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psblas3/base/modules/psb_gps_mod.f90

758 lines
26 KiB
Fortran

!!$
!!$ Parallel Sparse BLAS version 3.0
!!$ (C) Copyright 2010
!!$ Salvatore Filippone University of Rome Tor Vergata
!!$ Alfredo Buttari CNRS-IRIT, Toulouse
!!$
!!$ 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. The name of the PSBLAS group or the names of its contributors may
!!$ not be used to endorse or promote products derived from this
!!$ software without specific written permission.
!!$
!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
!!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
!!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS
!!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
!!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
!!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
!!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
!!$ POSSIBILITY OF SUCH DAMAGE.
!!$
!!$
! 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(psb_out_unit,*) '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(psb_out_unit,*) '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(psb_out_unit,*) '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(psb_out_unit,*) 'GPS_PIKLVL: on fly reallocation of NHIGH'
CALL REALLOC(NHIGH,SZ,IDPTH)
END IF
SZ=SIZE(NLOW)
IF(SZ < IDPTH) THEN
write(psb_out_unit,*) '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(psb_out_unit,*) '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(psb_out_unit,*) '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(psb_out_unit,*) '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(psb_out_unit,*) '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(psb_out_unit,*) '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(psb_out_unit,*) '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(psb_out_unit,*) 'Error! Memory allocation failure in REALLOC'
STOP
END IF
RETURN
END SUBROUTINE REALLOC
!
END MODULE psb_gps_mod