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C***********************************************************************
C***********************************************************************
C
C Version: 0.3
C Last modified: December 27, 1994
C Authors: Esmond G. Ng and Barry W. Peyton
C
C Mathematical Sciences Section, Oak Ridge National Laboratory
C
C***********************************************************************
C***********************************************************************
C**** ORDMMD ..... MULTIPLE MINIMUM EXTERNAL DEGREE ************
C***********************************************************************
C***********************************************************************
C
C PURPOSE - THIS ROUTINE CALLS LIU'S MULTIPLE MINIMUM DEGREE
C ROUTINE.
C
C INPUT PARAMETERS -
C NEQNS - NUMBER OF EQUATIONS.
C (XADJ,ADJNCY) - THE ADJACENCY STRUCTURE.
C IWSIZ - SIZE OF INTEGER WORKING STORAGE.
C
C OUTPUT PARAMETERS -
C PERM - THE MINIMUM DEGREE ORDERING.
C INVP - THE INVERSE OF PERM.
C NOFSUB - AN UPPER BOUND ON THE NUMBER OF NONZERO
C SUBSCRIPTS FOR THE COMPRESSED STORAGE SCHEME.
C IFLAG - ERROR FLAG.
C 0: SUCCESSFUL ORDERING
C -1: INSUFFICIENT WORKING STORAGE
C [IWORK(*)].
C
C WORKING PARAMETERS -
C IWORK - INTEGER WORKSPACE OF LENGTH 4*NEQNS.
C
C***********************************************************************
C
SUBROUTINE ORDMMD ( NEQNS , XADJ , ADJNCY, INVP , PERM ,
1 IWSIZ , IWORK , NOFSUB, IFLAG )
C
C***********************************************************************
C
INTEGER ADJNCY(1), INVP(1) , IWORK(1) , PERM(1)
INTEGER XADJ(1)
INTEGER DELTA , IFLAG , IWSIZ , MAXINT, NEQNS ,
& NOFSUB
C
C*********************************************************************
C
IFLAG = 0
IF ( IWSIZ .LT. 4*NEQNS ) THEN
IFLAG = -1
RETURN
ENDIF
C
C DELTA - TOLERANCE VALUE FOR MULTIPLE ELIMINATION.
C MAXINT - MAXIMUM MACHINE REPRESENTABLE (SHORT) INTEGER
C (ANY SMALLER ESTIMATE WILL DO) FOR MARKING
C NODES.
C
DELTA = 0
MAXINT = 32767
CALL GENMMD ( NEQNS , XADJ , ADJNCY, INVP , PERM ,
1 DELTA ,
1 IWORK(1) ,
1 IWORK(NEQNS+1) ,
1 IWORK(2*NEQNS+1) ,
1 IWORK(3*NEQNS+1) ,
1 MAXINT, NOFSUB )
RETURN
C
END
C***********************************************************************
C***********************************************************************
C
C Version: 0.3
C Last modified: December 27, 1994
C Authors: Joseph W.H. Liu
C
C Mathematical Sciences Section, Oak Ridge National Laboratory
C
C***********************************************************************
C***********************************************************************
C--- SPARSPAK-A (ANSI FORTRAN) RELEASE III --- NAME = GENMMD
C (C) UNIVERSITY OF WATERLOO JANUARY 1984
C***********************************************************************
C***********************************************************************
C**** GENMMD ..... MULTIPLE MINIMUM EXTERNAL DEGREE ************
C***********************************************************************
C***********************************************************************
C
C PURPOSE - THIS ROUTINE IMPLEMENTS THE MINIMUM DEGREE
C ALGORITHM. IT MAKES USE OF THE IMPLICIT REPRESENTATION
C OF ELIMINATION GRAPHS BY QUOTIENT GRAPHS, AND THE
C NOTION OF INDISTINGUISHABLE NODES. IT ALSO IMPLEMENTS
C THE MODIFICATIONS BY MULTIPLE ELIMINATION AND MINIMUM
C EXTERNAL DEGREE.
C ---------------------------------------------
C CAUTION - THE ADJACENCY VECTOR ADJNCY WILL BE
C DESTROYED.
C ---------------------------------------------
C
C INPUT PARAMETERS -
C NEQNS - NUMBER OF EQUATIONS.
C (XADJ,ADJNCY) - THE ADJACENCY STRUCTURE.
C DELTA - TOLERANCE VALUE FOR MULTIPLE ELIMINATION.
C MAXINT - MAXIMUM MACHINE REPRESENTABLE (SHORT) INTEGER
C (ANY SMALLER ESTIMATE WILL DO) FOR MARKING
C NODES.
C
C OUTPUT PARAMETERS -
C PERM - THE MINIMUM DEGREE ORDERING.
C INVP - THE INVERSE OF PERM.
C NOFSUB - AN UPPER BOUND ON THE NUMBER OF NONZERO
C SUBSCRIPTS FOR THE COMPRESSED STORAGE SCHEME.
C
C WORKING PARAMETERS -
C DHEAD - VECTOR FOR HEAD OF DEGREE LISTS.
C INVP - USED TEMPORARILY FOR DEGREE FORWARD LINK.
C PERM - USED TEMPORARILY FOR DEGREE BACKWARD LINK.
C QSIZE - VECTOR FOR SIZE OF SUPERNODES.
C LLIST - VECTOR FOR TEMPORARY LINKED LISTS.
C MARKER - A TEMPORARY MARKER VECTOR.
C
C PROGRAM SUBROUTINES -
C MMDELM, MMDINT, MMDNUM, MMDUPD.
C
C***********************************************************************
C
SUBROUTINE GENMMD ( NEQNS, XADJ, ADJNCY, INVP, PERM,
1 DELTA, DHEAD, QSIZE, LLIST, MARKER,
1 MAXINT, NOFSUB )
C
C***********************************************************************
C
INTEGER ADJNCY(1), DHEAD(1) , INVP(1) , LLIST(1) ,
1 MARKER(1), PERM(1) , QSIZE(1)
INTEGER XADJ(1)
INTEGER DELTA , EHEAD , I , MAXINT, MDEG ,
1 MDLMT , MDNODE, NEQNS , NEXTMD, NOFSUB,
1 NUM, TAG
C
C***********************************************************************
C
IF ( NEQNS .LE. 0 ) RETURN
C
C ------------------------------------------------
C INITIALIZATION FOR THE MINIMUM DEGREE ALGORITHM.
C ------------------------------------------------
NOFSUB = 0
CALL MMDINT ( NEQNS, XADJ, ADJNCY, DHEAD, INVP, PERM,
1 QSIZE, LLIST, MARKER )
C
C ----------------------------------------------
C NUM COUNTS THE NUMBER OF ORDERED NODES PLUS 1.
C ----------------------------------------------
NUM = 1
C
C -----------------------------
C ELIMINATE ALL ISOLATED NODES.
C -----------------------------
NEXTMD = DHEAD(1)
100 CONTINUE
IF ( NEXTMD .LE. 0 ) GO TO 200
MDNODE = NEXTMD
NEXTMD = INVP(MDNODE)
MARKER(MDNODE) = MAXINT
INVP(MDNODE) = - NUM
NUM = NUM + 1
GO TO 100
C
200 CONTINUE
C ----------------------------------------
C SEARCH FOR NODE OF THE MINIMUM DEGREE.
C MDEG IS THE CURRENT MINIMUM DEGREE;
C TAG IS USED TO FACILITATE MARKING NODES.
C ----------------------------------------
IF ( NUM .GT. NEQNS ) GO TO 1000
TAG = 1
DHEAD(1) = 0
MDEG = 2
300 CONTINUE
IF ( DHEAD(MDEG) .GT. 0 ) GO TO 400
MDEG = MDEG + 1
GO TO 300
400 CONTINUE
C -------------------------------------------------
C USE VALUE OF DELTA TO SET UP MDLMT, WHICH GOVERNS
C WHEN A DEGREE UPDATE IS TO BE PERFORMED.
C -------------------------------------------------
MDLMT = MDEG + DELTA
EHEAD = 0
C
500 CONTINUE
MDNODE = DHEAD(MDEG)
IF ( MDNODE .GT. 0 ) GO TO 600
MDEG = MDEG + 1
IF ( MDEG .GT. MDLMT ) GO TO 900
GO TO 500
600 CONTINUE
C ----------------------------------------
C REMOVE MDNODE FROM THE DEGREE STRUCTURE.
C ----------------------------------------
NEXTMD = INVP(MDNODE)
DHEAD(MDEG) = NEXTMD
IF ( NEXTMD .GT. 0 ) PERM(NEXTMD) = - MDEG
INVP(MDNODE) = - NUM
NOFSUB = NOFSUB + MDEG + QSIZE(MDNODE) - 2
IF ( NUM+QSIZE(MDNODE) .GT. NEQNS ) GO TO 1000
C ----------------------------------------------
C ELIMINATE MDNODE AND PERFORM QUOTIENT GRAPH
C TRANSFORMATION. RESET TAG VALUE IF NECESSARY.
C ----------------------------------------------
TAG = TAG + 1
IF ( TAG .LT. MAXINT ) GO TO 800
TAG = 1
DO 700 I = 1, NEQNS
IF ( MARKER(I) .LT. MAXINT ) MARKER(I) = 0
700 CONTINUE
800 CONTINUE
CALL MMDELM ( MDNODE, XADJ, ADJNCY, DHEAD, INVP,
1 PERM, QSIZE, LLIST, MARKER, MAXINT,
1 TAG )
NUM = NUM + QSIZE(MDNODE)
LLIST(MDNODE) = EHEAD
EHEAD = MDNODE
IF ( DELTA .GE. 0 ) GO TO 500
900 CONTINUE
C -------------------------------------------
C UPDATE DEGREES OF THE NODES INVOLVED IN THE
C MINIMUM DEGREE NODES ELIMINATION.
C -------------------------------------------
IF ( NUM .GT. NEQNS ) GO TO 1000
CALL MMDUPD ( EHEAD, NEQNS, XADJ, ADJNCY, DELTA, MDEG,
1 DHEAD, INVP, PERM, QSIZE, LLIST, MARKER,
1 MAXINT, TAG )
GO TO 300
C
1000 CONTINUE
CALL MMDNUM ( NEQNS, PERM, INVP, QSIZE )
RETURN
C
END
C***********************************************************************
C***********************************************************************
C
C Version: 0.3
C Last modified: December 27, 1994
C Authors: Joseph W.H. Liu
C
C Mathematical Sciences Section, Oak Ridge National Laboratory
C
C***********************************************************************
C***********************************************************************
C--- SPARSPAK-A (ANSI FORTRAN) RELEASE III --- NAME = MMDINT
C (C) UNIVERSITY OF WATERLOO JANUARY 1984
C***********************************************************************
C***********************************************************************
C*** MMDINT ..... MULT MINIMUM DEGREE INITIALIZATION ***********
C***********************************************************************
C***********************************************************************
C
C PURPOSE - THIS ROUTINE PERFORMS INITIALIZATION FOR THE
C MULTIPLE ELIMINATION VERSION OF THE MINIMUM DEGREE
C ALGORITHM.
C
C INPUT PARAMETERS -
C NEQNS - NUMBER OF EQUATIONS.
C (XADJ,ADJNCY) - ADJACENCY STRUCTURE.
C
C OUTPUT PARAMETERS -
C (DHEAD,DFORW,DBAKW) - DEGREE DOUBLY LINKED STRUCTURE.
C QSIZE - SIZE OF SUPERNODE (INITIALIZED TO ONE).
C LLIST - LINKED LIST.
C MARKER - MARKER VECTOR.
C
C***********************************************************************
C
SUBROUTINE MMDINT ( NEQNS, XADJ, ADJNCY, DHEAD, DFORW,
1 DBAKW, QSIZE, LLIST, MARKER )
C
C***********************************************************************
C
INTEGER ADJNCY(1), DBAKW(1) , DFORW(1) , DHEAD(1) ,
1 LLIST(1) , MARKER(1), QSIZE(1)
INTEGER XADJ(1)
INTEGER FNODE , NDEG , NEQNS , NODE
C
C***********************************************************************
C
DO 100 NODE = 1, NEQNS
DHEAD(NODE) = 0
QSIZE(NODE) = 1
MARKER(NODE) = 0
LLIST(NODE) = 0
100 CONTINUE
C ------------------------------------------
C INITIALIZE THE DEGREE DOUBLY LINKED LISTS.
C ------------------------------------------
DO 200 NODE = 1, NEQNS
NDEG = XADJ(NODE+1) - XADJ(NODE) + 1
FNODE = DHEAD(NDEG)
DFORW(NODE) = FNODE
DHEAD(NDEG) = NODE
IF ( FNODE .GT. 0 ) DBAKW(FNODE) = NODE
DBAKW(NODE) = - NDEG
200 CONTINUE
RETURN
C
END
C***********************************************************************
C***********************************************************************
C
C Version: 0.3
C Last modified: December 27, 1994
C Authors: Joseph W.H. Liu
C
C Mathematical Sciences Section, Oak Ridge National Laboratory
C
C***********************************************************************
C***********************************************************************
C--- SPARSPAK-A (ANSI FORTRAN) RELEASE III --- NAME = MMDELM
C (C) UNIVERSITY OF WATERLOO JANUARY 1984
C***********************************************************************
C***********************************************************************
C** MMDELM ..... MULTIPLE MINIMUM DEGREE ELIMINATION ***********
C***********************************************************************
C***********************************************************************
C
C PURPOSE - THIS ROUTINE ELIMINATES THE NODE MDNODE OF
C MINIMUM DEGREE FROM THE ADJACENCY STRUCTURE, WHICH
C IS STORED IN THE QUOTIENT GRAPH FORMAT. IT ALSO
C TRANSFORMS THE QUOTIENT GRAPH REPRESENTATION OF THE
C ELIMINATION GRAPH.
C
C INPUT PARAMETERS -
C MDNODE - NODE OF MINIMUM DEGREE.
C MAXINT - ESTIMATE OF MAXIMUM REPRESENTABLE (SHORT)
C INTEGER.
C TAG - TAG VALUE.
C
C UPDATED PARAMETERS -
C (XADJ,ADJNCY) - UPDATED ADJACENCY STRUCTURE.
C (DHEAD,DFORW,DBAKW) - DEGREE DOUBLY LINKED STRUCTURE.
C QSIZE - SIZE OF SUPERNODE.
C MARKER - MARKER VECTOR.
C LLIST - TEMPORARY LINKED LIST OF ELIMINATED NABORS.
C
C***********************************************************************
C
SUBROUTINE MMDELM ( MDNODE, XADJ, ADJNCY, DHEAD, DFORW,
1 DBAKW, QSIZE, LLIST, MARKER, MAXINT,
1 TAG )
C
C***********************************************************************
C
INTEGER ADJNCY(1), DBAKW(1) , DFORW(1) , DHEAD(1) ,
1 LLIST(1) , MARKER(1), QSIZE(1)
INTEGER XADJ(1)
INTEGER ELMNT , I , ISTOP , ISTRT , J ,
1 JSTOP , JSTRT , LINK , MAXINT, MDNODE,
1 NABOR , NODE , NPV , NQNBRS, NXNODE,
1 PVNODE, RLMT , RLOC , RNODE , TAG ,
1 XQNBR
C
C***********************************************************************
C
C -----------------------------------------------
C FIND REACHABLE SET AND PLACE IN DATA STRUCTURE.
C -----------------------------------------------
MARKER(MDNODE) = TAG
ISTRT = XADJ(MDNODE)
ISTOP = XADJ(MDNODE+1) - 1
C -------------------------------------------------------
C ELMNT POINTS TO THE BEGINNING OF THE LIST OF ELIMINATED
C NABORS OF MDNODE, AND RLOC GIVES THE STORAGE LOCATION
C FOR THE NEXT REACHABLE NODE.
C -------------------------------------------------------
ELMNT = 0
RLOC = ISTRT
RLMT = ISTOP
DO 200 I = ISTRT, ISTOP
NABOR = ADJNCY(I)
IF ( NABOR .EQ. 0 ) GO TO 300
IF ( MARKER(NABOR) .GE. TAG ) GO TO 200
MARKER(NABOR) = TAG
IF ( DFORW(NABOR) .LT. 0 ) GO TO 100
ADJNCY(RLOC) = NABOR
RLOC = RLOC + 1
GO TO 200
100 CONTINUE
LLIST(NABOR) = ELMNT
ELMNT = NABOR
200 CONTINUE
300 CONTINUE
C -----------------------------------------------------
C MERGE WITH REACHABLE NODES FROM GENERALIZED ELEMENTS.
C -----------------------------------------------------
IF ( ELMNT .LE. 0 ) GO TO 1000
ADJNCY(RLMT) = - ELMNT
LINK = ELMNT
400 CONTINUE
JSTRT = XADJ(LINK)
JSTOP = XADJ(LINK+1) - 1
DO 800 J = JSTRT, JSTOP
NODE = ADJNCY(J)
LINK = - NODE
IF ( NODE ) 400, 900, 500
500 CONTINUE
IF ( MARKER(NODE) .GE. TAG .OR.
1 DFORW(NODE) .LT. 0 ) GO TO 800
MARKER(NODE) = TAG
C ---------------------------------
C USE STORAGE FROM ELIMINATED NODES
C IF NECESSARY.
C ---------------------------------
600 CONTINUE
IF ( RLOC .LT. RLMT ) GO TO 700
LINK = - ADJNCY(RLMT)
RLOC = XADJ(LINK)
RLMT = XADJ(LINK+1) - 1
GO TO 600
700 CONTINUE
ADJNCY(RLOC) = NODE
RLOC = RLOC + 1
800 CONTINUE
900 CONTINUE
ELMNT = LLIST(ELMNT)
GO TO 300
1000 CONTINUE
IF ( RLOC .LE. RLMT ) ADJNCY(RLOC) = 0
C --------------------------------------------------------
C FOR EACH NODE IN THE REACHABLE SET, DO THE FOLLOWING ...
C --------------------------------------------------------
LINK = MDNODE
1100 CONTINUE
ISTRT = XADJ(LINK)
ISTOP = XADJ(LINK+1) - 1
DO 1700 I = ISTRT, ISTOP
RNODE = ADJNCY(I)
LINK = - RNODE
IF ( RNODE ) 1100, 1800, 1200
1200 CONTINUE
C --------------------------------------------
C IF RNODE IS IN THE DEGREE LIST STRUCTURE ...
C --------------------------------------------
PVNODE = DBAKW(RNODE)
IF ( PVNODE .EQ. 0 .OR.
1 PVNODE .EQ. (-MAXINT) ) GO TO 1300
C -------------------------------------
C THEN REMOVE RNODE FROM THE STRUCTURE.
C -------------------------------------
NXNODE = DFORW(RNODE)
IF ( NXNODE .GT. 0 ) DBAKW(NXNODE) = PVNODE
IF ( PVNODE .GT. 0 ) DFORW(PVNODE) = NXNODE
NPV = - PVNODE
IF ( PVNODE .LT. 0 ) DHEAD(NPV) = NXNODE
1300 CONTINUE
C ----------------------------------------
C PURGE INACTIVE QUOTIENT NABORS OF RNODE.
C ----------------------------------------
JSTRT = XADJ(RNODE)
JSTOP = XADJ(RNODE+1) - 1
XQNBR = JSTRT
DO 1400 J = JSTRT, JSTOP
NABOR = ADJNCY(J)
IF ( NABOR .EQ. 0 ) GO TO 1500
IF ( MARKER(NABOR) .GE. TAG ) GO TO 1400
ADJNCY(XQNBR) = NABOR
XQNBR = XQNBR + 1
1400 CONTINUE
1500 CONTINUE
C ----------------------------------------
C IF NO ACTIVE NABOR AFTER THE PURGING ...
C ----------------------------------------
NQNBRS = XQNBR - JSTRT
IF ( NQNBRS .GT. 0 ) GO TO 1600
C -----------------------------
C THEN MERGE RNODE WITH MDNODE.
C -----------------------------
QSIZE(MDNODE) = QSIZE(MDNODE) + QSIZE(RNODE)
QSIZE(RNODE) = 0
MARKER(RNODE) = MAXINT
DFORW(RNODE) = - MDNODE
DBAKW(RNODE) = - MAXINT
GO TO 1700
1600 CONTINUE
C --------------------------------------
C ELSE FLAG RNODE FOR DEGREE UPDATE, AND
C ADD MDNODE AS A NABOR OF RNODE.
C --------------------------------------
DFORW(RNODE) = NQNBRS + 1
DBAKW(RNODE) = 0
ADJNCY(XQNBR) = MDNODE
XQNBR = XQNBR + 1
IF ( XQNBR .LE. JSTOP ) ADJNCY(XQNBR) = 0
C
1700 CONTINUE
1800 CONTINUE
RETURN
C
END
C***********************************************************************
C***********************************************************************
C
C Version: 0.3
C Last modified: December 27, 1994
C Authors: Joseph W.H. Liu
C
C Mathematical Sciences Section, Oak Ridge National Laboratory
C
C***********************************************************************
C***********************************************************************
C--- SPARSPAK-A (ANSI FORTRAN) RELEASE III --- NAME = MMDNUM
C (C) UNIVERSITY OF WATERLOO JANUARY 1984
C***********************************************************************
C***********************************************************************
C***** MMDNUM ..... MULTI MINIMUM DEGREE NUMBERING *************
C***********************************************************************
C***********************************************************************
C
C PURPOSE - THIS ROUTINE PERFORMS THE FINAL STEP IN
C PRODUCING THE PERMUTATION AND INVERSE PERMUTATION
C VECTORS IN THE MULTIPLE ELIMINATION VERSION OF THE
C MINIMUM DEGREE ORDERING ALGORITHM.
C
C INPUT PARAMETERS -
C NEQNS - NUMBER OF EQUATIONS.
C QSIZE - SIZE OF SUPERNODES AT ELIMINATION.
C
C UPDATED PARAMETERS -
C INVP - INVERSE PERMUTATION VECTOR. ON INPUT,
C IF QSIZE(NODE)=0, THEN NODE HAS BEEN MERGED
C INTO THE NODE -INVP(NODE); OTHERWISE,
C -INVP(NODE) IS ITS INVERSE LABELLING.
C
C OUTPUT PARAMETERS -
C PERM - THE PERMUTATION VECTOR.
C
C***********************************************************************
C
SUBROUTINE MMDNUM ( NEQNS, PERM, INVP, QSIZE )
C
C***********************************************************************
C
INTEGER INVP(1) , PERM(1) , QSIZE(1)
INTEGER FATHER, NEQNS , NEXTF , NODE , NQSIZE,
1 NUM , ROOT
C
C***********************************************************************
C
DO 100 NODE = 1, NEQNS
NQSIZE = QSIZE(NODE)
IF ( NQSIZE .LE. 0 ) PERM(NODE) = INVP(NODE)
IF ( NQSIZE .GT. 0 ) PERM(NODE) = - INVP(NODE)
100 CONTINUE
C ------------------------------------------------------
C FOR EACH NODE WHICH HAS BEEN MERGED, DO THE FOLLOWING.
C ------------------------------------------------------
DO 500 NODE = 1, NEQNS
IF ( PERM(NODE) .GT. 0 ) GO TO 500
C -----------------------------------------
C TRACE THE MERGED TREE UNTIL ONE WHICH HAS
C NOT BEEN MERGED, CALL IT ROOT.
C -----------------------------------------
FATHER = NODE
200 CONTINUE
IF ( PERM(FATHER) .GT. 0 ) GO TO 300
FATHER = - PERM(FATHER)
GO TO 200
300 CONTINUE
C -----------------------
C NUMBER NODE AFTER ROOT.
C -----------------------
ROOT = FATHER
NUM = PERM(ROOT) + 1
INVP(NODE) = - NUM
PERM(ROOT) = NUM
C ------------------------
C SHORTEN THE MERGED TREE.
C ------------------------
FATHER = NODE
400 CONTINUE
NEXTF = - PERM(FATHER)
IF ( NEXTF .LE. 0 ) GO TO 500
PERM(FATHER) = - ROOT
FATHER = NEXTF
GO TO 400
500 CONTINUE
C ----------------------
C READY TO COMPUTE PERM.
C ----------------------
DO 600 NODE = 1, NEQNS
NUM = - INVP(NODE)
INVP(NODE) = NUM
PERM(NUM) = NODE
600 CONTINUE
RETURN
C
END
C***********************************************************************
C***********************************************************************
C
C Version: 0.3
C Last modified: December 27, 1994
C Authors: Joseph W.H. Liu
C
C Mathematical Sciences Section, Oak Ridge National Laboratory
C
C***********************************************************************
C***********************************************************************
C--- SPARSPAK-A (ANSI FORTRAN) RELEASE III --- NAME = MMDUPD
C (C) UNIVERSITY OF WATERLOO JANUARY 1984
C***********************************************************************
C***********************************************************************
C***** MMDUPD ..... MULTIPLE MINIMUM DEGREE UPDATE *************
C***********************************************************************
C***********************************************************************
C
C PURPOSE - THIS ROUTINE UPDATES THE DEGREES OF NODES
C AFTER A MULTIPLE ELIMINATION STEP.
C
C INPUT PARAMETERS -
C EHEAD - THE BEGINNING OF THE LIST OF ELIMINATED
C NODES (I.E., NEWLY FORMED ELEMENTS).
C NEQNS - NUMBER OF EQUATIONS.
C (XADJ,ADJNCY) - ADJACENCY STRUCTURE.
C DELTA - TOLERANCE VALUE FOR MULTIPLE ELIMINATION.
C MAXINT - MAXIMUM MACHINE REPRESENTABLE (SHORT)
C INTEGER.
C
C UPDATED PARAMETERS -
C MDEG - NEW MINIMUM DEGREE AFTER DEGREE UPDATE.
C (DHEAD,DFORW,DBAKW) - DEGREE DOUBLY LINKED STRUCTURE.
C QSIZE - SIZE OF SUPERNODE.
C LLIST - WORKING LINKED LIST.
C MARKER - MARKER VECTOR FOR DEGREE UPDATE.
C TAG - TAG VALUE.
C
C***********************************************************************
C
SUBROUTINE MMDUPD ( EHEAD, NEQNS, XADJ, ADJNCY, DELTA,
1 MDEG, DHEAD, DFORW, DBAKW, QSIZE,
1 LLIST, MARKER, MAXINT, TAG )
C
C***********************************************************************
C
INTEGER ADJNCY(1), DBAKW(1) , DFORW(1) , DHEAD(1) ,
1 LLIST(1) , MARKER(1), QSIZE(1)
INTEGER XADJ(1)
INTEGER DEG , DEG0 , DELTA , EHEAD , ELMNT ,
1 ENODE , FNODE , I , IQ2 , ISTOP ,
1 ISTRT , J , JSTOP , JSTRT , LINK ,
1 MAXINT, MDEG , MDEG0 , MTAG , NABOR ,
1 NEQNS , NODE , Q2HEAD, QXHEAD, TAG
C
C***********************************************************************
C
MDEG0 = MDEG + DELTA
ELMNT = EHEAD
100 CONTINUE
C -------------------------------------------------------
C FOR EACH OF THE NEWLY FORMED ELEMENT, DO THE FOLLOWING.
C (RESET TAG VALUE IF NECESSARY.)
C -------------------------------------------------------
IF ( ELMNT .LE. 0 ) RETURN
MTAG = TAG + MDEG0
IF ( MTAG .LT. MAXINT ) GO TO 300
TAG = 1
DO 200 I = 1, NEQNS
IF ( MARKER(I) .LT. MAXINT ) MARKER(I) = 0
200 CONTINUE
MTAG = TAG + MDEG0
300 CONTINUE
C ---------------------------------------------
C CREATE TWO LINKED LISTS FROM NODES ASSOCIATED
C WITH ELMNT: ONE WITH TWO NABORS (Q2HEAD) IN
C ADJACENCY STRUCTURE, AND THE OTHER WITH MORE
C THAN TWO NABORS (QXHEAD). ALSO COMPUTE DEG0,
C NUMBER OF NODES IN THIS ELEMENT.
C ---------------------------------------------
Q2HEAD = 0
QXHEAD = 0
DEG0 = 0
LINK = ELMNT
400 CONTINUE
ISTRT = XADJ(LINK)
ISTOP = XADJ(LINK+1) - 1
DO 700 I = ISTRT, ISTOP
ENODE = ADJNCY(I)
LINK = - ENODE
IF ( ENODE ) 400, 800, 500
C
500 CONTINUE
IF ( QSIZE(ENODE) .EQ. 0 ) GO TO 700
DEG0 = DEG0 + QSIZE(ENODE)
MARKER(ENODE) = MTAG
C ----------------------------------
C IF ENODE REQUIRES A DEGREE UPDATE,
C THEN DO THE FOLLOWING.
C ----------------------------------
IF ( DBAKW(ENODE) .NE. 0 ) GO TO 700
C ---------------------------------------
C PLACE EITHER IN QXHEAD OR Q2HEAD LISTS.
C ---------------------------------------
IF ( DFORW(ENODE) .EQ. 2 ) GO TO 600
LLIST(ENODE) = QXHEAD
QXHEAD = ENODE
GO TO 700
600 CONTINUE
LLIST(ENODE) = Q2HEAD
Q2HEAD = ENODE
700 CONTINUE
800 CONTINUE
C --------------------------------------------
C FOR EACH ENODE IN Q2 LIST, DO THE FOLLOWING.
C --------------------------------------------
ENODE = Q2HEAD
IQ2 = 1
900 CONTINUE
IF ( ENODE .LE. 0 ) GO TO 1500
IF ( DBAKW(ENODE) .NE. 0 ) GO TO 2200
TAG = TAG + 1
DEG = DEG0
C ------------------------------------------
C IDENTIFY THE OTHER ADJACENT ELEMENT NABOR.
C ------------------------------------------
ISTRT = XADJ(ENODE)
NABOR = ADJNCY(ISTRT)
IF ( NABOR .EQ. ELMNT ) NABOR = ADJNCY(ISTRT+1)
C ------------------------------------------------
C IF NABOR IS UNELIMINATED, INCREASE DEGREE COUNT.
C ------------------------------------------------
LINK = NABOR
IF ( DFORW(NABOR) .LT. 0 ) GO TO 1000
DEG = DEG + QSIZE(NABOR)
GO TO 2100
1000 CONTINUE
C --------------------------------------------
C OTHERWISE, FOR EACH NODE IN THE 2ND ELEMENT,
C DO THE FOLLOWING.
C --------------------------------------------
ISTRT = XADJ(LINK)
ISTOP = XADJ(LINK+1) - 1
DO 1400 I = ISTRT, ISTOP
NODE = ADJNCY(I)
LINK = - NODE
IF ( NODE .EQ. ENODE ) GO TO 1400
IF ( NODE ) 1000, 2100, 1100
C
1100 CONTINUE
IF ( QSIZE(NODE) .EQ. 0 ) GO TO 1400
IF ( MARKER(NODE) .GE. TAG ) GO TO 1200
C -------------------------------------
C CASE WHEN NODE IS NOT YET CONSIDERED.
C -------------------------------------
MARKER(NODE) = TAG
DEG = DEG + QSIZE(NODE)
GO TO 1400
1200 CONTINUE
C ----------------------------------------
C CASE WHEN NODE IS INDISTINGUISHABLE FROM
C ENODE. MERGE THEM INTO A NEW SUPERNODE.
C ----------------------------------------
IF ( DBAKW(NODE) .NE. 0 ) GO TO 1400
IF ( DFORW(NODE) .NE. 2 ) GO TO 1300
QSIZE(ENODE) = QSIZE(ENODE) +
1 QSIZE(NODE)
QSIZE(NODE) = 0
MARKER(NODE) = MAXINT
DFORW(NODE) = - ENODE
DBAKW(NODE) = - MAXINT
GO TO 1400
1300 CONTINUE
C --------------------------------------
C CASE WHEN NODE IS OUTMATCHED BY ENODE.
C --------------------------------------
IF ( DBAKW(NODE) .EQ.0 )
1 DBAKW(NODE) = - MAXINT
1400 CONTINUE
GO TO 2100
1500 CONTINUE
C ------------------------------------------------
C FOR EACH ENODE IN THE QX LIST, DO THE FOLLOWING.
C ------------------------------------------------
ENODE = QXHEAD
IQ2 = 0
1600 CONTINUE
IF ( ENODE .LE. 0 ) GO TO 2300
IF ( DBAKW(ENODE) .NE. 0 ) GO TO 2200
TAG = TAG + 1
DEG = DEG0
C ---------------------------------
C FOR EACH UNMARKED NABOR OF ENODE,
C DO THE FOLLOWING.
C ---------------------------------
ISTRT = XADJ(ENODE)
ISTOP = XADJ(ENODE+1) - 1
DO 2000 I = ISTRT, ISTOP
NABOR = ADJNCY(I)
IF ( NABOR .EQ. 0 ) GO TO 2100
IF ( MARKER(NABOR) .GE. TAG ) GO TO 2000
MARKER(NABOR) = TAG
LINK = NABOR
C ------------------------------
C IF UNELIMINATED, INCLUDE IT IN
C DEG COUNT.
C ------------------------------
IF ( DFORW(NABOR) .LT. 0 ) GO TO 1700
DEG = DEG + QSIZE(NABOR)
GO TO 2000
1700 CONTINUE
C -------------------------------
C IF ELIMINATED, INCLUDE UNMARKED
C NODES IN THIS ELEMENT INTO THE
C DEGREE COUNT.
C -------------------------------
JSTRT = XADJ(LINK)
JSTOP = XADJ(LINK+1) - 1
DO 1900 J = JSTRT, JSTOP
NODE = ADJNCY(J)
LINK = - NODE
IF ( NODE ) 1700, 2000, 1800
C
1800 CONTINUE
IF ( MARKER(NODE) .GE. TAG )
1 GO TO 1900
MARKER(NODE) = TAG
DEG = DEG + QSIZE(NODE)
1900 CONTINUE
2000 CONTINUE
2100 CONTINUE
C -------------------------------------------
C UPDATE EXTERNAL DEGREE OF ENODE IN DEGREE
C STRUCTURE, AND MDEG (MIN DEG) IF NECESSARY.
C -------------------------------------------
DEG = DEG - QSIZE(ENODE) + 1
FNODE = DHEAD(DEG)
DFORW(ENODE) = FNODE
DBAKW(ENODE) = - DEG
IF ( FNODE .GT. 0 ) DBAKW(FNODE) = ENODE
DHEAD(DEG) = ENODE
IF ( DEG .LT. MDEG ) MDEG = DEG
2200 CONTINUE
C ----------------------------------
C GET NEXT ENODE IN CURRENT ELEMENT.
C ----------------------------------
ENODE = LLIST(ENODE)
IF ( IQ2 .EQ. 1 ) GO TO 900
GO TO 1600
2300 CONTINUE
C -----------------------------
C GET NEXT ELEMENT IN THE LIST.
C -----------------------------
TAG = MTAG
ELMNT = LLIST(ELMNT)
GO TO 100
C
END
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