typedef int shortint;
/* *************************************************************** */
/* *************************************************************** */
/* **** GENMMD ..... MULTIPLE MINIMUM EXTERNAL DEGREE **** */
/* *************************************************************** */
/* *************************************************************** */
/* AUTHOR - JOSEPH W.H. LIU */
/* DEPT OF COMPUTER SCIENCE, YORK UNIVERSITY. */
/* PURPOSE - THIS ROUTINE IMPLEMENTS THE MINIMUM DEGREE */
/* ALGORITHM. IT MAKES USE OF THE IMPLICIT REPRESENTATION */
/* OF ELIMINATION GRAPHS BY QUOTIENT GRAPHS, AND THE */
/* NOTION OF INDISTINGUISHABLE NODES. IT ALSO IMPLEMENTS */
/* THE MODIFICATIONS BY MULTIPLE ELIMINATION AND MINIMUM */
/* EXTERNAL DEGREE. */
/* --------------------------------------------- */
/* CAUTION - THE ADJACENCY VECTOR ADJNCY WILL BE */
/* DESTROYED. */
/* --------------------------------------------- */
/* INPUT PARAMETERS - */
/* NEQNS - NUMBER OF EQUATIONS. */
/* (XADJ,ADJNCY) - THE ADJACENCY STRUCTURE. */
/* DELTA - TOLERANCE VALUE FOR MULTIPLE ELIMINATION. */
/* MAXINT - MAXIMUM MACHINE REPRESENTABLE (SHORT) INTEGER */
/* (ANY SMALLER ESTIMATE WILL DO) FOR MARKING */
/* NODES. */
/* OUTPUT PARAMETERS - */
/* PERM - THE MINIMUM DEGREE ORDERING. */
/* INVP - THE INVERSE OF PERM. */
/* NOFSUB - AN UPPER BOUND ON THE NUMBER OF NONZERO */
/* SUBSCRIPTS FOR THE COMPRESSED STORAGE SCHEME. */
/* WORKING PARAMETERS - */
/* DHEAD - VECTOR FOR HEAD OF DEGREE LISTS. */
/* INVP - USED TEMPORARILY FOR DEGREE FORWARD LINK. */
/* PERM - USED TEMPORARILY FOR DEGREE BACKWARD LINK. */
/* QSIZE - VECTOR FOR SIZE OF SUPERNODES. */
/* LLIST - VECTOR FOR TEMPORARY LINKED LISTS. */
/* MARKER - A TEMPORARY MARKER VECTOR. */
/* PROGRAM SUBROUTINES - */
/* MMDELM, MMDINT, MMDNUM, MMDUPD. */
/* *************************************************************** */
/* Subroutine */ int genmmd_(int *neqns, int *xadj, shortint *adjncy,
shortint *invp, shortint *perm, int *delta, shortint *dhead,
shortint *qsize, shortint *llist, shortint *marker, int *maxint,
int *nofsub)
{
/* System generated locals */
int i__1;
/* Local variables */
static int mdeg, ehead, i, mdlmt, mdnode;
extern /* Subroutine */ int mmdelm_(int *, int *, shortint *,
shortint *, shortint *, shortint *, shortint *, shortint *,
shortint *, int *, int *), mmdupd_(int *, int *,
int *, shortint *, int *, int *, shortint *, shortint
*, shortint *, shortint *, shortint *, shortint *, int *,
int *), mmdint_(int *, int *, shortint *, shortint *,
shortint *, shortint *, shortint *, shortint *, shortint *),
mmdnum_(int *, shortint *, shortint *, shortint *);
static int nextmd, tag, num;
/* *************************************************************** */
/* *************************************************************** */
/* Parameter adjustments */
--marker;
--llist;
--qsize;
--dhead;
--perm;
--invp;
--adjncy;
--xadj;
/* Function Body */
if (*neqns <= 0) {
return 0;
}
/* ------------------------------------------------ */
/* INITIALIZATION FOR THE MINIMUM DEGREE ALGORITHM. */
/* ------------------------------------------------ */
*nofsub = 0;
mmdint_(neqns, &xadj[1], &adjncy[1], &dhead[1], &invp[1], &perm[1], &
qsize[1], &llist[1], &marker[1]);
/* ---------------------------------------------- */
/* NUM COUNTS THE NUMBER OF ORDERED NODES PLUS 1. */
/* ---------------------------------------------- */
num = 1;
/* ----------------------------- */
/* ELIMINATE ALL ISOLATED NODES. */
/* ----------------------------- */
nextmd = dhead[1];
L100:
if (nextmd <= 0) {
goto L200;
}
mdnode = nextmd;
nextmd = invp[mdnode];
marker[mdnode] = *maxint;
invp[mdnode] = -num;
++num;
goto L100;
L200:
/* ---------------------------------------- */
/* SEARCH FOR NODE OF THE MINIMUM DEGREE. */
/* MDEG IS THE CURRENT MINIMUM DEGREE; */
/* TAG IS USED TO FACILITATE MARKING NODES. */
/* ---------------------------------------- */
if (num > *neqns) {
goto L1000;
}
tag = 1;
dhead[1] = 0;
mdeg = 2;
L300:
if (dhead[mdeg] > 0) {
goto L400;
}
++mdeg;
goto L300;
L400:
/* ------------------------------------------------- */
/* USE VALUE OF DELTA TO SET UP MDLMT, WHICH GOVERNS */
/* WHEN A DEGREE UPDATE IS TO BE PERFORMED. */
/* ------------------------------------------------- */
mdlmt = mdeg + *delta;
ehead = 0;
L500:
mdnode = dhead[mdeg];
if (mdnode > 0) {
goto L600;
}
++mdeg;
if (mdeg > mdlmt) {
goto L900;
}
goto L500;
L600:
/* ---------------------------------------- */
/* REMOVE MDNODE FROM THE DEGREE STRUCTURE. */
/* ---------------------------------------- */
nextmd = invp[mdnode];
dhead[mdeg] = nextmd;
if (nextmd > 0) {
perm[nextmd] = -mdeg;
}
invp[mdnode] = -num;
*nofsub = *nofsub + mdeg + qsize[mdnode] - 2;
if (num + qsize[mdnode] > *neqns) {
goto L1000;
}
/* ---------------------------------------------- */
/* ELIMINATE MDNODE AND PERFORM QUOTIENT GRAPH */
/* TRANSFORMATION. RESET TAG VALUE IF NECESSARY. */
/* ---------------------------------------------- */
++tag;
if (tag < *maxint) {
goto L800;
}
tag = 1;
i__1 = *neqns;
for (i = 1; i <= i__1; ++i) {
if (marker[i] < *maxint) {
marker[i] = 0;
}
/* L700: */
}
L800:
mmdelm_(&mdnode, &xadj[1], &adjncy[1], &dhead[1], &invp[1], &perm[1], &
qsize[1], &llist[1], &marker[1], maxint, &tag);
num += qsize[mdnode];
llist[mdnode] = ehead;
ehead = mdnode;
if (*delta >= 0) {
goto L500;
}
L900:
/* ------------------------------------------- */
/* UPDATE DEGREES OF THE NODES INVOLVED IN THE */
/* MINIMUM DEGREE NODES ELIMINATION. */
/* ------------------------------------------- */
if (num > *neqns) {
goto L1000;
}
mmdupd_(&ehead, neqns, &xadj[1], &adjncy[1], delta, &mdeg, &dhead[1], &
invp[1], &perm[1], &qsize[1], &llist[1], &marker[1], maxint, &tag)
;
goto L300;
L1000:
mmdnum_(neqns, &perm[1], &invp[1], &qsize[1]);
return 0;
} /* genmmd_ */
/* *************************************************************** */
/* *************************************************************** */
/* *** MMDINT ..... MULT MINIMUM DEGREE INITIALIZATION *** */
/* *************************************************************** */
/* *************************************************************** */
/* AUTHOR - JOSEPH W.H. LIU */
/* DEPT OF COMPUTER SCIENCE, YORK UNIVERSITY. */
/* PURPOSE - THIS ROUTINE PERFORMS INITIALIZATION FOR THE */
/* MULTIPLE ELIMINATION VERSION OF THE MINIMUM DEGREE */
/* ALGORITHM. */
/* INPUT PARAMETERS - */
/* NEQNS - NUMBER OF EQUATIONS. */
/* (XADJ,ADJNCY) - ADJACENCY STRUCTURE. */
/* OUTPUT PARAMETERS - */
/* (DHEAD,DFORW,DBAKW) - DEGREE DOUBLY LINKED STRUCTURE. */
/* QSIZE - SIZE OF SUPERNODE (INITIALIZED TO ONE). */
/* LLIST - LINKED LIST. */
/* MARKER - MARKER VECTOR. */
/* *************************************************************** */
/* Subroutine */ int mmdint_(int *neqns, int *xadj, shortint *adjncy,
shortint *dhead, shortint *dforw, shortint *dbakw, shortint *qsize,
shortint *llist, shortint *marker)
{
/* System generated locals */
int i__1;
/* Local variables */
static int ndeg, node, fnode;
/* *************************************************************** */
/* *************************************************************** */
/* Parameter adjustments */
--marker;
--llist;
--qsize;
--dbakw;
--dforw;
--dhead;
--adjncy;
--xadj;
/* Function Body */
i__1 = *neqns;
for (node = 1; node <= i__1; ++node) {
dhead[node] = 0;
qsize[node] = 1;
marker[node] = 0;
llist[node] = 0;
/* L100: */
}
/* ------------------------------------------ */
/* INITIALIZE THE DEGREE DOUBLY LINKED LISTS. */
/* ------------------------------------------ */
i__1 = *neqns;
for (node = 1; node <= i__1; ++node) {
ndeg = xadj[node + 1] - xadj[node] + 1;
fnode = dhead[ndeg];
dforw[node] = fnode;
dhead[ndeg] = node;
if (fnode > 0) {
dbakw[fnode] = node;
}
dbakw[node] = -ndeg;
/* L200: */
}
return 0;
} /* mmdint_ */
/* *************************************************************** */
/* *************************************************************** */
/* ** MMDELM ..... MULTIPLE MINIMUM DEGREE ELIMINATION *** */
/* *************************************************************** */
/* *************************************************************** */
/* AUTHOR - JOSEPH W.H. LIU */
/* DEPT OF COMPUTER SCIENCE, YORK UNIVERSITY. */
/* PURPOSE - THIS ROUTINE ELIMINATES THE NODE MDNODE OF */
/* MINIMUM DEGREE FROM THE ADJACENCY STRUCTURE, WHICH */
/* IS STORED IN THE QUOTIENT GRAPH FORMAT. IT ALSO */
/* TRANSFORMS THE QUOTIENT GRAPH REPRESENTATION OF THE */
/* ELIMINATION GRAPH. */
/* INPUT PARAMETERS - */
/* MDNODE - NODE OF MINIMUM DEGREE. */
/* MAXINT - ESTIMATE OF MAXIMUM REPRESENTABLE (SHORT) */
/* INT. */
/* TAG - TAG VALUE. */
/* UPDATED PARAMETERS - */
/* (XADJ,ADJNCY) - UPDATED ADJACENCY STRUCTURE. */
/* (DHEAD,DFORW,DBAKW) - DEGREE DOUBLY LINKED STRUCTURE. */
/* QSIZE - SIZE OF SUPERNODE. */
/* MARKER - MARKER VECTOR. */
/* LLIST - TEMPORARY LINKED LIST OF ELIMINATED NABORS. */
/* *************************************************************** */
/* Subroutine */ int mmdelm_(int *mdnode, int *xadj, shortint *adjncy,
shortint *dhead, shortint *dforw, shortint *dbakw, shortint *qsize,
shortint *llist, shortint *marker, int *maxint, int *tag)
{
/* System generated locals */
int i__1, i__2;
/* Local variables */
static int node, link, rloc, rlmt, i, j, nabor, rnode, elmnt, xqnbr,
istop, jstop, istrt, jstrt, nxnode, pvnode, nqnbrs, npv;
/* *************************************************************** */
/* *************************************************************** */
/* ----------------------------------------------- */
/* FIND REACHABLE SET AND PLACE IN DATA STRUCTURE. */
/* ----------------------------------------------- */
/* Parameter adjustments */
--marker;
--llist;
--qsize;
--dbakw;
--dforw;
--dhead;
--adjncy;
--xadj;
/* Function Body */
marker[*mdnode] = *tag;
istrt = xadj[*mdnode];
istop = xadj[*mdnode + 1] - 1;
/* ------------------------------------------------------- */
/* ELMNT POINTS TO THE BEGINNING OF THE LIST OF ELIMINATED */
/* NABORS OF MDNODE, AND RLOC GIVES THE STORAGE LOCATION */
/* FOR THE NEXT REACHABLE NODE. */
/* ------------------------------------------------------- */
elmnt = 0;
rloc = istrt;
rlmt = istop;
i__1 = istop;
for (i = istrt; i <= i__1; ++i) {
nabor = adjncy[i];
if (nabor == 0) {
goto L300;
}
if (marker[nabor] >= *tag) {
goto L200;
}
marker[nabor] = *tag;
if (dforw[nabor] < 0) {
goto L100;
}
adjncy[rloc] = nabor;
++rloc;
goto L200;
L100:
llist[nabor] = elmnt;
elmnt = nabor;
L200:
;
}
L300:
/* ----------------------------------------------------- */
/* MERGE WITH REACHABLE NODES FROM GENERALIZED ELEMENTS. */
/* ----------------------------------------------------- */
if (elmnt <= 0) {
goto L1000;
}
adjncy[rlmt] = -elmnt;
link = elmnt;
L400:
jstrt = xadj[link];
jstop = xadj[link + 1] - 1;
i__1 = jstop;
for (j = jstrt; j <= i__1; ++j) {
node = adjncy[j];
link = -node;
if (node < 0) {
goto L400;
} else if (node == 0) {
goto L900;
} else {
goto L500;
}
L500:
if (marker[node] >= *tag || dforw[node] < 0) {
goto L800;
}
marker[node] = *tag;
/* --------------------------------- */
/* USE STORAGE FROM ELIMINATED NODES */
/* IF NECESSARY. */
/* --------------------------------- */
L600:
if (rloc < rlmt) {
goto L700;
}
link = -adjncy[rlmt];
rloc = xadj[link];
rlmt = xadj[link + 1] - 1;
goto L600;
L700:
adjncy[rloc] = node;
++rloc;
L800:
;
}
L900:
elmnt = llist[elmnt];
goto L300;
L1000:
if (rloc <= rlmt) {
adjncy[rloc] = 0;
}
/* -------------------------------------------------------- */
/* FOR EACH NODE IN THE REACHABLE SET, DO THE FOLLOWING ... */
/* -------------------------------------------------------- */
link = *mdnode;
L1100:
istrt = xadj[link];
istop = xadj[link + 1] - 1;
i__1 = istop;
for (i = istrt; i <= i__1; ++i) {
rnode = adjncy[i];
link = -rnode;
if (rnode < 0) {
goto L1100;
} else if (rnode == 0) {
goto L1800;
} else {
goto L1200;
}
L1200:
/* -------------------------------------------- */
/* IF RNODE IS IN THE DEGREE LIST STRUCTURE ... */
/* -------------------------------------------- */
pvnode = dbakw[rnode];
if (pvnode == 0 || pvnode == -(*maxint)) {
goto L1300;
}
/* ------------------------------------- */
/* THEN REMOVE RNODE FROM THE STRUCTURE. */
/* ------------------------------------- */
nxnode = dforw[rnode];
if (nxnode > 0) {
dbakw[nxnode] = pvnode;
}
if (pvnode > 0) {
dforw[pvnode] = nxnode;
}
npv = -pvnode;
if (pvnode < 0) {
dhead[npv] = nxnode;
}
L1300:
/* ---------------------------------------- */
/* PURGE INACTIVE QUOTIENT NABORS OF RNODE. */
/* ---------------------------------------- */
jstrt = xadj[rnode];
jstop = xadj[rnode + 1] - 1;
xqnbr = jstrt;
i__2 = jstop;
for (j = jstrt; j <= i__2; ++j) {
nabor = adjncy[j];
if (nabor == 0) {
goto L1500;
}
if (marker[nabor] >= *tag) {
goto L1400;
}
adjncy[xqnbr] = nabor;
++xqnbr;
L1400:
;
}
L1500:
/* ---------------------------------------- */
/* IF NO ACTIVE NABOR AFTER THE PURGING ... */
/* ---------------------------------------- */
nqnbrs = xqnbr - jstrt;
if (nqnbrs > 0) {
goto L1600;
}
/* ----------------------------- */
/* THEN MERGE RNODE WITH MDNODE. */
/* ----------------------------- */
qsize[*mdnode] += qsize[rnode];
qsize[rnode] = 0;
marker[rnode] = *maxint;
dforw[rnode] = -(*mdnode);
dbakw[rnode] = -(*maxint);
goto L1700;
L1600:
/* -------------------------------------- */
/* ELSE FLAG RNODE FOR DEGREE UPDATE, AND */
/* ADD MDNODE AS A NABOR OF RNODE. */
/* -------------------------------------- */
dforw[rnode] = nqnbrs + 1;
dbakw[rnode] = 0;
adjncy[xqnbr] = *mdnode;
++xqnbr;
if (xqnbr <= jstop) {
adjncy[xqnbr] = 0;
}
L1700:
;
}
L1800:
return 0;
} /* mmdelm_ */
/* *************************************************************** */
/* *************************************************************** */
/* ***** MMDUPD ..... MULTIPLE MINIMUM DEGREE UPDATE ***** */
/* *************************************************************** */
/* *************************************************************** */
/* AUTHOR - JOSEPH W.H. LIU */
/* DEPT OF COMPUTER SCIENCE, YORK UNIVERSITY. */
/* PURPOSE - THIS ROUTINE UPDATES THE DEGREES OF NODES */
/* AFTER A MULTIPLE ELIMINATION STEP. */
/* INPUT PARAMETERS - */
/* EHEAD - THE BEGINNING OF THE LIST OF ELIMINATED */
/* NODES (I.E., NEWLY FORMED ELEMENTS). */
/* NEQNS - NUMBER OF EQUATIONS. */
/* (XADJ,ADJNCY) - ADJACENCY STRUCTURE. */
/* DELTA - TOLERANCE VALUE FOR MULTIPLE ELIMINATION. */
/* MAXINT - MAXIMUM MACHINE REPRESENTABLE (SHORT) */
/* INTEGER. */
/* UPDATED PARAMETERS - */
/* MDEG - NEW MINIMUM DEGREE AFTER DEGREE UPDATE. */
/* (DHEAD,DFORW,DBAKW) - DEGREE DOUBLY LINKED STRUCTURE. */
/* QSIZE - SIZE OF SUPERNODE. */
/* LLIST - WORKING LINKED LIST. */
/* MARKER - MARKER VECTOR FOR DEGREE UPDATE. */
/* TAG - TAG VALUE. */
/* *************************************************************** */
/* Subroutine */ int mmdupd_(int *ehead, int *neqns, int *xadj,
shortint *adjncy, int *delta, int *mdeg, shortint *dhead,
shortint *dforw, shortint *dbakw, shortint *qsize, shortint *llist,
shortint *marker, int *maxint, int *tag)
{
/* System generated locals */
int i__1, i__2;
/* Local variables */
static int node, mtag, link, mdeg0, i, j, enode, fnode, nabor, elmnt,
istop, jstop, q2head, istrt, jstrt, qxhead, iq2, deg, deg0;
/* *************************************************************** */
/* *************************************************************** */
/* Parameter adjustments */
--marker;
--llist;
--qsize;
--dbakw;
--dforw;
--dhead;
--adjncy;
--xadj;
/* Function Body */
mdeg0 = *mdeg + *delta;
elmnt = *ehead;
L100:
/* ------------------------------------------------------- */
/* FOR EACH OF THE NEWLY FORMED ELEMENT, DO THE FOLLOWING. */
/* (RESET TAG VALUE IF NECESSARY.) */
/* ------------------------------------------------------- */
if (elmnt <= 0) {
return 0;
}
mtag = *tag + mdeg0;
if (mtag < *maxint) {
goto L300;
}
*tag = 1;
i__1 = *neqns;
for (i = 1; i <= i__1; ++i) {
if (marker[i] < *maxint) {
marker[i] = 0;
}
/* L200: */
}
mtag = *tag + mdeg0;
L300:
/* --------------------------------------------- */
/* CREATE TWO LINKED LISTS FROM NODES ASSOCIATED */
/* WITH ELMNT: ONE WITH TWO NABORS (Q2HEAD) IN */
/* ADJACENCY STRUCTURE, AND THE OTHER WITH MORE */
/* THAN TWO NABORS (QXHEAD). ALSO COMPUTE DEG0, */
/* NUMBER OF NODES IN THIS ELEMENT. */
/* --------------------------------------------- */
q2head = 0;
qxhead = 0;
deg0 = 0;
link = elmnt;
L400:
istrt = xadj[link];
istop = xadj[link + 1] - 1;
i__1 = istop;
for (i = istrt; i <= i__1; ++i) {
enode = adjncy[i];
link = -enode;
if (enode < 0) {
goto L400;
} else if (enode == 0) {
goto L800;
} else {
goto L500;
}
L500:
if (qsize[enode] == 0) {
goto L700;
}
deg0 += qsize[enode];
marker[enode] = mtag;
/* ---------------------------------- */
/* IF ENODE REQUIRES A DEGREE UPDATE, */
/* THEN DO THE FOLLOWING. */
/* ---------------------------------- */
if (dbakw[enode] != 0) {
goto L700;
}
/* ---------------------------------------
*/
/* PLACE EITHER IN QXHEAD OR Q2HEAD LISTS.
*/
/* ---------------------------------------
*/
if (dforw[enode] == 2) {
goto L600;
}
llist[enode] = qxhead;
qxhead = enode;
goto L700;
L600:
llist[enode] = q2head;
q2head = enode;
L700:
;
}
L800:
/* -------------------------------------------- */
/* FOR EACH ENODE IN Q2 LIST, DO THE FOLLOWING. */
/* -------------------------------------------- */
enode = q2head;
iq2 = 1;
L900:
if (enode <= 0) {
goto L1500;
}
if (dbakw[enode] != 0) {
goto L2200;
}
++(*tag);
deg = deg0;
/* ------------------------------------------ */
/* IDENTIFY THE OTHER ADJACENT ELEMENT NABOR. */
/* ------------------------------------------ */
istrt = xadj[enode];
nabor = adjncy[istrt];
if (nabor == elmnt) {
nabor = adjncy[istrt + 1];
}
/* ------------------------------------------------ */
/* IF NABOR IS UNELIMINATED, INCREASE DEGREE COUNT. */
/* ------------------------------------------------ */
link = nabor;
if (dforw[nabor] < 0) {
goto L1000;
}
deg += qsize[nabor];
goto L2100;
L1000:
/* -------------------------------------------- */
/* OTHERWISE, FOR EACH NODE IN THE 2ND ELEMENT, */
/* DO THE FOLLOWING. */
/* -------------------------------------------- */
istrt = xadj[link];
istop = xadj[link + 1] - 1;
i__1 = istop;
for (i = istrt; i <= i__1; ++i) {
node = adjncy[i];
link = -node;
if (node == enode) {
goto L1400;
}
if (node < 0) {
goto L1000;
} else if (node == 0) {
goto L2100;
} else {
goto L1100;
}
L1100:
if (qsize[node] == 0) {
goto L1400;
}
if (marker[node] >= *tag) {
goto L1200;
}
/* -----------------------------------
-- */
/* CASE WHEN NODE IS NOT YET CONSIDERED
. */
/* -----------------------------------
-- */
marker[node] = *tag;
deg += qsize[node];
goto L1400;
L1200:
/* ----------------------------------------
*/
/* CASE WHEN NODE IS INDISTINGUISHABLE FROM
*/
/* ENODE. MERGE THEM INTO A NEW SUPERNODE.
*/
/* ----------------------------------------
*/
if (dbakw[node] != 0) {
goto L1400;
}
if (dforw[node] != 2) {
goto L1300;
}
qsize[enode] += qsize[node];
qsize[node] = 0;
marker[node] = *maxint;
dforw[node] = -enode;
dbakw[node] = -(*maxint);
goto L1400;
L1300:
/* --------------------------------------
*/
/* CASE WHEN NODE IS OUTMATCHED BY ENODE.
*/
/* --------------------------------------
*/
if (dbakw[node] == 0) {
dbakw[node] = -(*maxint);
}
L1400:
;
}
goto L2100;
L1500:
/* ------------------------------------------------ */
/* FOR EACH ENODE IN THE QX LIST, DO THE FOLLOWING. */
/* ------------------------------------------------ */
enode = qxhead;
iq2 = 0;
L1600:
if (enode <= 0) {
goto L2300;
}
if (dbakw[enode] != 0) {
goto L2200;
}
++(*tag);
deg = deg0;
/* --------------------------------- */
/* FOR EACH UNMARKED NABOR OF ENODE, */
/* DO THE FOLLOWING. */
/* --------------------------------- */
istrt = xadj[enode];
istop = xadj[enode + 1] - 1;
i__1 = istop;
for (i = istrt; i <= i__1; ++i) {
nabor = adjncy[i];
if (nabor == 0) {
goto L2100;
}
if (marker[nabor] >= *tag) {
goto L2000;
}
marker[nabor] = *tag;
link = nabor;
/* ------------------------------ */
/* IF UNELIMINATED, INCLUDE IT IN */
/* DEG COUNT. */
/* ------------------------------ */
if (dforw[nabor] < 0) {
goto L1700;
}
deg += qsize[nabor];
goto L2000;
L1700:
/* -------------------------------
*/
/* IF ELIMINATED, INCLUDE UNMARKED
*/
/* NODES IN THIS ELEMENT INTO THE
*/
/* DEGREE COUNT. */
/* -------------------------------
*/
jstrt = xadj[link];
jstop = xadj[link + 1] - 1;
i__2 = jstop;
for (j = jstrt; j <= i__2; ++j) {
node = adjncy[j];
link = -node;
if (node < 0) {
goto L1700;
} else if (node == 0) {
goto L2000;
} else {
goto L1800;
}
L1800:
if (marker[node] >= *tag) {
goto L1900;
}
marker[node] = *tag;
deg += qsize[node];
L1900:
;
}
L2000:
;
}
L2100:
/* ------------------------------------------- */
/* UPDATE EXTERNAL DEGREE OF ENODE IN DEGREE */
/* STRUCTURE, AND MDEG (MIN DEG) IF NECESSARY. */
/* ------------------------------------------- */
deg = deg - qsize[enode] + 1;
fnode = dhead[deg];
dforw[enode] = fnode;
dbakw[enode] = -deg;
if (fnode > 0) {
dbakw[fnode] = enode;
}
dhead[deg] = enode;
if (deg < *mdeg) {
*mdeg = deg;
}
L2200:
/* ---------------------------------- */
/* GET NEXT ENODE IN CURRENT ELEMENT. */
/* ---------------------------------- */
enode = llist[enode];
if (iq2 == 1) {
goto L900;
}
goto L1600;
L2300:
/* ----------------------------- */
/* GET NEXT ELEMENT IN THE LIST. */
/* ----------------------------- */
*tag = mtag;
elmnt = llist[elmnt];
goto L100;
} /* mmdupd_ */
/* *************************************************************** */
/* *************************************************************** */
/* ***** MMDNUM ..... MULTI MINIMUM DEGREE NUMBERING ***** */
/* *************************************************************** */
/* *************************************************************** */
/* AUTHOR - JOSEPH W.H. LIU */
/* DEPT OF COMPUTER SCIENCE, YORK UNIVERSITY. */
/* PURPOSE - THIS ROUTINE PERFORMS THE FINAL STEP IN */
/* PRODUCING THE PERMUTATION AND INVERSE PERMUTATION */
/* VECTORS IN THE MULTIPLE ELIMINATION VERSION OF THE */
/* MINIMUM DEGREE ORDERING ALGORITHM. */
/* INPUT PARAMETERS - */
/* NEQNS - NUMBER OF EQUATIONS. */
/* QSIZE - SIZE OF SUPERNODES AT ELIMINATION. */
/* UPDATED PARAMETERS - */
/* INVP - INVERSE PERMUTATION VECTOR. ON INPUT, */
/* IF QSIZE(NODE)=0, THEN NODE HAS BEEN MERGED */
/* INTO THE NODE -INVP(NODE); OTHERWISE, */
/* -INVP(NODE) IS ITS INVERSE LABELLING. */
/* OUTPUT PARAMETERS - */
/* PERM - THE PERMUTATION VECTOR. */
/* *************************************************************** */
/* Subroutine */ int mmdnum_(int *neqns, shortint *perm, shortint *invp,
shortint *qsize)
{
/* System generated locals */
int i__1;
/* Local variables */
static int node, root, nextf, father, nqsize, num;
/* *************************************************************** */
/* *************************************************************** */
/* Parameter adjustments */
--qsize;
--invp;
--perm;
/* Function Body */
i__1 = *neqns;
for (node = 1; node <= i__1; ++node) {
nqsize = qsize[node];
if (nqsize <= 0) {
perm[node] = invp[node];
}
if (nqsize > 0) {
perm[node] = -invp[node];
}
/* L100: */
}
/* ------------------------------------------------------ */
/* FOR EACH NODE WHICH HAS BEEN MERGED, DO THE FOLLOWING. */
/* ------------------------------------------------------ */
i__1 = *neqns;
for (node = 1; node <= i__1; ++node) {
if (perm[node] > 0) {
goto L500;
}
/* ----------------------------------------- */
/* TRACE THE MERGED TREE UNTIL ONE WHICH HAS */
/* NOT BEEN MERGED, CALL IT ROOT. */
/* ----------------------------------------- */
father = node;
L200:
if (perm[father] > 0) {
goto L300;
}
father = -perm[father];
goto L200;
L300:
/* ----------------------- */
/* NUMBER NODE AFTER ROOT. */
/* ----------------------- */
root = father;
num = perm[root] + 1;
invp[node] = -num;
perm[root] = num;
/* ------------------------ */
/* SHORTEN THE MERGED TREE. */
/* ------------------------ */
father = node;
L400:
nextf = -perm[father];
if (nextf <= 0) {
goto L500;
}
perm[father] = -root;
father = nextf;
goto L400;
L500:
;
}
/* ---------------------- */
/* READY TO COMPUTE PERM. */
/* ---------------------- */
i__1 = *neqns;
for (node = 1; node <= i__1; ++node) {
num = -invp[node];
invp[node] = num;
perm[num] = node;
/* L600: */
}
return 0;
} /* mmdnum_ */