Actual source code: slo.c


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

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

  6: PetscErrorCode MINPACKslo(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)
  7: {
  8:   /* System generated locals */
  9:   PetscInt i__1, i__2, i__3, i__4;

 11:   /* Local variables */
 12:   PetscInt jcol, ic, ip, jp, ir, mindeg, numdeg, numord;

 14:   /*     Given the sparsity pattern of an m by n matrix A, this */
 15:   /*     subroutine determines the smallest-last ordering of the */
 16:   /*     columns of A. */
 17:   /*     The smallest-last ordering is defined for the loopless */
 18:   /*     graph G with vertices a(j), j = 1,2,...,n where a(j) is the */
 19:   /*     j-th column of A and with edge (a(i),a(j)) if and only if */
 20:   /*     columns i and j have a non-zero in the same row position. */
 21:   /*     The smallest-last ordering is determined recursively by */
 22:   /*     letting list(k), k = n,...,1 be a column with least degree */
 23:   /*     in the subgraph spanned by the un-ordered columns. */
 24:   /*     Note that the value of m is not needed by slo and is */
 25:   /*     therefore not present in the subroutine statement. */
 26:   /*     The subroutine statement is */
 27:   /*       subroutine slo(n,indrow,jpntr,indcol,ipntr,ndeg,list, */
 28:   /*                      maxclq,iwa1,iwa2,iwa3,iwa4) */
 29:   /*     where */
 30:   /*       n is a positive integer input variable set to the number */
 31:   /*         of columns of A. */
 32:   /*       indrow is an integer input array which contains the row */
 33:   /*         indices for the non-zeroes in the matrix A. */
 34:   /*       jpntr is an integer input array of length n + 1 which */
 35:   /*         specifies the locations of the row indices in indrow. */
 36:   /*         The row indices for column j are */
 37:   /*               indrow(k), k = jpntr(j),...,jpntr(j+1)-1. */
 38:   /*         Note that jpntr(n+1)-1 is then the number of non-zero */
 39:   /*         elements of the matrix A. */
 40:   /*       indcol is an integer input array which contains the */
 41:   /*         column indices for the non-zeroes in the matrix A. */
 42:   /*       ipntr is an integer input array of length m + 1 which */
 43:   /*         specifies the locations of the column indices in indcol. */
 44:   /*         The column indices for row i are */
 45:   /*               indcol(k), k = ipntr(i),...,ipntr(i+1)-1. */
 46:   /*         Note that ipntr(m+1)-1 is then the number of non-zero */
 47:   /*         elements of the matrix A. */
 48:   /*       ndeg is an integer input array of length n which specifies */
 49:   /*         the degree sequence. The degree of the j-th column */
 50:   /*         of A is ndeg(j). */
 51:   /*       list is an integer output array of length n which specifies */
 52:   /*         the smallest-last ordering of the columns of A. The j-th */
 53:   /*         column in this order is list(j). */
 54:   /*       maxclq is an integer output variable set to the size */
 55:   /*         of the largest clique found during the ordering. */
 56:   /*       iwa1,iwa2,iwa3, and iwa4 are integer work arrays of length n. */
 57:   /*     Subprograms called */
 58:   /*       FORTRAN-supplied ... min */
 59:   /*     Argonne National Laboratory. MINPACK Project. August 1984. */
 60:   /*     Thomas F. Coleman, Burton S. Garbow, Jorge J. More' */

 62:   /* Parameter adjustments */
 63:   --iwa4;
 64:   --iwa3;
 65:   --iwa2;
 66:   --list;
 67:   --ndeg;
 68:   --ipntr;
 69:   --indcol;
 70:   --jpntr;
 71:   --indrow;

 73:   /* Function Body */
 74:   mindeg = *n;
 75:   i__1   = *n;
 76:   for (jp = 1; jp <= i__1; ++jp) {
 77:     iwa1[jp - 1] = 0;
 78:     iwa4[jp]     = *n;
 79:     list[jp]     = ndeg[jp];
 80:     /* Computing MIN */
 81:     i__2   = mindeg;
 82:     i__3   = ndeg[jp];
 83:     mindeg = PetscMin(i__2, i__3);
 84:   }

 86:   /*     Create a doubly-linked list to access the degrees of the */
 87:   /*     columns. The pointers for the linked list are as follows. */

 89:   /*     Each un-ordered column ic is in a list (the degree list) */
 90:   /*     of columns with the same degree. */

 92:   /*     iwa1(numdeg) is the first column in the numdeg list */
 93:   /*     unless iwa1(numdeg) = 0. In this case there are */
 94:   /*     no columns in the numdeg list. */

 96:   /*     iwa2(ic) is the column before ic in the degree list */
 97:   /*     unless iwa2(ic) = 0. In this case ic is the first */
 98:   /*     column in this degree list. */

100:   /*     iwa3(ic) is the column after ic in the degree list */
101:   /*     unless iwa3(ic) = 0. In this case ic is the last */
102:   /*     column in this degree list. */

104:   /*     If ic is an un-ordered column, then list(ic) is the */
105:   /*     degree of ic in the graph induced by the un-ordered */
106:   /*     columns. If jcol is an ordered column, then list(jcol) */
107:   /*     is the smallest-last order of column jcol. */

109:   i__1 = *n;
110:   for (jp = 1; jp <= i__1; ++jp) {
111:     numdeg   = ndeg[jp];
112:     iwa2[jp] = 0;
113:     iwa3[jp] = iwa1[numdeg];
114:     if (iwa1[numdeg] > 0) iwa2[iwa1[numdeg]] = jp;
115:     iwa1[numdeg] = jp;
116:   }
117:   *maxclq = 0;
118:   numord  = *n;

120:   /*     Beginning of iteration loop. */

122: L30:

124:   /*        Choose a column jcol of minimal degree mindeg. */

126: L40:
127:   jcol = iwa1[mindeg];
128:   if (jcol > 0) goto L50;
129:   ++mindeg;
130:   goto L40;
131: L50:
132:   list[jcol] = numord;

134:   /*        Mark the size of the largest clique */
135:   /*        found during the ordering. */

137:   if (mindeg + 1 == numord && !*maxclq) *maxclq = numord;

139:   /*        Termination test. */

141:   --numord;
142:   if (!numord) goto L80;

144:   /*        Delete column jcol from the mindeg list. */

146:   iwa1[mindeg] = iwa3[jcol];
147:   if (iwa3[jcol] > 0) iwa2[iwa3[jcol]] = 0;

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

151:   iwa4[jcol] = 0;

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

156:   i__1 = jpntr[jcol + 1] - 1;
157:   for (jp = jpntr[jcol]; jp <= i__1; ++jp) {
158:     ir = indrow[jp];

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

163:     i__2 = ipntr[ir + 1] - 1;
164:     for (ip = ipntr[ir]; ip <= i__2; ++ip) {
165:       ic = indcol[ip];

167:       /*              Array iwa4 marks columns which are adjacent to */
168:       /*              column jcol. */

170:       if (iwa4[ic] > numord) {
171:         iwa4[ic] = numord;

173:         /*                 Update the pointers to the current degree lists. */

175:         numdeg = list[ic];
176:         --list[ic];
177:         /* Computing MIN */
178:         i__3   = mindeg;
179:         i__4   = list[ic];
180:         mindeg = PetscMin(i__3, i__4);

182:         /*                 Delete column ic from the numdeg list. */

184:         if (!iwa2[ic]) iwa1[numdeg] = iwa3[ic];
185:         else iwa3[iwa2[ic]] = iwa3[ic];

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

189:         /*                 Add column ic to the numdeg-1 list. */

191:         iwa2[ic] = 0;
192:         iwa3[ic] = iwa1[numdeg - 1];
193:         if (iwa1[numdeg - 1] > 0) iwa2[iwa1[numdeg - 1]] = ic;
194:         iwa1[numdeg - 1] = ic;
195:       }
196:     }
197:   }

199:   /*        End of iteration loop. */

201:   goto L30;
202: L80:

204:   /*     Invert the array list. */

206:   i__1 = *n;
207:   for (jcol = 1; jcol <= i__1; ++jcol) iwa2[list[jcol]] = jcol;

209:   i__1 = *n;
210:   for (jp = 1; jp <= i__1; ++jp) list[jp] = iwa2[jp];
211:   return 0;
212: }