

      5: static PetscInt c_n1 = -1;

      7: PetscErrorCode MINPACKido(PetscInt *m, PetscInt *n, const PetscInt *indrow, const PetscInt *jpntr, const PetscInt *indcol, const PetscInt *ipntr, PetscInt *ndeg, PetscInt *list, PetscInt *maxclq, PetscInt *iwa1, PetscInt *iwa2, PetscInt *iwa3, PetscInt *iwa4)
      8: {
      9:   /* System generated locals */
     10:   PetscInt i__1, i__2, i__3, i__4;

     12:   /* Local variables */
     13:   PetscInt jcol = 0, ncomp = 0, ic, ip, jp, ir, maxinc, numinc, numord, maxlst, numwgt, numlst;

     15:   /*     Given the sparsity pattern of an m by n matrix A, this */
     16:   /*     subroutine determines an incidence-degree ordering of the */
     17:   /*     columns of A. */
     18:   /*     The incidence-degree ordering is defined for the loopless */
     19:   /*     graph G with vertices a(j), j = 1,2,...,n where a(j) is the */
     20:   /*     j-th column of A and with edge (a(i),a(j)) if and only if */
     21:   /*     columns i and j have a non-zero in the same row position. */
     22:   /*     The incidence-degree ordering is determined recursively by */
     23:   /*     letting list(k), k = 1,...,n be a column with maximal */
     24:   /*     incidence to the subgraph spanned by the ordered columns. */
     25:   /*     Among all the columns of maximal incidence, ido chooses a */
     26:   /*     column of maximal degree. */
     27:   /*     The subroutine statement is */
     28:   /*       subroutine ido(m,n,indrow,jpntr,indcol,ipntr,ndeg,list, */
     29:   /*                      maxclq,iwa1,iwa2,iwa3,iwa4) */
     30:   /*     where */
     31:   /*       m is a positive integer input variable set to the number */
     32:   /*         of rows of A. */
     33:   /*       n is a positive integer input variable set to the number */
     34:   /*         of columns of A. */
     35:   /*       indrow is an integer input array which contains the row */
     36:   /*         indices for the non-zeroes in the matrix A. */
     37:   /*       jpntr is an integer input array of length n + 1 which */
     38:   /*         specifies the locations of the row indices in indrow. */
     39:   /*         The row indices for column j are */
     40:   /*               indrow(k), k = jpntr(j),...,jpntr(j+1)-1. */
     41:   /*         Note that jpntr(n+1)-1 is then the number of non-zero */
     42:   /*         elements of the matrix A. */
     43:   /*       indcol is an integer input array which contains the */
     44:   /*         column indices for the non-zeroes in the matrix A. */
     45:   /*       ipntr is an integer input array of length m + 1 which */
     46:   /*         specifies the locations of the column indices in indcol. */
     47:   /*         The column indices for row i are */
     48:   /*               indcol(k), k = ipntr(i),...,ipntr(i+1)-1. */
     49:   /*         Note that ipntr(m+1)-1 is then the number of non-zero */
     50:   /*         elements of the matrix A. */
     51:   /*       ndeg is an integer input array of length n which specifies */
     52:   /*         the degree sequence. The degree of the j-th column */
     53:   /*         of A is ndeg(j). */
     54:   /*       list is an integer output array of length n which specifies */
     55:   /*         the incidence-degree ordering of the columns of A. The j-th */
     56:   /*         column in this order is list(j). */
     57:   /*       maxclq is an integer output variable set to the size */
     58:   /*         of the largest clique found during the ordering. */
     59:   /*       iwa1,iwa2,iwa3, and iwa4 are integer work arrays of length n. */
     60:   /*     Subprograms called */
     61:   /*       MINPACK-supplied ... numsrt */
     62:   /*       FORTRAN-supplied ... max */
     63:   /*     Argonne National Laboratory. MINPACK Project. August 1984. */
     64:   /*     Thomas F. Coleman, Burton S. Garbow, Jorge J. More' */

     66:   /*     Sort the degree sequence. */

     68:   PetscFunctionBegin;
     69:   /* Parameter adjustments */
     70:   --iwa4;
     71:   --iwa3;
     72:   --iwa2;
     73:   --list;
     74:   --ndeg;
     75:   --ipntr;
     76:   --indcol;
     77:   --jpntr;
     78:   --indrow;

     80:   /* Function Body */
     81:   i__1 = *n - 1;
     82:   PetscCall(MINPACKnumsrt(n, &i__1, &ndeg[1], &c_n1, &iwa4[1], &iwa2[1], &iwa3[1]));

     84:   /*     Initialization block. */
     85:   /*     Create a doubly-linked list to access the incidences of the */
     86:   /*     columns. The pointers for the linked list are as follows. */
     87:   /*     Each un-ordered column ic is in a list (the incidence list) */
     88:   /*     of columns with the same incidence. */
     89:   /*     iwa1(numinc) is the first column in the numinc list */
     90:   /*     unless iwa1(numinc) = 0. In this case there are */
     91:   /*     no columns in the numinc list. */
     92:   /*     iwa2(ic) is the column before ic in the incidence list */
     93:   /*     unless iwa2(ic) = 0. In this case ic is the first */
     94:   /*     column in this incidence list. */
     95:   /*     iwa3(ic) is the column after ic in the incidence list */
     96:   /*     unless iwa3(ic) = 0. In this case ic is the last */
     97:   /*     column in this incidence list. */
     98:   /*     If ic is an un-ordered column, then list(ic) is the */
     99:   /*     incidence of ic to the graph induced by the ordered */
    100:   /*     columns. If jcol is an ordered column, then list(jcol) */
    101:   /*     is the incidence-degree order of column jcol. */

    103:   maxinc = 0;
    104:   for (jp = *n; jp >= 1; --jp) {
    105:     ic            = iwa4[jp];
    106:     iwa1[*n - jp] = 0;
    107:     iwa2[ic]      = 0;
    108:     iwa3[ic]      = iwa1[0];
    109:     if (iwa1[0] > 0) iwa2[iwa1[0]] = ic;
    110:     iwa1[0]  = ic;
    111:     iwa4[jp] = 0;
    112:     list[jp] = 0;
    113:   }

    115:   /*     Determine the maximal search length for the list */
    116:   /*     of columns of maximal incidence. */

    118:   maxlst = 0;
    119:   i__1   = *m;
    120:   for (ir = 1; ir <= i__1; ++ir) {
    121:     /* Computing 2nd power */
    122:     i__2 = ipntr[ir + 1] - ipntr[ir];
    123:     maxlst += i__2 * i__2;
    124:   }
    125:   maxlst /= *n;
    126:   *maxclq = 0;
    127:   numord  = 1;

    129:   /*     Beginning of iteration loop. */

    131: L30:

    133:   /*        Choose a column jcol of maximal degree among the */
    134:   /*        columns of maximal incidence maxinc. */

    136: L40:
    137:   jp = iwa1[maxinc];
    138:   if (jp > 0) goto L50;
    139:   --maxinc;
    140:   goto L40;
    141: L50:
    142:   numwgt = -1;
    143:   i__1   = maxlst;
    144:   for (numlst = 1; numlst <= i__1; ++numlst) {
    145:     if (ndeg[jp] > numwgt) {
    146:       numwgt = ndeg[jp];
    147:       jcol   = jp;
    148:     }
    149:     jp = iwa3[jp];
    150:     if (jp <= 0) goto L70;
    151:   }
    152: L70:
    153:   list[jcol] = numord;

    155:   /*        Update the size of the largest clique */
    156:   /*        found during the ordering. */

    158:   if (!maxinc) ncomp = 0;
    159:   ++ncomp;
    160:   if (maxinc + 1 == ncomp) *maxclq = PetscMax(*maxclq, ncomp);

    162:   /*        Termination test. */

    164:   ++numord;
    165:   if (numord > *n) goto L100;

    167:   /*        Delete column jcol from the maxinc list. */

    169:   if (!iwa2[jcol]) iwa1[maxinc] = iwa3[jcol];
    170:   else iwa3[iwa2[jcol]] = iwa3[jcol];

    172:   if (iwa3[jcol] > 0) iwa2[iwa3[jcol]] = iwa2[jcol];

    174:   /*        Find all columns adjacent to column jcol. */

    176:   iwa4[jcol] = *n;

    178:   /*        Determine all positions (ir,jcol) which correspond */
    179:   /*        to non-zeroes in the matrix. */

    181:   i__1 = jpntr[jcol + 1] - 1;
    182:   for (jp = jpntr[jcol]; jp <= i__1; ++jp) {
    183:     ir = indrow[jp];

    185:     /*           For each row ir, determine all positions (ir,ic) */
    186:     /*           which correspond to non-zeroes in the matrix. */

    188:     i__2 = ipntr[ir + 1] - 1;
    189:     for (ip = ipntr[ir]; ip <= i__2; ++ip) {
    190:       ic = indcol[ip];

    192:       /*              Array iwa4 marks columns which are adjacent to */
    193:       /*              column jcol. */

    195:       if (iwa4[ic] < numord) {
    196:         iwa4[ic] = numord;

    198:         /*                 Update the pointers to the current incidence lists. */

    200:         numinc = list[ic];
    201:         ++list[ic];
    202:         /* Computing MAX */
    203:         i__3   = maxinc;
    204:         i__4   = list[ic];
    205:         maxinc = PetscMax(i__3, i__4);

    207:         /*                 Delete column ic from the numinc list. */

    209:         if (!iwa2[ic]) iwa1[numinc] = iwa3[ic];
    210:         else iwa3[iwa2[ic]] = iwa3[ic];

    212:         if (iwa3[ic] > 0) iwa2[iwa3[ic]] = iwa2[ic];

    214:         /*                 Add column ic to the numinc+1 list. */

    216:         iwa2[ic] = 0;
    217:         iwa3[ic] = iwa1[numinc + 1];
    218:         if (iwa1[numinc + 1] > 0) iwa2[iwa1[numinc + 1]] = ic;
    219:         iwa1[numinc + 1] = ic;
    220:       }
    221:     }
    222:   }

    224:   /*        End of iteration loop. */

    226:   goto L30;
    227: L100:

    229:   /*     Invert the array list. */

    231:   i__1 = *n;
    232:   for (jcol = 1; jcol <= i__1; ++jcol) iwa2[list[jcol]] = jcol;
    233:   i__1 = *n;
    234:   for (jp = 1; jp <= i__1; ++jp) list[jp] = iwa2[jp];
    235:   PetscFunctionReturn(PETSC_SUCCESS);
    236: }