!!$ !!$ Parallel Sparse BLAS version 2.2 !!$ (C) Copyright 2006/2007/2008 !!$ Salvatore Filippone University of Rome Tor Vergata !!$ Alfredo Buttari University of Rome Tor Vergata !!$ !!$ Redistribution and use in source and binary forms, with or without !!$ modification, are permitted provided that the following conditions !!$ are met: !!$ 1. Redistributions of source code must retain the above copyright !!$ notice, this list of conditions and the following disclaimer. !!$ 2. Redistributions in binary form must reproduce the above copyright !!$ notice, this list of conditions, and the following disclaimer in the !!$ documentation and/or other materials provided with the distribution. !!$ 3. 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Author: Gibbs-Poole-Stockmeyer (revised by Stefano Toninel) ! ! Routines for Gibbs-Poole-Stockmeyer matrix bandwidth and profile reduction. ! Originally released in ACM-TOMS no. 508 written in Fortran77. ! Now revised and ported to Fortran90. ! Further revised and ported into the PSBLAS environment. ! module psb_gps_mod use psb_realloc_mod ! public psb_gps_reduce ! ! COMMON /GRA/ N, IDPTH, IDEG ! private ! common /CC/ XCC,SIZEG,STPT INTEGER, save :: xcc,n,idpth,ideg INTEGER,allocatable,SAVE ::SIZEG(:),STPT(:) ! ! COMMON /LVLW/ NHIGH,NLOW,NACUM INTEGER,allocatable,target,save :: NHIGH(:),NLOW(:),NACUM(:),AUX(:) INTEGER,PARAMETER :: INIT=500 ! CONTAINS ! SUBROUTINE psb_gps_reduce(NDSTK, NR, IOLD, RENUM, NDEG, LVL, LVLS1, LVLS2,& & CCSTOR, IBW2, IPF2,NE,IDPTHE,IDEGE) ! SUBROUTINE REDUCE DETERMINES A ROW AND COLUMN PERMUTATION WHICH, ! WHEN APPLIED TO A GIVEN SPARSE MATRIX, PRODUCES A PERMUTED ! MATRIX WITH A SMALLER BANDWIDTH AND PROFILE. ! THE INPUT ARRAY IS A CONNECTION TABLE WHICH REPRESENTS THE ! INDICES OF THE NONZERO ELEMENTS OF THE MATRIX, A. THE ALGO- ! RITHM IS DESCRIBED IN TERMS OF THE ADJACENCY GRAPH WHICH ! HAS THE CHARACTERISTIC THAT THERE IS AN EDGE (CONNECTION) ! BETWEEN NODES I AND J IF A(I,J) /= 0 AND I /= J. ! DIMENSIONING INFORMATION--THE FOLLOWING INTEGER ARRAYS MUST BE ! DIMENSIONED IN THE CALLING ROUTINE. ! NDSTK(NR,D1) D1 IS >= MAXIMUM DEGREE OF ALL NODES. ! IOLD(D2) D2 AND NR ARE >= THE TOTAL NUMBER OF ! RENUM(D2+1) NODES IN THE GRAPH. ! NDEG(D2) STORAGE REQUIREMENTS CAN BE SIGNIFICANTLY ! LVL(D2) DECREASED FOR IBM 360 AND 370 COMPUTERS ! LVLS1(D2) BY REPLACING INTEGER NDSTK BY ! LVLS2(D2) INTEGER*2 NDSTK IN SUBROUTINES REDUCE, ! CCSTOR(D2) DGREE, FNDIAM, TREE AND NUMBER. ! COMMON INFORMATION--THE FOLLOWING COMMON BLOCK MUST BE IN THE ! CALLING ROUTINE. ! COMMON/GRA/N,IDPTH,IDEG ! EXPLANATION OF INPUT VARIABLES-- ! NDSTK- CONNECTION TABLE REPRESENTING GRAPH. ! NDSTK(I,J)=NODE NUMBER OF JTH CONNECTION TO NODE ! NUMBER I. A CONNECTION OF A NODE TO ITSELF IS NOT ! LISTED. EXTRA POSITIONS MUST HAVE ZERO FILL. ! NR- ROW DIMENSION ASSIGNED NDSTK IN CALLING PROGRAM. ! IOLD(I)- NUMBERING OF ITH NODE UPON INPUT. ! IF NO NUMBERING EXISTS THEN IOLD(I)=I. ! N- NUMBER OF NODES IN GRAPH (EQUAL TO ORDER OF MATRIX). ! IDEG- MAXIMUM DEGREE OF ANY NODE IN THE GRAPH. ! EXPLANATION OF OUTPUT VARIABLES-- ! RENUM(I)- THE NEW NUMBER FOR THE ITH NODE. ! NDEG(I)- THE DEGREE OF THE ITH NODE. ! IBW2- THE BANDWIDTH AFTER RENUMBERING. ! IPF2- THE PROFILE AFTER RENUMBERING. ! IDPTH- NUMBER OF LEVELS IN REDUCE LEVEL STRUCTURE. ! THE FOLLOWING ONLY HAVE MEANING IF THE GRAPH WAS CONNECTED-- ! LVL(I)- INDEX INTO LVLS1 TO THE FIRST NODE IN LEVEL I. ! LVL(I+1)-LVL(I)= NUMBER OF NODES IN ITH LEVEL ! LVLS1- NODE NUMBERS LISTED BY LEVEL. ! LVLS2(I)- THE LEVEL ASSIGNED TO NODE I BY REDUCE. ! WORKING STORAGE VARIABLE-- ! CCSTOR ! LOCAL STORAGE-- ! COMMON/CC/-SUBROUTINES REDUCE, SORT2 AND PIKLVL ASSUME THAT ! THE GRAPH HAS AT MOST 50 CONNECTED COMPONENTS. ! SUBROUTINE FNDIAM ASSUMES THAT THERE ARE AT MOST ! 100 NODES IN THE LAST LEVEL. ! COMMON/LVLW/-SUBROUTINES SETUP AND PIKLVL ASSUME THAT THERE ! ARE AT MOST 100 LEVELS. ! USE INTEGER*2 NDSTK WITH AN IBM 360 OR 370. INTEGER NDSTK INTEGER STNODE, RVNODE, RENUM, STNUM, CCSTOR, SBNUM ! COMMON /GRA/ N, IDPTH, IDEG ! IT IS ASSUMED THAT THE GRAPH HAS AT MOST 50 CONNECTED COMPONENTS. ! COMMON /CC/ XCC, SIZEG(50), STPT(50) ! COMMON /LVLW/ NHIGH(100), NLOW(100), NACUM(100) DIMENSION CCSTOR(1), IOLD(NE) DIMENSION NDSTK(NR,IDEGE), LVL(NE), LVLS1(1), LVLS2(1), RENUM(NE+1), NDEG(NE) n = ne ideg = idege idpth = 0 ALLOCATE(SIZEG(NR),STPT(NR), STAT=INFO) IF(INFO /= psb_success_) THEN WRITE(*,*) 'ERROR! MEMORY ALLOCATION # 1 FAILED IN GPS' STOP END IF ! ALLOCATE(NHIGH(INIT), NLOW(INIT), NACUM(INIT), AUX(INIT), STAT=INFO) IF(INFO /= psb_success_) THEN WRITE(*,*) 'ERROR! MEMORY ALLOCATION # 2 FAILED IN GPS' STOP END IF ! IBW2 = 0 IPF2 = 0 ! SET RENUM(I)=0 FOR ALL I TO INDICATE NODE I IS UNNUMBERED DO I=1,N RENUM(I) = 0 END DO ! COMPUTE DEGREE OF EACH NODE AND ORIGINAL BANDWIDTH AND PROFILE CALL DGREE(NDSTK, NR, NDEG, IOLD, IBW1, IPF1) ! SBNUM= LOW END OF AVAILABLE NUMBERS FOR RENUMBERING ! STNUM= HIGH END OF AVAILABLE NUMBERS FOR RENUMBERING SBNUM = 1 STNUM = N ! NUMBER THE NODES OF DEGREE ZERO DO I=1,N IF (NDEG(I) > 0) CYCLE RENUM(I) = STNUM STNUM = STNUM - 1 END DO ! FIND AN UNNUMBERED NODE OF MIN DEGREE TO START ON do LOWDG = IDEG + 1 NFLG = 1 ISDIR = 1 DO I=1,N IF (NDEG(I) >= LOWDG) CYCLE IF (RENUM(I) > 0) CYCLE LOWDG = NDEG(I) STNODE = I END DO ! FIND PSEUDO-DIAMETER AND ASSOCIATED LEVEL STRUCTURES. ! STNODE AND RVNODE ARE THE ENDS OF THE DIAM AND LVLS1 AND LVLS2 ! ARE THE RESPECTIVE LEVEL STRUCTURES. CALL FNDIAM(STNODE, RVNODE, NDSTK, NR, NDEG, LVL, LVLS1,LVLS2, CCSTOR, IDFLT) IF (.not.(ndeg(stnode) <= ndeg(rvnode))) then ! NFLG INDICATES THE END TO BEGIN NUMBERING ON NFLG = -1 STNODE = RVNODE endif CALL SETUP(LVL, LVLS1, LVLS2) ! FIND ALL THE CONNECTED COMPONENTS (XCC COUNTS THEM) XCC = 0 LROOT = 1 LVLN = 1 DO I=1,N IF (LVL(I) /= 0) CYCLE XCC = XCC + 1 STPT(XCC) = LROOT CALL TREE(I, NDSTK, NR, LVL, CCSTOR, NDEG, LVLWTH, LVLBOT,LVLN, MAXLW, N) SIZEG(XCC) = LVLBOT + LVLWTH - LROOT LROOT = LVLBOT + LVLWTH LVLN = LROOT END DO if (sort2() /= 0) then CALL PIKLVL(LVLS1, LVLS2, CCSTOR, IDFLT, ISDIR) endif ! ON RETURN FROM PIKLVL, ISDIR INDICATES THE DIRECTION THE LARGEST ! COMPONENT FELL. ISDIR IS MODIFIED NOW TO INDICATE THE NUMBERING ! DIRECTION. NUM IS SET TO THE PROPER VALUE FOR THIS DIRECTION. ISDIR = ISDIR*NFLG NUM = SBNUM IF (ISDIR < 0) NUM = STNUM CALL NUMBER(STNODE, NUM, NDSTK, LVLS2, NDEG, RENUM, LVLS1,LVL,& & NR, NFLG, IBW2, IPF2, CCSTOR, ISDIR) ! UPDATE STNUM OR SBNUM AFTER NUMBERING IF (ISDIR < 0) STNUM = NUM IF (ISDIR > 0) SBNUM = NUM IF (.not.(sbnum <= stnum)) exit end do IF (IBW2 > IBW1) then ! IF ORIGINAL NUMBERING IS BETTER THAN NEW ONE, SET UP TO RETURN IT DO I=1,N RENUM(I) = IOLD(I) END DO IBW2 = IBW1 IPF2 = IPF1 ! endif DEALLOCATE(SIZEG,STPT,NHIGH,NLOW,AUX,NACUM) idpthe = idpth RETURN END SUBROUTINE PSB_GPS_REDUCE ! SUBROUTINE DGREE(NDSTK, NR, NDEG, IOLD, IBW1, IPF1) ! DGREE COMPUTES THE DEGREE OF EACH NODE IN NDSTK AND STORES ! IT IN THE ARRAY NDEG. THE BANDWIDTH AND PROFILE FOR THE ORIGINAL ! OR INPUT RENUMBERING OF THE GRAPH IS COMPUTED ALSO. ! USE INTEGER*2 NDSTK WITH AN IBM 360 OR 370. INTEGER NDSTK ! COMMON /GRA/ N, IDPTH, IDEG DIMENSION NDSTK(NR,IDEG), NDEG(N), IOLD(N) IBW1 = 0 IPF1 = 0 DO I=1,N NDEG(I) = 0 IRW = 0 DO J=1,IDEG ITST = NDSTK(I,J) IF(ITST <= 0) EXIT NDEG(I) = NDEG(I) + 1 IDIF = IOLD(I) - IOLD(ITST) IF (IRW < IDIF) IRW = IDIF END DO IPF1 = IPF1 + IRW IF (IRW > IBW1) IBW1 = IRW END DO RETURN END SUBROUTINE DGREE ! SUBROUTINE FNDIAM(SND1, SND2, NDSTK, NR, NDEG, LVL, LVLS1,LVLS2, IWK, IDFLT) ! FNDIAM IS THE CONTROL PROCEDURE FOR FINDING THE PSEUDO-DIAMETER OF ! NDSTK AS WELL AS THE LEVEL STRUCTURE FROM EACH END ! SND1- ON INPUT THIS IS THE NODE NUMBER OF THE FIRST ! ATTEMPT AT FINDING A DIAMETER. ON OUTPUT IT ! CONTAINS THE ACTUAL NUMBER USED. ! SND2- ON OUTPUT CONTAINS OTHER END OF DIAMETER ! LVLS1- ARRAY CONTAINING LEVEL STRUCTURE WITH SND1 AS ROOT ! LVLS2- ARRAY CONTAINING LEVEL STRUCTURE WITH SND2 AS ROOT ! IDFLT- FLAG USED IN PICKING FINAL LEVEL STRUCTURE, SET ! =1 IF WIDTH OF LVLS1 <= WIDTH OF LVLS2, OTHERWISE =2 ! LVL,IWK- WORKING STORAGE ! USE INTEGER*2 NDSTK WITH AN IBM 360 OR 370. INTEGER NDSTK INTEGER FLAG, SND, SND1, SND2 ! COMMON /GRA/ N, IDPTH, IDEG ! IT IS ASSUMED THAT THE LAST LEVEL HAS AT MOST 100 NODES. ! COMMON /CC/ NDLST(100) INTEGER,POINTER :: NDLST(:) DIMENSION NDSTK(NR,IDEG), NDEG(1), LVL(N), LVLS1(N), LVLS2(N),IWK(N) ! NDLST => AUX ! FLAG = 0 MTW2 = N SND = SND1 ! ZERO LVL TO INDICATE ALL NODES ARE AVAILABLE TO TREE 10 DO 20 I=1,N LVL(I) = 0 20 END DO LVLN = 1 ! DROP A TREE FROM SND CALL TREE(SND, NDSTK, NR, LVL, IWK, NDEG, LVLWTH, LVLBOT,LVLN, MAXLW, MTW2) IF (FLAG >= 1) GO TO 50 FLAG = 1 30 IDPTH = LVLN - 1 MTW1 = MAXLW ! COPY LEVEL STRUCTURE INTO LVLS1 DO 40 I=1,N LVLS1(I) = LVL(I) 40 END DO NDXN = 1 NDXL = 0 MTW2 = N ! SORT LAST LEVEL BY DEGREE AND STORE IN NDLST CALL SORTDG(NDLST, IWK(LVLBOT), NDXL, LVLWTH, NDEG) SND = NDLST(1) GO TO 10 50 IF (IDPTH >= LVLN-1) GO TO 60 ! START AGAIN WITH NEW STARTING NODE SND1 = SND GO TO 30 60 IF (MAXLW >= MTW2) GO TO 80 MTW2 = MAXLW SND2 = SND ! STORE NARROWEST REVERSE LEVEL STRUCTURE IN LVLS2 DO 70 I=1,N LVLS2(I) = LVL(I) 70 END DO 80 IF (NDXN == NDXL) GO TO 90 ! TRY NEXT NODE IN NDLST NDXN = NDXN + 1 SND = NDLST(NDXN) GO TO 10 90 IDFLT = 1 IF (MTW2 <= MTW1) IDFLT = 2 NULLIFY(NDLST) RETURN END SUBROUTINE FNDIAM ! SUBROUTINE TREE(IROOT, NDSTK, NR, LVL, IWK, NDEG, LVLWTH, LVLBOT, LVLN, MAXLW, IBORT) ! TREE DROPS A TREE IN NDSTK FROM IROOT ! LVL- ARRAY INDICATING AVAILABLE NODES IN NDSTK WITH ZERO ! ENTRIES. TREE ENTERS LEVEL NUMBERS ASSIGNED ! DURING EXECUTION OF THIS PROCEDURE ! IWK- ON OUTPUT CONTAINS NODE NUMBERS USED IN TREE ! ARRANGED BY LEVELS (IWK(LVLN) CONTAINS IROOT ! AND IWK(LVLBOT+LVLWTH-1) CONTAINS LAST NODE ENTERED) ! LVLWTH- ON OUTPUT CONTAINS WIDTH OF LAST LEVEL ! LVLBOT- ON OUTPUT CONTAINS INDEX INTO IWK OF FIRST ! NODE IN LAST LEVEL ! MAXLW- ON OUTPUT CONTAINS THE MAXIMUM LEVEL WIDTH ! LVLN- ON INPUT THE FIRST AVAILABLE LOCATION IN IWK ! USUALLY ONE BUT IF IWK IS USED TO STORE PREVIOUS ! CONNECTED COMPONENTS, LVLN IS NEXT AVAILABLE LOCATION. ! ON OUTPUT THE TOTAL NUMBER OF LEVELS + 1 ! IBORT- INPUT PARAM WHICH TRIGGERS EARLY RETURN IF ! MAXLW BECOMES >= IBORT ! USE INTEGER*2 NDSTK WITH AN IBM 360 OR 370. INTEGER NDSTK DIMENSION NDSTK(NR,IDEG), LVL(N), IWK(N), NDEG(N) MAXLW = 0 ITOP = LVLN INOW = LVLN LVLBOT = LVLN LVLTOP = LVLN + 1 LVLN = 1 LVL(IROOT) = 1 IWK(ITOP) = IROOT 10 LVLN = LVLN + 1 20 IWKNOW = IWK(INOW) NDROW = NDEG(IWKNOW) DO 30 J=1,NDROW ITEST = NDSTK(IWKNOW,J) IF (LVL(ITEST) /= 0) CYCLE LVL(ITEST) = LVLN ITOP = ITOP + 1 IWK(ITOP) = ITEST 30 END DO INOW = INOW + 1 IF (INOW < LVLTOP) GO TO 20 LVLWTH = LVLTOP - LVLBOT IF (MAXLW < LVLWTH) MAXLW = LVLWTH IF (MAXLW >= IBORT) RETURN IF (ITOP < LVLTOP) RETURN LVLBOT = INOW LVLTOP = ITOP + 1 GO TO 10 END SUBROUTINE TREE ! SUBROUTINE SORTDG(STK1, STK2, X1, X2, NDEG) ! SORTDG SORTS STK2 BY DEGREE OF THE NODE AND ADDS IT TO THE END ! OF STK1 IN ORDER OF LOWEST TO HIGHEST DEGREE. X1 AND X2 ARE THE ! NUMBER OF NODES IN STK1 AND STK2 RESPECTIVELY. INTEGER X1, X2, STK1, STK2, TEMP ! COMMON /GRA/ N, IDPTH, IDEG DIMENSION NDEG(N), STK1(X1+X2), STK2(X2) IND = X2 10 ITEST = 0 IND = IND - 1 IF (IND < 1) GO TO 30 DO 20 I=1,IND J = I + 1 ISTK2 = STK2(I) JSTK2 = STK2(J) IF (NDEG(ISTK2) <= NDEG(JSTK2)) CYCLE ITEST = 1 TEMP = STK2(I) STK2(I) = STK2(J) STK2(J) = TEMP 20 END DO IF (ITEST == 1) GO TO 10 30 DO 40 I=1,X2 X1 = X1 + 1 STK1(X1) = STK2(I) 40 END DO RETURN END SUBROUTINE SORTDG ! SUBROUTINE SETUP(LVL, LVLS1, LVLS2) ! SETUP COMPUTES THE REVERSE LEVELING INFO FROM LVLS2 AND STORES ! IT INTO LVLS2. NACUM(I) IS INITIALIZED TO NODES/ITH LEVEL FOR NODES ! ON THE PSEUDO-DIAMETER OF THE GRAPH. LVL IS INITIALIZED TO NON- ! ZERO FOR NODES ON THE PSEUDO-DIAM AND NODES IN A DIFFERENT ! COMPONENT OF THE GRAPH. ! COMMON /GRA/ N, IDPTH, IDEG ! IT IS ASSUMED THAT THERE ARE AT MOST 100 LEVELS. ! COMMON /LVLW/ NHIGH(100), NLOW(100), NACUM(100) DIMENSION LVL(N), LVLS1(N), LVLS2(N) INTEGER :: SZ !----------------------------------------------------- SZ=SIZE(NACUM) IF(SZ < IDPTH) THEN WRITE(*,*) 'GPS_SETUP: on fly reallocation of NACUM' CALL REALLOC(NACUM,SZ,IDPTH) END IF !----------------------------------------------------- DO 10 I=1,IDPTH NACUM(I) = 0 10 END DO DO 30 I=1,N LVL(I) = 1 LVLS2(I) = IDPTH + 1 - LVLS2(I) ITEMP = LVLS2(I) IF (ITEMP > IDPTH) CYCLE IF (ITEMP /= LVLS1(I)) GO TO 20 NACUM(ITEMP) = NACUM(ITEMP) + 1 CYCLE 20 LVL(I) = 0 30 END DO RETURN END SUBROUTINE SETUP ! INTEGER FUNCTION SORT2() ! SORT2 SORTS SIZEG AND STPT INTO DESCENDING ORDER ACCORDING TO ! VALUES OF SIZEG. XCC=NUMBER OF ENTRIES IN EACH ARRAY INTEGER TEMP ! IT IS ASSUMED THAT THE GRAPH HAS AT MOST 50 CONNECTED COMPONENTS. !COMMON /CC/ XCC, SIZEG(50), STPT(50) SORT2 = 0 IF (XCC == 0) RETURN SORT2 = 1 IND = XCC 10 ITEST = 0 IND = IND - 1 IF (IND < 1) RETURN DO 20 I=1,IND J = I + 1 IF (SIZEG(I) >= SIZEG(J)) CYCLE ITEST = 1 TEMP = SIZEG(I) SIZEG(I) = SIZEG(J) SIZEG(J) = TEMP TEMP = STPT(I) STPT(I) = STPT(J) STPT(J) = TEMP 20 END DO IF (ITEST == 1) GO TO 10 RETURN END FUNCTION SORT2 ! SUBROUTINE PIKLVL(LVLS1, LVLS2, CCSTOR, IDFLT, ISDIR) ! PIKLVL CHOOSES THE LEVEL STRUCTURE USED IN NUMBERING GRAPH ! LVLS1- ON INPUT CONTAINS FORWARD LEVELING INFO ! LVLS2- ON INPUT CONTAINS REVERSE LEVELING INFO ! ON OUTPUT THE FINAL LEVEL STRUCTURE CHOSEN ! CCSTOR- ON INPUT CONTAINS CONNECTED COMPONENT INFO ! IDFLT- ON INPUT =1 IF WDTH LVLS1 <= WDTH LVLS2, =2 OTHERWISE ! NHIGH KEEPS TRACK OF LEVEL WIDTHS FOR HIGH NUMBERING ! NLOW- KEEPS TRACK OF LEVEL WIDTHS FOR LOW NUMBERING ! NACUM- KEEPS TRACK OF LEVEL WIDTHS FOR CHOSEN LEVEL STRUCTURE ! XCC- NUMBER OF CONNECTED COMPONENTS ! SIZEG(I)- SIZE OF ITH CONNECTED COMPONENT ! STPT(I)- INDEX INTO CCSTORE OF 1ST NODE IN ITH CON COMPT ! ISDIR- FLAG WHICH INDICATES WHICH WAY THE LARGEST CONNECTED ! COMPONENT FELL. =+1 IF LOW AND -1 IF HIGH INTEGER CCSTOR, ENDC ! COMMON /GRA/ N, IDPTH, IDEG ! IT IS ASSUMED THAT THE GRAPH HAS AT MOST 50 COMPONENTS AND ! THAT THERE ARE AT MOST 100 LEVELS. ! COMMON /LVLW/ NHIGH(100), NLOW(100), NACUM(100) ! COMMON /CC/ XCC, SIZEG(50), STPT(50) DIMENSION LVLS1(N), LVLS2(N), CCSTOR(N) INTEGER :: SZ ! FOR EACH CONNECTED COMPONENT DO DO 80 I=1,XCC J = STPT(I) ENDC= SIZEG(I) + J - 1 ! SET NHIGH AND NLOW EQUAL TO NACUM !----------------------------------------------------- SZ=SIZE(NHIGH) IF(SZ < IDPTH) THEN WRITE(*,*) 'GPS_PIKLVL: on fly reallocation of NHIGH' CALL REALLOC(NHIGH,SZ,IDPTH) END IF SZ=SIZE(NLOW) IF(SZ < IDPTH) THEN WRITE(*,*) 'GPS_PIKLVL: on fly reallocation of NLOW' CALL REALLOC(NLOW,SZ,IDPTH) END IF !----------------------------------------------------- DO 10 K=1,IDPTH NHIGH(K) = NACUM(K) NLOW(K) = NACUM(K) 10 END DO ! UPDATE NHIGH AND NLOW FOR EACH NODE IN CONNECTED COMPONENT DO 20 K=J,ENDC INODE = CCSTOR(K) LVLNH = LVLS1(INODE) NHIGH(LVLNH) = NHIGH(LVLNH) + 1 LVLNL = LVLS2(INODE) NLOW(LVLNL) = NLOW(LVLNL) + 1 20 END DO MAX1 = 0 MAX2 = 0 ! SET MAX1=LARGEST NEW NUMBER IN NHIGH ! SET MAX2=LARGEST NEW NUMBER IN NLOW DO 30 K=1,IDPTH IF (2*NACUM(K) == NLOW(K)+NHIGH(K)) CYCLE IF (NHIGH(K) > MAX1) MAX1 = NHIGH(K) IF (NLOW(K) > MAX2) MAX2 = NLOW(K) 30 END DO ! SET IT= NUMBER OF LEVEL STRUCTURE TO BE USED IT = 1 IF (MAX1 > MAX2) IT = 2 IF (MAX1 == MAX2) IT = IDFLT IF (IT == 2) GO TO 60 IF (I == 1) ISDIR = -1 ! COPY LVLS1 INTO LVLS2 FOR EACH NODE IN CONNECTED COMPONENT DO 40 K=J,ENDC INODE = CCSTOR(K) LVLS2(INODE) = LVLS1(INODE) 40 END DO ! UPDATE NACUM TO BE THE SAME AS NHIGH DO 50 K=1,IDPTH NACUM(K) = NHIGH(K) 50 END DO CYCLE ! UPDATE NACUM TO BE THE SAME AS NLOW 60 DO 70 K=1,IDPTH NACUM(K) = NLOW(K) 70 END DO 80 END DO RETURN END SUBROUTINE PIKLVL ! SUBROUTINE NUMBER(SND, NUM, NDSTK, LVLS2, NDEG, RENUM, LVLST,LSTPT,& & NR, NFLG, IBW2, IPF2, IPFA, ISDIR) ! NUMBER PRODUCES THE NUMBERING OF THE GRAPH FOR MIN BANDWIDTH ! SND- ON INPUT THE NODE TO BEGIN NUMBERING ON ! NUM- ON INPUT AND OUTPUT, THE NEXT AVAILABLE NUMBER ! LVLS2- THE LEVEL STRUCTURE TO BE USED IN NUMBERING ! RENUM- THE ARRAY USED TO STORE THE NEW NUMBERING ! LVLST- ON OUTPUT CONTAINS LEVEL STRUCTURE ! LSTPT(I)- ON OUTPUT, INDEX INTO LVLST TO FIRST NODE IN ITH LVL ! LSTPT(I+1) - LSTPT(I) = NUMBER OF NODES IN ITH LVL ! NFLG- =+1 IF SND IS FORWARD END OF PSEUDO-DIAM ! =-1 IF SND IS REVERSE END OF PSEUDO-DIAM ! IBW2- BANDWIDTH OF NEW NUMBERING COMPUTED BY NUMBER ! IPF2- PROFILE OF NEW NUMBERING COMPUTED BY NUMBER ! IPFA- WORKING STORAGE USED TO COMPUTE PROFILE AND BANDWIDTH ! ISDIR- INDICATES STEP DIRECTION USED IN NUMBERING(+1 OR -1) ! USE INTEGER*2 NDSTK WITH AN IBM 360 OR 370. INTEGER NDSTK INTEGER SND, XA, XB, XC, XD, CX, ENDC,RENUM, TEST ! COMMON /GRA/ N, IDPTH, IDEG ! THE STORAGE IN COMMON BLOCKS CC AND LVLW IS NOW FREE AND CAN ! BE USED FOR STACKS. !COMMON /LVLW/ STKA(100), STKB(100), STKC(100) !COMMON /CC/ STKD(100) DIMENSION IPFA(N) DIMENSION NDSTK(NR,IDEG), LVLS2(N), NDEG(N), RENUM(N+1), LVLST(N),LSTPT(N) INTEGER,POINTER :: STKA(:),STKB(:),STKC(:),STKD(:) INTEGER :: SZ1,SZ2 ! STKA => NHIGH STKB => NLOW STKC => NACUM STKD => AUX ! ! SET UP LVLST AND LSTPT FROM LVLS2 DO 10 I=1,N IPFA(I) = 0 10 END DO NSTPT = 1 DO 30 I=1,IDPTH LSTPT(I) = NSTPT DO 20 J=1,N IF (LVLS2(J) /= I) CYCLE LVLST(NSTPT) = J NSTPT = NSTPT + 1 20 END DO 30 END DO LSTPT(IDPTH+1) = NSTPT ! STKA, STKB, STKC AND STKD ARE STACKS WITH POINTERS ! XA,XB,XC, AND XD. CX IS A SPECIAL POINTER INTO STKC WHICH ! INDICATES THE PARTICULAR NODE BEING PROCESSED. ! LVLN KEEPS TRACK OF THE LEVEL WE ARE WORKING AT. ! INITIALLY STKC CONTAINS ONLY THE INITIAL NODE, SND. LVLN = 0 IF (NFLG < 0) LVLN = IDPTH + 1 XC = 1 STKC(XC) = SND 40 CX = 1 XD = 0 LVLN = LVLN + NFLG LST = LSTPT(LVLN) LND = LSTPT(LVLN+1) - 1 ! BEGIN PROCESSING NODE STKC(CX) 50 IPRO = STKC(CX) RENUM(IPRO) = NUM NUM = NUM + ISDIR ENDC = NDEG(IPRO) XA = 0 XB = 0 ! CHECK ALL ADJACENT NODES DO 80 I=1,ENDC TEST = NDSTK(IPRO,I) INX = RENUM(TEST) ! ONLY NODES NOT NUMBERED OR ALREADY ON A STACK ARE ADDED IF (INX == 0) GO TO 60 IF (INX < 0) CYCLE ! DO PRELIMINARY BANDWIDTH AND PROFILE CALCULATIONS NBW = (RENUM(IPRO)-INX)*ISDIR IF (ISDIR > 0) INX = RENUM(IPRO) IF (IPFA(INX) < NBW) IPFA(INX) = NBW CYCLE 60 RENUM(TEST) = -1 ! PUT NODES ON SAME LEVEL ON STKA, ALL OTHERS ON STKB IF (LVLS2(TEST) == LVLS2(IPRO)) GO TO 70 XB = XB + 1 STKB(XB) = TEST CYCLE 70 XA = XA + 1 STKA(XA) = TEST 80 END DO ! SORT STKA AND STKB INTO INCREASING DEGREE AND ADD STKA TO STKC ! AND STKB TO STKD IF (XA == 0) GO TO 100 IF (XA == 1) GO TO 90 !----------------------------------------------------------------- SZ1=SIZE(STKC) SZ2=XC+XA IF(SZ1 < SZ2) THEN WRITE(*,*) 'GPS_NUMBER - Check #1: on fly reallocation of STKC' CALL REALLOC(NACUM,SZ1,SZ2) STKC => NACUM END IF !----------------------------------------------------------------- CALL SORTDG(STKC, STKA, XC, XA, NDEG) GO TO 100 90 XC = XC + 1 !----------------------------------------------------------------- SZ1=SIZE(STKC) SZ2=XC IF(SZ1 < SZ2) THEN WRITE(*,*) 'GPS_NUMBER - Check #2: on fly reallocation of STKC' SZ2=SZ2+INIT CALL REALLOC(NACUM,SZ1,SZ2) STKC => NACUM END IF !----------------------------------------------------------------- STKC(XC) = STKA(XA) 100 IF (XB == 0) GO TO 120 IF (XB == 1) GO TO 110 !----------------------------------------------------------------- SZ1=SIZE(STKD) SZ2=XD+XB IF(SZ1 < SZ2) THEN WRITE(*,*) 'GPS_NUMBER - Check #3: on fly reallocation of STKD' CALL REALLOC(AUX,SZ1,SZ2) STKD => AUX END IF !----------------------------------------------------------------- CALL SORTDG(STKD, STKB, XD, XB, NDEG) GO TO 120 110 XD = XD + 1 !----------------------------------------------------------------- SZ1=SIZE(STKD) SZ2=XD IF(SZ1 < SZ2) THEN WRITE(*,*) 'GPS_NUMBER - Check #4: on fly reallocation of STKD' SZ2=SZ2+INIT CALL REALLOC(AUX,SZ1,SZ2) STKD => AUX END IF !----------------------------------------------------------------- STKD(XD) = STKB(XB) ! BE SURE TO PROCESS ALL NODES IN STKC 120 CX = CX + 1 IF (XC >= CX) GO TO 50 ! WHEN STKC IS EXHAUSTED LOOK FOR MIN DEGREE NODE IN SAME LEVEL ! WHICH HAS NOT BEEN PROCESSED MAX = IDEG + 1 SND = N + 1 DO 130 I=LST,LND TEST = LVLST(I) IF (RENUM(TEST) /= 0) CYCLE IF (NDEG(TEST) >= MAX) CYCLE RENUM(SND) = 0 RENUM(TEST) = -1 MAX = NDEG(TEST) SND = TEST 130 END DO IF (SND == N+1) GO TO 140 XC = XC + 1 !----------------------------------------------------------------- SZ1=SIZE(STKC) SZ2=XC IF(SZ1 < SZ2) THEN WRITE(*,*) 'GPS_NUMBER - Check #5: on fly reallocation of STKC' SZ2=SZ2+INIT CALL REALLOC(NACUM,SZ1,SZ2) STKC => NACUM END IF !----------------------------------------------------------------- STKC(XC) = SND GO TO 50 ! IF STKD IS EMPTY WE ARE DONE, OTHERWISE COPY STKD ONTO STKC ! AND BEGIN PROCESSING NEW STKC 140 IF (XD == 0) GO TO 160 !----------------------------------------------------------------- SZ1=SIZE(STKC) SZ2=XD IF(SZ1 < SZ2) THEN WRITE(*,*) 'GPS_NUMBER - Check #6: on fly reallocation of STKC' SZ2=SZ2+INIT CALL REALLOC(NACUM,SZ1,SZ2) STKC => NACUM END IF !----------------------------------------------------------------- DO 150 I=1,XD STKC(I) = STKD(I) 150 END DO XC = XD GO TO 40 ! DO FINAL BANDWIDTH AND PROFILE CALCULATIONS 160 DO 170 I=1,N IF (IPFA(I) > IBW2) IBW2 = IPFA(I) IPF2 = IPF2 + IPFA(I) 170 END DO ! RETURN END SUBROUTINE NUMBER ! ! --------------------------------------------------------- SUBROUTINE REALLOC(VET,SZ1,SZ2) ! PERFORM ON FLY REALLOCATION OF POINTER VET INCREASING ! ITS SIZE FROM SZ1 TO SZ2 IMPLICIT NONE INTEGER,allocatable :: VET(:),TMP(:) INTEGER :: SZ1,SZ2,INFO call psb_realloc(sz2,vet,info) IF(INFO /= psb_success_) THEN WRITE(*,*) 'Error! Memory allocation failure in REALLOC' STOP END IF RETURN END SUBROUTINE REALLOC ! END MODULE psb_gps_mod