2: /* slo.f -- translated by f2c (version of 25 March 1992 12:58:56).*/
4: #include <../src/mat/color/color.h>
8: PetscErrorCode MINPACKslo(PetscInt *n,const PetscInt * indrow,const PetscInt * jpntr,const PetscInt * indcol,const PetscInt *ipntr, PetscInt *ndeg,PetscInt * list, 9: PetscInt * maxclq,PetscInt *iwa1,PetscInt * iwa2,PetscInt * iwa3,PetscInt * iwa4) 10: {
11: /* System generated locals */
12: PetscInt i__1, i__2, i__3, i__4;
14: /* Local variables */
15: PetscInt jcol, ic, ip, jp, ir, mindeg, numdeg, numord;
17: /* Given the sparsity pattern of an m by n matrix A, this */
18: /* subroutine determines the smallest-last ordering of the */
19: /* columns of A. */
20: /* The smallest-last ordering is defined for the loopless */
21: /* graph G with vertices a(j), j = 1,2,...,n where a(j) is the */
22: /* j-th column of A and with edge (a(i),a(j)) if and only if */
23: /* columns i and j have a non-zero in the same row position. */
24: /* The smallest-last ordering is determined recursively by */
25: /* letting list(k), k = n,...,1 be a column with least degree */
26: /* in the subgraph spanned by the un-ordered columns. */
27: /* Note that the value of m is not needed by slo and is */
28: /* therefore not present in the subroutine statement. */
29: /* The subroutine statement is */
30: /* subroutine slo(n,indrow,jpntr,indcol,ipntr,ndeg,list, */
31: /* maxclq,iwa1,iwa2,iwa3,iwa4) */
32: /* where */
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 smallest-last 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: /* FORTRAN-supplied ... min */
62: /* Argonne National Laboratory. MINPACK Project. August 1984. */
63: /* Thomas F. Coleman, Burton S. Garbow, Jorge J. More' */
66: /* Parameter adjustments */
67: --iwa4;
68: --iwa3;
69: --iwa2;
70: --list;
71: --ndeg;
72: --ipntr;
73: --indcol;
74: --jpntr;
75: --indrow;
77: /* Function Body */
78: mindeg = *n;
79: i__1 = *n;
80: for (jp = 1; jp <= i__1; ++jp) {
81: iwa1[jp - 1] = 0;
82: iwa4[jp] = *n;
83: list[jp] = ndeg[jp];
84: /* Computing MIN */
85: i__2 = mindeg, i__3 = ndeg[jp];
86: mindeg = PetscMin(i__2,i__3);
87: }
89: /* Create a doubly-linked list to access the degrees of the */
90: /* columns. The pointers for the linked list are as follows. */
92: /* Each un-ordered column ic is in a list (the degree list) */
93: /* of columns with the same degree. */
95: /* iwa1(numdeg) is the first column in the numdeg list */
96: /* unless iwa1(numdeg) = 0. In this case there are */
97: /* no columns in the numdeg list. */
99: /* iwa2(ic) is the column before ic in the degree list */
100: /* unless iwa2(ic) = 0. In this case ic is the first */
101: /* column in this degree list. */
103: /* iwa3(ic) is the column after ic in the degree list */
104: /* unless iwa3(ic) = 0. In this case ic is the last */
105: /* column in this degree list. */
107: /* If ic is an un-ordered column, then list(ic) is the */
108: /* degree of ic in the graph induced by the un-ordered */
109: /* columns. If jcol is an ordered column, then list(jcol) */
110: /* is the smallest-last order of column jcol. */
112: i__1 = *n;
113: for (jp = 1; jp <= i__1; ++jp) {
114: numdeg = ndeg[jp];
115: iwa2[jp] = 0;
116: iwa3[jp] = iwa1[numdeg];
117: if (iwa1[numdeg] > 0) {
118: iwa2[iwa1[numdeg]] = jp;
119: }
120: iwa1[numdeg] = jp;
121: }
122: *maxclq = 0;
123: numord = *n;
125: /* Beginning of iteration loop. */
127: L30:129: /* Choose a column jcol of minimal degree mindeg. */
131: L40:132: jcol = iwa1[mindeg];
133: if (jcol > 0) goto L50;
134: ++mindeg;
135: goto L40;
136: L50:137: list[jcol] = numord;
139: /* Mark the size of the largest clique */
140: /* found during the ordering. */
142: if (mindeg + 1 == numord && !*maxclq) *maxclq = numord;
144: /* Termination test. */
146: --numord;
147: if (!numord) goto L80;
149: /* Delete column jcol from the mindeg list. */
151: iwa1[mindeg] = iwa3[jcol];
152: if (iwa3[jcol] > 0) iwa2[iwa3[jcol]] = 0;
154: /* Find all columns adjacent to column jcol. */
156: iwa4[jcol] = 0;
158: /* Determine all positions (ir,jcol) which correspond */
159: /* to non-zeroes in the matrix. */
161: i__1 = jpntr[jcol + 1] - 1;
162: for (jp = jpntr[jcol]; jp <= i__1; ++jp) {
163: ir = indrow[jp];
165: /* For each row ir, determine all positions (ir,ic) */
166: /* which correspond to non-zeroes in the matrix. */
168: i__2 = ipntr[ir + 1] - 1;
169: for (ip = ipntr[ir]; ip <= i__2; ++ip) {
170: ic = indcol[ip];
172: /* Array iwa4 marks columns which are adjacent to */
173: /* column jcol. */
175: if (iwa4[ic] > numord) {
176: iwa4[ic] = numord;
178: /* Update the pointers to the current degree lists. */
180: numdeg = list[ic];
181: --list[ic];
182: /* Computing MIN */
183: i__3 = mindeg, i__4 = list[ic];
184: mindeg = PetscMin(i__3,i__4);
186: /* Delete column ic from the numdeg list. */
188: if (!iwa2[ic]) iwa1[numdeg] = iwa3[ic];
189: else iwa3[iwa2[ic]] = iwa3[ic];
191: if (iwa3[ic] > 0) iwa2[iwa3[ic]] = iwa2[ic];
193: /* Add column ic to the numdeg-1 list. */
195: iwa2[ic] = 0;
196: iwa3[ic] = iwa1[numdeg - 1];
197: if (iwa1[numdeg - 1] > 0) iwa2[iwa1[numdeg - 1]] = ic;
198: iwa1[numdeg - 1] = ic;
199: }
200: }
201: }
203: /* End of iteration loop. */
205: goto L30;
206: L80:208: /* Invert the array list. */
210: i__1 = *n;
211: for (jcol = 1; jcol <= i__1; ++jcol) iwa2[list[jcol]] = jcol;
213: i__1 = *n;
214: for (jp = 1; jp <= i__1; ++jp) list[jp] = iwa2[jp];
215: return(0);
216: }