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C SPDX-FileCopyrightText: 2023 SAP SE
C
C SPDX-License-Identifier: Apache-2.0
C
SUBROUTINE SPRRNM ( MSPAR , MSICA , IWORK , LPU , IERR )
C ------------------------------------------------------------------
IMPLICIT NONE
INTEGER LPU , IERR
INTEGER MSPAR(*) , MSICA(*) , IWORK(*)
C ======================================================================
C S A M library routine : SPRRNM GROUP 9 / PUBLIC
C ======================================================================
C
C Purpose
C -------
C
C --- To order the finite-element variables by means of the SPR-node
C partition.
C
C Created : Jan. 11, 1994 (acd)
C Revisions : Aug. 24, 1998 (acd)
C MSPAR(50) -> MSPAR(*), and added superelement option.
C May. 16, 2003 (kmo)
C Added checks that MSICA and IWORK are great enough.
C Reduced the size of NODEL by SPRNOD.
C
C
C MSPAR - INTEGER(*)
C Entry : As on exit from SPRSAS.
C Exit : Not changed, except for MSPAR(1) that is set to 2 in case
C of sucessful exit, and to -2 else.
C MSICA - INTEGER(NMSICA)
C Entry : As on exit from SPRSAS.
C Exit : Not changed.
C NMSICA - INTEGER
C Entry : The length of MSICA.
C Exit : Not changed.
C NIWORK - INTEGER
C Entry : The length of IWORK.
C Exit : Not changed.
C LPU - INTEGER
C Entry : Output unit for error messages.
C Exit : Not changed.
C IERR - INTEGER
C Entry : Not defined
C Exit : Is set to zero if a successful call,
C = -1 if error from SPRSAS is not cleared.
C = -2 if MSICA and/or IWORK are not great enough.
C
C Working arrays
C --------------
C
C IWORK - INTEGER(MSPAR(37))
C Entry : Not defined.
C The array is partitioned by the routine for use in SPRMMD
C as follows:
C INVP : On exit from SPRMMD, the inverse permutation.
C XFLNOD : Pointer to FLNOD.
C FLNOD : List of nodes in element headed by its length.
C XFNODL : Pointer to FNODL.
C FNODL : List of elements at nodes headed by its length.
C HEAD : Head of doubly linked degree structure.
C QSIZE : Size of supernodes.
C ELMLNK : List of new elements in each elimination step.
C FLAG : Marker vector.
C STOREL : List of nodes that may be indist or outmatched.
C MARKER : Marker vector.
C Exit : Need not be saved.
C
C Procedures
C ----------
C
C SPRCN1
C SPRMMD
C SPRCMD
C SPRER1
C
C Intrinsic
C ---------
C
C MAX
C
C Include Blocks
C --------------
C
C None
C
C Common Blocks
C -------------
C
C None
C
C ------------------------------------------------------------------
INTEGER DELTA , ELMLNK, ELNOD , FLAG , FLNOD , FNODL ,
$ HEAD , INVP , IWUSED, MARKER, MAXMRK, MAXNEL,
$ NCOMPR, NEL , NEQ , NODEL , NODES ,
$ PERM , QSIZE , SPRCON, SPRNOD, STOREL, XELNOD,
$ XFLNOD, XFNODL, XNODEL, XNODES, SEPSZE, SEPNUM,
$ SEPCNT, SEPARR, VWGHT
LOGICAL LWEIGH
INTRINSIC MAX
EXTERNAL SPRCN1, SPRMMD, SPRCMD, SPRER1
C ==================================================================
C --------------------
C GET INFO FROM MSPAR.
C --------------------
IF ( MSPAR(1) .LT. 0 ) THEN
MSPAR(1) = -2
IERR = -1
CALL SPRER1 ( 30, 'SPRRNM', 0, 0, 0, LPU, IERR )
RETURN
ELSE
MSPAR(1) = 2
IERR = 0
ENDIF
NEL = MSPAR( 5)
SPRNOD = MSPAR( 6)
SPRCON = MSPAR( 7)
NEQ = MSPAR( 8)
SEPSZE = MSPAR(40)
C ----------------------------------
C DIVIDE IWORK AND CHECK ITS LENGTH.
C ----------------------------------
INVP = 1
XFLNOD = INVP + SPRNOD
FLNOD = XFLNOD + NEL
XFNODL = FLNOD + SPRCON + NEL
FNODL = XFNODL + SPRNOD
HEAD = FNODL + SPRCON + SPRNOD
QSIZE = HEAD + NEQ + 1
VWGHT = QSIZE + SPRNOD
ELMLNK = VWGHT + SPRNOD
FLAG = ELMLNK + NEL
STOREL = FLAG + SPRNOD
MARKER = STOREL + SPRNOD
IWUSED = MARKER + SPRNOD - 1
IF ( IWUSED .GT. MSPAR(37) ) THEN
MSPAR(1) = -2
IERR = -2
CALL SPRER1 ( 34, 'SPRRNM', IWUSED, MSPAR(37), 0, LPU, IERR)
RETURN
ENDIF
C -------------------------------------------
C SET POINTERS TO MSICA AND CHECK ITS LENGTH.
C -------------------------------------------
XELNOD = 1
XNODEL = XELNOD + NEL + 1
XNODES = XNODEL + SPRNOD + 1
NODES = XNODES + SPRNOD + 1
PERM = NODES + NEQ
ELNOD = PERM + SPRNOD
NODEL = ELNOD + SPRCON
SEPARR = NODEL + SPRCON
IWUSED = SEPARR + SPRNOD - 1
IF ( IWUSED .GT. MSPAR(2) ) THEN
MSPAR(1) = -2
IERR = -2
CALL SPRER1 ( 32, 'SPRRNM', IWUSED, MSPAR(35), 0, LPU, IERR)
RETURN
ENDIF
C ==================================================================
C ---------------------
C COMPUTE XNODEL,NODEL.
C ---------------------
CALL SPRCN1 ( MSICA(XELNOD), MSICA(ELNOD), MSICA(XNODEL),
$ MSICA(NODEL), NEL, SPRNOD, SPRCON, IWORK(MARKER) )
C ==================================================================
C ------------------------------------
C ORDER THE NODES BY A CALL TO SPRMMD.
C ------------------------------------
MAXNEL = SPRCON + NEL
MAXMRK = MAX(NEL,SPRNOD) + 1
DELTA = 0
IF ( SEPSZE.LE.0 ) THEN
* ------ Standard ordering
CALL SPRMMD ( NEL, SPRNOD, SPRCON, MAXNEL, MAXMRK, DELTA,
$ MSICA(XELNOD), MSICA(ELNOD), MSICA(XNODEL),
$ MSICA(NODEL), NCOMPR, MSICA(PERM), IWORK(INVP),
$ IWORK(XFLNOD), IWORK(FLNOD), IWORK(XFNODL),
$ IWORK(FNODL), IWORK(HEAD), IWORK(QSIZE),
$ IWORK(ELMLNK), IWORK(FLAG), IWORK(STOREL),
$ IWORK(MARKER) )
ELSE IF ( SEPSZE.LE.SPRNOD ) THEN
* ------ Constrained ordering for superelement technique.
* Reset SEPNUM and SEPCNT to the only legal values per now.
* Use standard minimum degree condition (LWEIGH=.FALSE.).
SEPNUM = 0
SEPCNT = 1
LWEIGH = .FALSE.
CALL SPRCMD
$ ( NEL,NEQ,SPRNOD,SPRCON,MAXNEL,MAXMRK,DELTA,LWEIGH,
$ NCOMPR,MSICA(XELNOD),MSICA(ELNOD),MSICA(XNODEL),
$ MSICA(NODEL),MSICA(XNODES),MSICA(PERM),IWORK(INVP),
$ IWORK(XFLNOD),IWORK(FLNOD),IWORK(XFNODL),IWORK(FNODL),
$ IWORK(HEAD),IWORK(QSIZE),IWORK(VWGHT),IWORK(ELMLNK),
$ IWORK(FLAG),IWORK(STOREL),IWORK(MARKER),SEPNUM,
$ SEPSZE,SEPCNT,MSICA(SEPARR),LPU )
ELSE
* ------ There are no subgraphs to order. It is assumed that
* PERM is already initialized according to the initial
* order of the nodes.
ENDIF
C ==================================================================
RETURN
C ------------------------------------------------------------------
C END OF MODULE SPRRNM
END
SUBROUTINE SPRMMD ( NELS , NNODS , NELNOD, MAXNEL, MAXMRK,
$ DELTA , XELNOD, ELNOD , XNODEL, NODEL ,
$ NCOMPR, PERM , INVP , XFLNOD, FLNOD ,
$ XFNODL, FNODL , HEAD , QSIZE , ELMLNK,
$ FLAG , STOREL, MARKER )
C ------------------------------------------------------------------
INTEGER NELS , NNODS , NELNOD, MAXNEL, MAXMRK, DELTA ,
$ NCOMPR
INTEGER XELNOD(NELS+1) , ELNOD(NELNOD) ,
$ XNODEL(NNODS+1) , NODEL(NELNOD) ,
$ PERM(NNODS) , INVP(NNODS) ,
$ XFLNOD(NELS) , FLNOD(MAXNEL) ,
$ XFNODL(NNODS) , FNODL(NNODS+NELNOD) ,
$ HEAD(NNODS) , QSIZE(NNODS) ,
$ ELMLNK(NELS) , FLAG(NNODS) ,
$ STOREL(NNODS) , MARKER(NNODS)
C ------------------------------------------------------------------
C
C PURPOSE
C -------
C
C SPRMMD
C
C --- TO PERFORM A MINIMUM DEGREE PERMUTATION. THE ROUTINE UTILIZES THE
C INHERENT CLIQUE STRUCTURE OF THE FINITE ELEMENT MESH.
C
C CREATED : JAN. 11, 1994 (ACD)
C REVISIONS : MNT. XX, 199X (ACD)
C
C
C ON ENTRY
C --------
C
C NELS : INTEGER
C NUMBER OF ELEMENTS.
C NNODS : INTEGER
C NUMBER OF NODES.
C NELNOD : INTEGER
C SIZE OF CONNECTIVITY ARRAYS.
C MAXNEL : INTEGER
C SIZE OF ARRAY FLNOD. THE SIZE MUST BE AT LEAST
C NELS+NELNOD, BUT THE NUMBER OF WORKSPACE COMPRESSIONS
C WILL DECREASE IF THE SIZE IS INCREASED.
C MAXMRK : INTEGER
C USED AS UPPER LIMIT FOR MARKING NODES AND ELEMENTS, ANY
C NUMBER LARGER THAN MAX(NNODS,NELS)+1 IS OK.
C DELTA : INTEGER
C TOLERANCE FOR MULTIPLE ELIMINATION.
C .LT. 0 : WITHOUT MULTIPLE ELIMINATION.
C .EQ. 0 : WITH MULTIPLE ELIMINATION.
C .GT. 0 : WITH MULTIPLE ELIMINATION AND RELAXED MINIMUM
C DEGREE CONDITION.
C (XELNOD,
C ELNOD) : INTEGER(NELS+1), INTEGER(NELNOD)
C ELEMENT-NODE CONNECTIVITY.
C (XNODEL,
C NODEL) : INTEGER(NNODS+1), INTEGER(NELNOD)
C NODE-ELEMENT CONNECTIVITY.
C
C ON EXIT
C -------
C
C NCOMPR : INTEGER
C NUMBER OF WORKSPACE COMPRESSIONS NEEDED IN SPRMM2.
C (PERM,
C INVP) : 2*INTEGER(NNODS)
C THE PERMUTATION.
C DURING EXECUTION THEY ARE USED AS WORKSPACE AS EXPLAINED
C BELOW.
C
C WORKING ARRAYS
C --------------
C
C XFLNOD : INTEGER(NELS)
C STORES THE POINTERS INTO THE LISTS OF NODES WHICH ARE
C CONNECTED TO THE ELEMENT. IF ELEMENTS ARE ABORBED, THEN
C XFLNOD=0 FOR THESE ELEMENTS.
C FLNOD : INTEGER(MAXNEL)
C STORES FOR EACH ELEMENT A LIST OF NODES CONNECTED TO THE
C ELEMENT. EACH LIST OF NODES IS HEADED BY ITS LENGTH.
C XFNODL : INTEGER(NNODS)
C STORES THE POINTERS INTO THE LISTS OF ELEMENTS WHICH ARE
C CONNECTED TO THE NODE. IF NODES ARE ELIMINATED, THEN
C XFNODL=0 FOR THESE NODES.
C FNODL : INTEGER(NNODS+NELNOD)
C STORES FOR EACH NODE A LIST OF ELEMENTS CONNECTED TO THE
C NODE. EACH LIST OF ELEMENTS IS HEADED BY ITS LENGTH.
C HEAD : INTEGER(NNODS)
C HEAD OF DEGREE LIST.
C QSIZE : INTEGER(NNODS)
C SUPERNODE SIZES.
C ELMLNK : INTEGER(NNODS)
C GENERALIZED ELEMENTS WHICH NEED DEGREE UPDATES.
C FLAG : INTEGER(NNODS)
C FLAGS ACTIVE NODES IN THE DEGREE UPDATE STEP.
C STOREL : INTEGER(NNODS)
C LIST OF NODES IN NEW GENERATED ELEMENTS AND LISTS
C OF NODES OF DIFFERENT TYPES IN DEGREE UPDATE STEP.
C MARKER : INTEGER(NNODS)
C MARK OF NODES.
C
C SUBPROGRAMS/FUNCTIONS
C ---------------------
C
C SPRMM1
C SPRMM2
C SPRMM3
C SPRMM4
C
C ------------------------------------------------------------------
INTEGER CMINDG, CURMDN, I , LIMIT , MARK , NUM ,
$ NUMELM, NXTMDN, NXTUSE
EXTERNAL SPRMM1, SPRMM2, SPRMM3, SPRMM4
C ==================================================================
C ----------------------------------
C SET NUM TO # ELIMINATED NODES + 1.
C NXTUSE IS SET TO NELS+NELNOD+1.
C ----------------------------------
NCOMPR = 0
NUM = 1
NXTUSE = NELS + NELNOD + 1
C ----------------------------------------------
C INITIALIZE FOR THE MINIMUM DEGREE ELIMINATION.
C ----------------------------------------------
CALL SPRMM1 ( NELS, NNODS, NELNOD, MAXNEL, MAXMRK, XELNOD, ELNOD,
$ XNODEL, NODEL, XFLNOD, FLNOD, XFNODL, FNODL, HEAD,
$ INVP, PERM, QSIZE, ELMLNK, MARKER, FLAG, STOREL )
C ==================================================================
IF ( HEAD(1) .GT. 0 ) THEN
C ------------------------------------
C ELIMINATE THE ISOLATED NODAL BLOCKS.
C ------------------------------------
NXTMDN = HEAD(1)
100 IF ( NXTMDN .GT. 0 ) THEN
CURMDN = NXTMDN
NXTMDN = INVP(CURMDN)
MARKER(CURMDN) = MAXMRK
INVP(CURMDN) = -NUM
NUM = NUM + QSIZE(CURMDN)
GOTO 100
ENDIF
C -----------------------------------------------
C GOTO NUMBERING IF ALL THE NODES ARE ELIMINATED.
C -----------------------------------------------
IF ( NUM .GT. NNODS )
$ GOTO 600
ENDIF
C --------------------------------------------
C INITIALIZE FOR THE NON-TRIVIAL ELIMINATIONS.
C --------------------------------------------
MARK = 1
CMINDG = 2
HEAD(1) = 0
C ================================
C START THE MAIN ELIMINATION LOOP.
C ================================
C -----------------------------
C FIND THE NEXT MINIMUM DEGREE.
C -----------------------------
200 IF ( HEAD(CMINDG) .LE. 0 ) THEN
CMINDG = CMINDG + 1
GOTO 200
ENDIF
LIMIT = CMINDG + DELTA
NUMELM = 0
C ====================================
C START THE MULTIPLE ELIMINATION STEP.
C ====================================
C -----------------------------------------
C RETRIEVE THE CURRENT MINIMUM DEGREE NODE.
C -----------------------------------------
300 CURMDN = HEAD(CMINDG)
IF ( CURMDN .LE. 0 ) THEN
CMINDG = CMINDG + 1
IF ( CMINDG .GT. LIMIT )
$ GOTO 500
GOTO 300
ENDIF
C -----------------------------------
C REMOVE THE MINIMUM DEGREE NODE FROM
C THE DOUBLY LINKED DEGREE STRUCTURE.
C AND SET ITS INVERSE PERMUTATION
C POSITION IN INVP.
C -----------------------------------
NXTMDN = INVP(CURMDN)
HEAD(CMINDG) = NXTMDN
IF ( NXTMDN .GT. 0 ) PERM(NXTMDN) = -CMINDG
INVP(CURMDN) = -NUM
C -----------------------------------------------
C GOTO NUMBERING IF ALL THE NODES ARE ELIMINATED.
C -----------------------------------------------
IF ( NUM + QSIZE(CURMDN) .GT. NNODS )
$ GOTO 600
C -----------------------
C UPDATE THE NODE MARKER.
C -----------------------
MARK = MARK + 1
IF ( MARK .GE. MAXMRK ) THEN
C ------------------------
C RESET THE MARKER VECTOR.
C ------------------------
MARK = 1
DO 400 I = 1, NNODS
IF ( MARKER(I) .LT. MAXMRK )
$ MARKER(I) = 0
400 CONTINUE
ENDIF
C ---------------------------------
C UPDATE THE GRAPH REPRESENTATION
C DUE TO THE ELIMINATION OF CURMDN.
C ---------------------------------
CALL SPRMM2 ( CURMDN, NELS, NNODS, NELNOD, MAXNEL, MARK,
$ MAXMRK, NUMELM, NXTUSE, NCOMPR, XFNODL, FNODL,
$ XFLNOD, FLNOD, HEAD, PERM, INVP, QSIZE, ELMLNK,
$ MARKER, STOREL )
NUM = NUM + QSIZE(CURMDN)
C -----------------------------------------------
C GOTO NUMBERING IF ALL THE NODES ARE ELIMINATED.
C -----------------------------------------------
IF ( NUM .GT. NNODS )
$ GOTO 600
C -------------------------------
C GOTO A NEW NODE ELIMINATION IN
C THIS MULTIPLE ELIMINATION STEP.
C -------------------------------
IF ( DELTA .GE. 0 )
$ GOTO 300
C -----------------------------------------------
C GOTO NUMBERING IF ALL THE NODES ARE ELIMINATED.
C -----------------------------------------------
500 IF ( NUM .GT. NNODS )
$ GOTO 600
C ----------------------------------
C UPDATE THE DEGREE OF ALL THE NODES
C WHICH ARE AFFECTED IN THE CURRENT
C MULTIPLE ELIMINATION STEP, EXCEPT
C THOSE WHICH ARE OUTMATCHED.
C ----------------------------------
CALL SPRMM3 ( NUMELM, CMINDG, MARK, NELS, NNODS,
$ NELNOD, MAXNEL, MAXMRK, XFNODL, FNODL,
$ XFLNOD, FLNOD, HEAD, INVP, PERM, QSIZE,
$ ELMLNK, MARKER, FLAG, STOREL )
C ----------------------------------------
C GOTO THE NEXT MULTIPLE ELIMINATION STEP.
C ----------------------------------------
GOTO 200
C =============================
C END OF MAIN ELIMINATION LOOP.
C =============================
600 CONTINUE
C -----------------------------------
C DETERMINE THE FINAL NODAL ORDERING.
C -----------------------------------
CALL SPRMM4 ( NNODS, PERM, INVP, QSIZE )
C ==================================================================
RETURN
C ------------------------------------------------------------------
C END OF MODULE SPRMMD
END
SUBROUTINE SPRMM1 ( NELS , NNODS , NELNOD, MAXNEL, MAXMRK,
$ XELNOD, ELNOD , XNODEL, NODEL , XFLNOD,
$ FLNOD , XFNODL, FNODL , HEAD , INVP ,
$ PERM , QSIZE , ELMLNK, MARKER, FLAG ,
$ MASK )
C ------------------------------------------------------------------
INTEGER NELS , NNODS , NELNOD, MAXNEL, MAXMRK
INTEGER XELNOD(NELS+1) , ELNOD(NELNOD) ,
$ XNODEL(NNODS+1) , NODEL(NELNOD) ,
$ XFLNOD(NELS) , FLNOD(MAXNEL) ,
$ XFNODL(NNODS) , FNODL(NNODS+NELNOD) ,
$ HEAD(NNODS) , INVP(NNODS) ,
$ PERM(NNODS) , QSIZE(NNODS) ,
$ ELMLNK(NELS) , MARKER(NNODS) ,
$ FLAG(NNODS) , MASK(NNODS)
C ------------------------------------------------------------------
C
C PURPOSE
C -------
C
C SPRMM1
C
C --- TO INITIALIZE FOR SPRMMD.
C
C CREATED : JAN. 11, 1994 (ACD)
C REVISIONS : MNT. XX, 199X (ACD)
C
C
C ON ENTRY
C --------
C
C NELS : INTEGER
C NUMBER OF ELEMENTS.
C NNODS : INTEGER
C NUMBER OF NODES.
C NELNOD : INTEGER
C SIZE OF CONNECTIVITY ARRAYS.
C MAXNEL : INTEGER
C WORKSPACE FOR FLNOD. AT LEAST NELS+NELNOD.
C (XELNOD,
C ELNOD) : INTEGER(NELS), INTEGER(NELNOD)
C ELEMENT-NODE CONNECTIVITY.
C (XNODEL,
C NODEL) : INTEGER(NNODS+1), INTEGER(NELNOD)
C NODE-ELEMENT CONNECTIVITY.
C
C ON EXIT
C -------
C
C XFLNOD : INTEGER(NELS)
C POINTER INTO FLNOD FOR LISTS OF NODES CONNECTED TO THE
C ELEMENTS.
C FLNOD : INTEGER(NELNOD+NELS)
C LISTS OF NODES, WHERE EACH LIST IS HEADED BY ITS LENGTH.
C XFNODL : INTEGER(NNODS)
C POINTER INTO FNODL FOR LISTS OF ELEMENTS CONNECTED TO
C THE NODES.
C FNODL : INTEGER(NELNOD+NNODS)
C LISTS OF ELEMENTS, WHERE EACH LIST IS HEADED BY ITS
C LENGTH.
C (HEAD,
C INVP,
C PERM) : 3*INTEGER(NNODS)
C DOUBLY LINKED DEGREE STRUCTURE WITH INITIAL DEGREE OF
C THE NODES.
C QSIZE : INTEGER(NNODS)
C SUPERNODE SIZES INITIALIZED TO 1.
C ELMLNK : INTEGER(NELS)
C LIST OF ELEMENTS IS NOW THE ZERO LIST.
C MARKER : INTEGER(NNODS)
C INITIALIZED TO ZERO.
C FLAG : INTEGER(NNODS)
C FLAGS ACTIVE NODES IN THE DEGREE UPDATE STEP.
C
C WORKING ARRAYS
C --------------
C
C MASK : INTEGER(NNODS)
C Used to hold the clique sizes for nodes that are
C candidates for merge.
C
C SUBPROGRAMS/FUNCTIONS
C ---------------------
C
C NONE
C
C ------------------------------------------------------------------
INTEGER DEG , ELEMNT, I , IDUMMY, IEL , INOD ,
$ IP , ISTRT , ISTOP , J , JSTRT , JSTOP ,
$ K , KSTRT , KSTOP , MERGED, NEWNOD, NEXT ,
$ NODE , NXTNOD, PREV
INTRINSIC ABS
C ==================================================================
C -----------
C INITIALIZE.
C -----------
DO 10 I = 1, NNODS
FLAG(I) = 0
HEAD(I) = 0
MARKER(I) = 0
QSIZE(I) = 1
10 CONTINUE
DO 20 I = 1, NELS
ELMLNK(I) = 0
20 CONTINUE
C ==================================================================
C -------------------------------------
C COMPUTE THE INITIAL DEGREE STRUCTURE.
C -------------------------------------
DO 300 NODE = 1, NNODS
MARKER(NODE) = NODE
ISTRT = XNODEL(NODE)
ISTOP = XNODEL(NODE+1) - 1
DEG = 1
DO 200 I = ISTRT, ISTOP
ELEMNT = NODEL(I)
JSTRT = XELNOD(ELEMNT)
JSTOP = XELNOD(ELEMNT+1) - 1
DO 100 J = JSTRT, JSTOP
NEWNOD = ELNOD(J)
IF ( MARKER(NEWNOD) .NE. NODE )
$ THEN
MARKER(NEWNOD) = NODE
DEG = DEG + 1
ENDIF
100 CONTINUE
200 CONTINUE
NEWNOD = HEAD(DEG)
INVP(NODE) = NEWNOD
HEAD(DEG) = NODE
IF ( NEWNOD .GT. 0 )
$ PERM(NEWNOD) = NODE
PERM(NODE) = -DEG
300 CONTINUE
C ---------------------
C RESET MARKER TO ZERO.
C ---------------------
DO 400 I = 1, NNODS
MARKER(I) = 0
400 CONTINUE
C ==================================================================
C -----------------------------------------------------
C BUILD THE GRAPH REPRESENTATION NEEDED BY THE ROUTINE.
C -----------------------------------------------------
IP = NELS + NELNOD
DO 600 I = NELS, 1, -1
JSTRT = XELNOD(I)
JSTOP = XELNOD(I+1)-1
DO 500 J = JSTOP, JSTRT, -1
FLNOD(IP) = ELNOD(J)
IP = IP - 1
500 CONTINUE
XFLNOD(I) = IP
FLNOD(IP) = JSTOP + 1 - JSTRT
IP = IP - 1
600 CONTINUE
IP = NNODS + NELNOD
DO 800 I = NNODS, 1, -1
JSTRT = XNODEL(I)
JSTOP = XNODEL(I+1)-1
DO 700 J = JSTOP, JSTRT, -1
FNODL(IP) = NODEL(J)
IP = IP - 1
700 CONTINUE
XFNODL(I) = IP
FNODL(IP) = JSTOP + 1 - JSTRT
IP = IP - 1
800 CONTINUE
C ==================================================================
C --- FIND THE STRUCTURALLY INDISTINGUISHABLE NODES ACCORDING TO
C ALGORITHM 2.1 IN MY THESIS.
MERGED = 0
DO 1300 IEL = 1, NELS
ISTRT = XFLNOD(IEL)
ISTOP = ISTRT + FLNOD(ISTRT)
DO 1200 I = ISTRT+1, ISTOP
INOD = FLNOD(I)
IF ( FLAG(INOD) .EQ. 0 ) THEN
FLAG(INOD) = INOD
C ------------ SET NXTNOD =-INOD IN ORDER TO INITIATE THE LINKED
C LIST OF NODES TO BE SCANNED.
NXTNOD = -INOD
JSTRT = XFNODL(INOD)
JSTOP = JSTRT + FNODL(JSTRT)
DO 1000 J = JSTRT+1, JSTOP
ELEMNT = FNODL(J)
KSTRT = XFLNOD(ELEMNT)
KSTOP = KSTRT + FLNOD(KSTRT)
DO 900 K = KSTRT+1, KSTOP
NODE = FLNOD(K)
IF ( FLAG(NODE) .EQ. 0 ) THEN
C --------------------- THIS NODE IS NOT YET VISITED, INITIALIZE THE
C GENERATED ELEMENT COUNTER, SET FLAG IN ORDER
C TO UPDATE LINKED LIST AND SET -NODE AS NEXT
C NODE.
MASK(NODE) = 1
FLAG(NODE) = NXTNOD
NXTNOD = -NODE
ELSEIF ( FLAG(NODE) .LT. 0 ) THEN
C --------------------- THIS NODE IS VISITED, INCREMENT ITS GENERATED
C ELEMENT COUNTER BY ONE.
MASK(NODE) = MASK(NODE) + 1
ENDIF
900 CONTINUE
1000 CONTINUE
C ------------ JSTOP IS USED AS CLIQUE NUMBER COUNTER FOR INOD.
JSTOP = FNODL(JSTRT)
DO 1100 IDUMMY = 1, NNODS
C --------------- DUMMY LOOP, WILL ONLY INCREMENT ACCORDING TO
C THE NUMBER OF MERGED NODES.
NODE = ABS(NXTNOD)
IF ( FLAG(NODE) .LT. 0 ) THEN
C ------------------ HAS NOT YET REACHED THE BOTTOM OF LIST. SET NXTNOD
C TO BE NEXT NODE IN LINKED LIST STORED IN FLAG.
NXTNOD = FLAG(NODE)
C ------------------ KSTOP IS USED AS CLIQUE NUMBER COUNTER FOR NODE.
KSTOP = FNODL(XFNODL(NODE))
IF ( ( MASK(NODE) .LT. KSTOP ).OR.
$ ( JSTOP .NE. KSTOP ) ) THEN
C --------------------- NODE CANNOT BE MERGED WITH INOD.
FLAG(NODE) = 0
ELSE
C --------------------- NODE CAN BE MERGED WITH INOD
C FIRST REMOVE NODE FROM THE DEGREE STRUCTURE.
PREV = PERM(NODE)
IF ( PREV .NE. 0 .AND. PREV .NE. -MAXMRK ) THEN
C ------------------------ IT IS IN THE DEGREE STRUCTURE, REMOVE IT.
NEXT = INVP(NODE)
IF ( NEXT .GT. 0 ) PERM(NEXT) = PREV
IF ( PREV .GT. 0 ) INVP(PREV) = NEXT
IF ( PREV .LT. 0 ) HEAD(-PREV) = NEXT
ENDIF
C --------------------- MERGE NODE WITH INOD.
QSIZE(INOD) = QSIZE(INOD) + QSIZE(NODE)
QSIZE(NODE) = 0
MARKER(NODE) = MAXMRK
INVP(NODE) = -INOD
XFNODL(NODE) = 0
C --------------------- ACCUMULATE THE NUMBER OF MERGED NODES
C AND MASK IT OFF IN FLAG.
MERGED = MERGED + 1
FLAG(NODE) = NODE
ENDIF
ELSE
C ------------------ END OF LIST, JUMP TO NEXT NODE.
GOTO 1150
ENDIF
1100 CONTINUE
1150 CONTINUE
ENDIF
1200 CONTINUE
1300 CONTINUE
DO 1400 I = 1, NNODS
FLAG(I) = 0
1400 CONTINUE
**DAM WRITE ( 6, '(/A,I6)' ) ' Number of nodes : ', NNODS
**DAM WRITE ( 6, '(A,I6/)' ) ' New number of nodes : ', NNODS-MERGED
C ==================================================================
RETURN
C ------------------------------------------------------------------
C END OF MODULE SPRMM1
END
SUBROUTINE SPRMM2 ( NODE , NELS , NNODS , NELNOD, MAXNEL,
$ MARK , MAXMRK, NUMELM, NXTUSE, NCOMPR,
$ XFNODL, FNODL , XFLNOD, FLNOD , HEAD ,
$ PERM , INVP , QSIZE , ELMLNK, MARKER,
$ STOREL )
C ------------------------------------------------------------------
INTEGER NODE , NELS , NNODS , NELNOD, MAXNEL, MARK ,
$ MAXMRK, NUMELM, NXTUSE, NCOMPR
INTEGER XFNODL(NNODS) , FNODL(NNODS+NELNOD) ,
$ XFLNOD(NELS) , FLNOD(MAXNEL) ,
$ HEAD(NNODS) , PERM(NNODS) ,
$ INVP(NNODS) , MARKER(NNODS) ,
$ QSIZE(NNODS) , ELMLNK(NELS) ,
$ STOREL(NNODS)
C ------------------------------------------------------------------
C
C PURPOSE
C -------
C
C SPRMM2
C
C --- TO UPDATE THE REPRESENTATION OF THE GRAPH DUE TO THE ELIMINATION
C OF NODE. THE ROUTINE WORKS ON THE IMPLIVIT REPRESENTATION OF THE
C GRAPH. THE IMPLICIT GRAPH STRUCTURE IS REPRESENTED BY THE ARRAYS
C (XFNODL,FNODL) $ (XFLNOD,FLNOD).
C
C CREATED : JAN. 11, 1994 (ACD)
C REVISIONS : MNT. XX, 199X (ACD)
C
C
C ON ENTRY
C --------
C
C NODE : INTEGER
C NODE TO BE ELIMINATED.
C NELS : INTEGER
C NUMBER OF FINITE ELEMENTS IN THE MESH.
C NNODS : INTEGER
C NUMBER OF NODES IN THE MESH.
C NELNOD : INTEGER
C SIZE OF INDICES STORED IN FNODL AND FLNOD AT FIRST ENTRY.
C MAXNEL : INTEGER
C SIZE OF FLNOD, WHERE MAXNEL .GE. NELS+NELNOD.
C MARK : INTEGER
C STAGE COUNTER, FACILITATES MARKING NODES.
C MAXMRK : INTEGER
C A LARGEST POSSIBLE INTEGER, HOWEVER,
C MAXMRK .GT. MAX(NELS,NNODS) IS ENOUGH.
C
C UPDATED PARAMETERS
C ------------------
C
C NUMELM : INTEGER
C NUMBER OF ACTIVE NEW GENERATED ELEMENTS AT THIS STAGE.
C NXTUSE : INTEGER
C THE NEXT FREE LOCATION OF FLNOD.
C ON THE FIRST ENTRY, IT MUST BE SET TO NELNOD+NELS+1.
C UPDATED BY THE ROUTINE TO ALWAYS POINT TO THE FIRST
C FREE LOCATION IN FLNOD.
C NCOMPR : INTEGER
C UPDATED WITH THE NUMBER OF WORKSPACE COMPRESSIONS NEEDED
C IN THIS GRAPH UPDATE.
C XFNODL : INTEGER(NNODS)
C POINTER INTO THE GENERATED ELEMENTS FOR EACH NODE.
C ABSORBED AND ELIMINATED NODES HAVE XFNODL(I)=0.
C ON EXIT FOR AN ELIMINATED NODE I, XFNODL(I)=0.
C FNODL : INTEGER(NELNOD+NNODS)
C THE LIST OF GENERATED ELEMENTS FOR EACH NODE HEADED BY
C THE LENGTH OF THE LIST.
C ON EXIT REFERENCE TO ABSORBED ELEMENTS IS REMOVED.
C XFLNOD : INTEGER(NELS)
C POINTER INTO THE LIST OF NODES FOR EACH ELEMENT.
C IF AN ELEMENT I IS ABSORBED, THEN XFLNOD(I)=0.
C FLNOD : INTEGER(MAXNEL)
C THE NODES IN A GENERATED ELEMENT HEADED BY THE LENGTH
C OF THE LIST.
C HEAD : INTEGER(NNODS)
C HEAD OF DEGREE LIST.
C PERM : INTEGER(NNODS)
C PREVIOUS NODE.
C INVP : INTEGER(NNODS)
C NEXT NODE.
C QSIZE : INTEGER(NNODS)
C SIZE OF THE SUPERNODES.
C ELMLNK : INTEGER(NELS)
C LIST OF GENERATED ELEMENTS WHERE SOME NODES NEED
C DEGREE UPDATE.
C MARKER : INTEGER(NNODS)
C MARKER VECTOR FOR EFFICIENT MASK OF TOUCHED NODES.
C
C ON EXIT
C -------
C
C NO PURE EXIT PARAMETERS.
C
C WORKING ARRAYS
C --------------
C
C STOREL : INTEGER(NNODS)
C TEMPORARY STORAGE OF THE NODES BELONGING TO THE NEW
C GENERATED ELEMENT.
C
C SUBPROGRAMS
C -----------
C
C SPRMM5
C
C FUNCTIONS
C ---------
C
C NONE
C
C INTRINSIC
C ---------
C
C NONE
C
C INCLUDE BLOCKS
C --------------
C
C NONE
C
C COMMON BLOCKS
C -------------
C
C NONE
C
C ------------------------------------------------------------------
INTEGER COUNT , ELEMNT, ELMSZE, FSTELM, GEFREE, I ,
$ IP , IPFSTL, ISTRT , ISTOP , J , JSTRT ,
$ JSTOP , MFLNOD, NEXT , PREV , RCHLOC, RCHNOD,
$ RCHSZE
EXTERNAL SPRMM5
C ------------------------------------------------------------------
C COUNT COUNTS THE NUMBER OF GENERATED ELEMENTS CONNECTED TO A NODE.
C ELEMNT ELEMENT INDEX.
C FSTELM THE FIRST ELEMENT IN THE LIST OF GENERATED ELEMENTS FOR
C NODE. USED AS REPRESENTATIVE FOR THE NEW ELEMENT.
C FSTIP FIRST POSITION IN FLNOD FOR AN ELEMENT WHEN LIST IS COM-
C PRESSED.
C GEFREE STORES THE SIZE OF FREE SPACE AT THE END OF FLNOD.
C IP USED AS ARRAY POINTER.
C I, J ARE LOOP COUNTERS
C ISTRT, ISTOP ARE ARRAY/LIST BOUNDS FOR LOOP INDEX I.
C JSTRT, JSTOP ARE ARRAY/LIST BOUNDS FOR LOOP INDEX J.
C MFLNOD IN CALLS TO SPRMM5, LAST LOCATION OF FLNOD IN USE.
C NEXT NEXT NODE IN DEGREE LIST.
C PREV PREVIOUS NODE IN THE DEGREE LIST.
C RCHLOC POINTER INTO THE GENERATED ELEMENT.
C RCHNOD NODE IN THE NEW GENERATED ELEMENT.
C RCHSZE SIZE OF THE NEW GENERATED ELEMENT.
C ------------------------------------------------------------------
C ==================================================================
C ---------------------------------------------------
C FETCH THE GENERATED ELEMENT AND STORE IT IN STOREL.
C ---------------------------------------------------