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778 lines
28 KiB
Fortran
778 lines
28 KiB
Fortran
!!$
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!!$ Parallel Sparse BLAS version 3.0
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!!$ (C) Copyright 2006, 2007, 2008, 2009, 2010, 2012
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!!$ Salvatore Filippone University of Rome Tor Vergata
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!!$ Alfredo Buttari CNRS-IRIT, Toulouse
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!!$
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!!$ Redistribution and use in source and binary forms, with or without
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!!$ modification, are permitted provided that the following conditions
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!!$ are met:
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!!$ 1. Redistributions of source code must retain the above copyright
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!!$ notice, this list of conditions and the following disclaimer.
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!!$ 2. Redistributions in binary form must reproduce the above copyright
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!!$ notice, this list of conditions, and the following disclaimer in the
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!!$ documentation and/or other materials provided with the distribution.
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!!$ 3. The name of the PSBLAS group or the names of its contributors may
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!!$ not be used to endorse or promote products derived from this
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!!$ software without specific written permission.
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!!$
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!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
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!!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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!!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS
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!!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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!!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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!!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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!!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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!!$ POSSIBILITY OF SUCH DAMAGE.
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!!$
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!!$
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! Author: Gibbs-Poole-Stockmeyer (revised by Stefano Toninel)
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!
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! Routines for Gibbs-Poole-Stockmeyer matrix bandwidth and profile reduction.
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! Originally released in ACM-TOMS no. 508 written in Fortran77.
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! Now revised and ported to Fortran90.
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! Further revised and ported into the PSBLAS environment.
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!
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module psb_gps_mod
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!
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use psb_base_mod, only : psb_ipk_
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public psb_gps_reduce
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!
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! COMMON /GRA/ N, IDPTH, IDEG
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!
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private
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! common /CC/ XCC,SIZEG,STPT
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integer(psb_ipk_), save :: xcc,n,idpth,ideg
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integer(psb_ipk_),allocatable,SAVE :: SIZEG(:),STPT(:)
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!
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! COMMON /LVLW/ NHIGH,NLOW,NACUM
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integer(psb_ipk_),allocatable,target,save :: NHIGH(:),NLOW(:),NACUM(:),AUX(:)
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integer(psb_ipk_),PARAMETER :: INIT=500
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!
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CONTAINS
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!
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!!$ SUBROUTINE psb_gps_reduce(NDSTK, NR, IOLD, RENUM, NDEG, LVL, LVLS1, LVLS2,&
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!!$ & CCSTOR, IBW2, IPF2,NE,IDPTHE,IDEGE)
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SUBROUTINE psb_gps_reduce(NDSTK, NR, IDEGE, IOLD, RENUM, NDEG,ibw2,ipf2,IDPTHE)
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! SUBROUTINE REDUCE DETERMINES A ROW AND COLUMN PERMUTATION WHICH,
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! WHEN APPLIED TO A GIVEN SPARSE MATRIX, PRODUCES A PERMUTED
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! MATRIX WITH A SMALLER BANDWIDTH AND PROFILE.
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! THE INPUT ARRAY IS A CONNECTION TABLE WHICH REPRESENTS THE
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! INDICES OF THE NONZERO ELEMENTS OF THE MATRIX, A. THE ALGO-
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! RITHM IS DESCRIBED IN TERMS OF THE ADJACENCY GRAPH WHICH
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! HAS THE CHARACTERISTIC THAT THERE IS AN EDGE (CONNECTION)
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! BETWEEN NODES I AND J IF A(I,J) /= 0 AND I /= J.
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! DIMENSIONING INFORMATION--THE FOLLOWING INTEGER ARRAYS MUST BE
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! DIMENSIONED IN THE CALLING ROUTINE.
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! NDSTK(NR,D1) D1 IS >= MAXIMUM DEGREE OF ALL NODES.
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! IOLD(D2) D2 AND NR ARE >= THE TOTAL NUMBER OF
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! RENUM(D2+1) NODES IN THE GRAPH.
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! NDEG(D2) STORAGE REQUIREMENTS CAN BE SIGNIFICANTLY
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! LVL(D2) DECREASED FOR IBM 360 AND 370 COMPUTERS
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! LVLS1(D2) BY REPLACING INTEGER NDSTK BY
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! LVLS2(D2) INTEGER*2 NDSTK IN SUBROUTINES REDUCE,
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! CCSTOR(D2) DGREE, FNDIAM, TREE AND NUMBER.
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! COMMON INFORMATION--THE FOLLOWING COMMON BLOCK MUST BE IN THE
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! CALLING ROUTINE.
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! COMMON/GRA/N,IDPTH,IDEG
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! EXPLANATION OF INPUT VARIABLES--
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! NDSTK- CONNECTION TABLE REPRESENTING GRAPH.
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! NDSTK(I,J)=NODE NUMBER OF JTH CONNECTION TO NODE
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! NUMBER I. A CONNECTION OF A NODE TO ITSELF IS NOT
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! LISTED. EXTRA POSITIONS MUST HAVE ZERO FILL.
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! NR- ROW DIMENSION ASSIGNED NDSTK IN CALLING PROGRAM.
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! IOLD(I)- NUMBERING OF ITH NODE UPON INPUT.
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! IF NO NUMBERING EXISTS THEN IOLD(I)=I.
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! N- NUMBER OF NODES IN GRAPH (EQUAL TO ORDER OF MATRIX).
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! IDEG- MAXIMUM DEGREE OF ANY NODE IN THE GRAPH.
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! EXPLANATION OF OUTPUT VARIABLES--
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! RENUM(I)- THE NEW NUMBER FOR THE ITH NODE.
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! NDEG(I)- THE DEGREE OF THE ITH NODE.
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! IBW2- THE BANDWIDTH AFTER RENUMBERING.
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! IPF2- THE PROFILE AFTER RENUMBERING.
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! IDPTH- NUMBER OF LEVELS IN REDUCE LEVEL STRUCTURE.
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! THE FOLLOWING ONLY HAVE MEANING IF THE GRAPH WAS CONNECTED--
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! LVL(I)- INDEX INTO LVLS1 TO THE FIRST NODE IN LEVEL I.
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! LVL(I+1)-LVL(I)= NUMBER OF NODES IN ITH LEVEL
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! LVLS1- NODE NUMBERS LISTED BY LEVEL.
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! LVLS2(I)- THE LEVEL ASSIGNED TO NODE I BY REDUCE.
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! WORKING STORAGE VARIABLE--
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! CCSTOR
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! LOCAL STORAGE--
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! COMMON/CC/-SUBROUTINES REDUCE, SORT2 AND PIKLVL ASSUME THAT
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! THE GRAPH HAS AT MOST 50 CONNECTED COMPONENTS.
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! SUBROUTINE FNDIAM ASSUMES THAT THERE ARE AT MOST
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! 100 NODES IN THE LAST LEVEL.
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! COMMON/LVLW/-SUBROUTINES SETUP AND PIKLVL ASSUME THAT THERE
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! ARE AT MOST 100 LEVELS.
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! USE INTEGER*2 NDSTK WITH AN IBM 360 OR 370.
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use psb_base_mod
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implicit none
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INTEGER(psb_ipk_) :: NR, IDEGE, IBW2, IPF2, IDPTHE
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! COMMON /GRA/ N, IDPTH, IDEG
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! IT IS ASSUMED THAT THE GRAPH HAS AT MOST 50 CONNECTED COMPONENTS.
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! COMMON /CC/ XCC, SIZEG(50), STPT(50)
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! COMMON /LVLW/ NHIGH(100), NLOW(100), NACUM(100)
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integer(psb_ipk_) :: stnode, rvnode, stnum, sbnum
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integer(psb_ipk_) :: ndstk(nr,idege), iold(nr), renum(nr+1), ndeg(nr)
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integer(psb_ipk_) :: lvl(nr), lvls1(nr), lvls2(nr), ccstor(nr)
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integer(psb_ipk_) :: nflg, info, i, ibw1, ipf1, idflt, isdir, lroot, lowdg
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integer(psb_ipk_) :: lvlbot, lvln, lvlwth, maxlw, num
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n = nr
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ideg = idege
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idpth = 0
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ALLOCATE(SIZEG(NR),STPT(NR), STAT=INFO)
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IF(INFO /= psb_success_) THEN
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write(psb_out_unit,*) 'ERROR! MEMORY ALLOCATION # 1 FAILED IN GPS'
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STOP
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END IF
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!
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ALLOCATE(NHIGH(INIT), NLOW(INIT), NACUM(INIT), AUX(INIT), STAT=INFO)
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IF(INFO /= psb_success_) THEN
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write(psb_out_unit,*) 'ERROR! MEMORY ALLOCATION # 2 FAILED IN GPS'
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STOP
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END IF
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!
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IBW2 = 0
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IPF2 = 0
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! SET RENUM(I)=0 FOR ALL I TO INDICATE NODE I IS UNNUMBERED
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DO I=1,N
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RENUM(I) = 0
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END DO
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! COMPUTE DEGREE OF EACH NODE AND ORIGINAL BANDWIDTH AND PROFILE
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CALL DGREE(NDSTK, NR, NDEG, IOLD, IBW1, IPF1)
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! SBNUM= LOW END OF AVAILABLE NUMBERS FOR RENUMBERING
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! STNUM= HIGH END OF AVAILABLE NUMBERS FOR RENUMBERING
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SBNUM = 1
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STNUM = N
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! NUMBER THE NODES OF DEGREE ZERO
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DO I=1,N
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IF (NDEG(I) > 0) CYCLE
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RENUM(I) = STNUM
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STNUM = STNUM - 1
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END DO
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! FIND AN UNNUMBERED NODE OF MIN DEGREE TO START ON
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do
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LOWDG = IDEG + 1
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NFLG = 1
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ISDIR = 1
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DO I=1,N
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IF (NDEG(I) >= LOWDG) CYCLE
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IF (RENUM(I) > 0) CYCLE
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LOWDG = NDEG(I)
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STNODE = I
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END DO
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! FIND PSEUDO-DIAMETER AND ASSOCIATED LEVEL STRUCTURES.
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! STNODE AND RVNODE ARE THE ENDS OF THE DIAM AND LVLS1 AND LVLS2
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! ARE THE RESPECTIVE LEVEL STRUCTURES.
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CALL FNDIAM(STNODE, RVNODE, NDSTK, NR, NDEG, LVL, LVLS1,LVLS2, CCSTOR, IDFLT)
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IF (.not.(ndeg(stnode) <= ndeg(rvnode))) then
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! NFLG INDICATES THE END TO BEGIN NUMBERING ON
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NFLG = -1
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STNODE = RVNODE
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endif
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CALL SETUP(LVL, LVLS1, LVLS2)
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! FIND ALL THE CONNECTED COMPONENTS (XCC COUNTS THEM)
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XCC = 0
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LROOT = 1
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LVLN = 1
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DO I=1,N
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IF (LVL(I) /= 0) CYCLE
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XCC = XCC + 1
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STPT(XCC) = LROOT
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CALL TREE(I, NDSTK, NR, LVL, CCSTOR, NDEG, LVLWTH, LVLBOT,LVLN, MAXLW, N)
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SIZEG(XCC) = LVLBOT + LVLWTH - LROOT
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LROOT = LVLBOT + LVLWTH
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LVLN = LROOT
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END DO
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if (sort2() /= 0) then
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CALL PIKLVL(LVLS1, LVLS2, CCSTOR, IDFLT, ISDIR)
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endif
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! ON RETURN FROM PIKLVL, ISDIR INDICATES THE DIRECTION THE LARGEST
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! COMPONENT FELL. ISDIR IS MODIFIED NOW TO INDICATE THE NUMBERING
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! DIRECTION. NUM IS SET TO THE PROPER VALUE FOR THIS DIRECTION.
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ISDIR = ISDIR*NFLG
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NUM = SBNUM
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IF (ISDIR < 0) NUM = STNUM
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CALL NUMBER(STNODE, NUM, NDSTK, LVLS2, NDEG, RENUM, LVLS1,LVL,&
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& NR, NFLG, IBW2, IPF2, CCSTOR, ISDIR)
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! UPDATE STNUM OR SBNUM AFTER NUMBERING
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IF (ISDIR < 0) STNUM = NUM
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IF (ISDIR > 0) SBNUM = NUM
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IF (.not.(sbnum <= stnum)) exit
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end do
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IF (IBW2 > IBW1) then
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! IF ORIGINAL NUMBERING IS BETTER THAN NEW ONE, SET UP TO RETURN IT
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DO I=1,N
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RENUM(I) = IOLD(I)
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END DO
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IBW2 = IBW1
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IPF2 = IPF1
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!
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endif
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DEALLOCATE(SIZEG,STPT,NHIGH,NLOW,AUX,NACUM)
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idpthe = idpth
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RETURN
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END SUBROUTINE PSB_GPS_REDUCE
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!
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SUBROUTINE DGREE(NDSTK, NR, NDEG, IOLD, IBW1, IPF1)
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! DGREE COMPUTES THE DEGREE OF EACH NODE IN NDSTK AND STORES
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! IT IN THE ARRAY NDEG. THE BANDWIDTH AND PROFILE FOR THE ORIGINAL
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! OR INPUT RENUMBERING OF THE GRAPH IS COMPUTED ALSO.
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! USE INTEGER*2 NDSTK WITH AN IBM 360 OR 370.
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implicit none
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INTEGER(psb_ipk_) :: NR, IBW1, IPF1, NDSTK(NR,IDEG), NDEG(N), IOLD(N)
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! COMMON /GRA/ N, IDPTH, IDEG
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integer(psb_ipk_) :: i, itst, j, idif, irw
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IBW1 = 0
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IPF1 = 0
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DO I=1,N
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NDEG(I) = 0
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IRW = 0
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DO J=1,IDEG
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ITST = NDSTK(I,J)
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IF(ITST <= 0) EXIT
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NDEG(I) = NDEG(I) + 1
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IDIF = IOLD(I) - IOLD(ITST)
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IF (IRW < IDIF) IRW = IDIF
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END DO
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IPF1 = IPF1 + IRW
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IF (IRW > IBW1) IBW1 = IRW
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END DO
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RETURN
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END SUBROUTINE DGREE
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!
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SUBROUTINE FNDIAM(SND1, SND2, NDSTK, NR, NDEG, LVL, LVLS1,LVLS2, IWK, IDFLT)
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! FNDIAM IS THE CONTROL PROCEDURE FOR FINDING THE PSEUDO-DIAMETER OF
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! NDSTK AS WELL AS THE LEVEL STRUCTURE FROM EACH END
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! SND1- ON INPUT THIS IS THE NODE NUMBER OF THE FIRST
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! ATTEMPT AT FINDING A DIAMETER. ON OUTPUT IT
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! CONTAINS THE ACTUAL NUMBER USED.
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! SND2- ON OUTPUT CONTAINS OTHER END OF DIAMETER
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! LVLS1- ARRAY CONTAINING LEVEL STRUCTURE WITH SND1 AS ROOT
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! LVLS2- ARRAY CONTAINING LEVEL STRUCTURE WITH SND2 AS ROOT
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! IDFLT- FLAG USED IN PICKING FINAL LEVEL STRUCTURE, SET
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! =1 IF WIDTH OF LVLS1 <= WIDTH OF LVLS2, OTHERWISE =2
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! LVL,IWK- WORKING STORAGE
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! USE INTEGER*2 NDSTK WITH AN IBM 360 OR 370.
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implicit none
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INTEGER(psb_ipk_) :: FLAG, SND, SND1, SND2, NR, idflt
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! COMMON /GRA/ N, IDPTH, IDEG
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! IT IS ASSUMED THAT THE LAST LEVEL HAS AT MOST 100 NODES.
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! COMMON /CC/ NDLST(100)
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integer(psb_ipk_),POINTER :: NDLST(:)
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integer(psb_ipk_) :: NDSTK(NR,IDEG), NDEG(1), LVL(N), LVLS1(N), LVLS2(N),IWK(N)
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integer(psb_ipk_) :: i, j, mtw2, ndxn, ndxl, inow, lvlbot,lvln,lvlwth
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integer(psb_ipk_) :: k,mtw1, maxlw
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!
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NDLST => AUX
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!
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FLAG = 0
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MTW2 = N
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SND = SND1
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! ZERO LVL TO INDICATE ALL NODES ARE AVAILABLE TO TREE
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10 DO 20 I=1,N
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LVL(I) = 0
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20 END DO
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LVLN = 1
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! DROP A TREE FROM SND
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CALL TREE(SND, NDSTK, NR, LVL, IWK, NDEG, LVLWTH, LVLBOT,LVLN, MAXLW, MTW2)
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IF (FLAG >= 1) GO TO 50
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FLAG = 1
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30 IDPTH = LVLN - 1
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MTW1 = MAXLW
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! COPY LEVEL STRUCTURE INTO LVLS1
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DO 40 I=1,N
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LVLS1(I) = LVL(I)
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40 END DO
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NDXN = 1
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NDXL = 0
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MTW2 = N
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! SORT LAST LEVEL BY DEGREE AND STORE IN NDLST
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CALL SORTDG(NDLST, IWK(LVLBOT), NDXL, LVLWTH, NDEG)
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SND = NDLST(1)
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GO TO 10
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50 IF (IDPTH >= LVLN-1) GO TO 60
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! START AGAIN WITH NEW STARTING NODE
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SND1 = SND
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GO TO 30
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60 IF (MAXLW >= MTW2) GO TO 80
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MTW2 = MAXLW
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SND2 = SND
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! STORE NARROWEST REVERSE LEVEL STRUCTURE IN LVLS2
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DO 70 I=1,N
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LVLS2(I) = LVL(I)
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70 END DO
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80 IF (NDXN == NDXL) GO TO 90
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! TRY NEXT NODE IN NDLST
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NDXN = NDXN + 1
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SND = NDLST(NDXN)
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GO TO 10
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90 IDFLT = 1
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IF (MTW2 <= MTW1) IDFLT = 2
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NULLIFY(NDLST)
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RETURN
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END SUBROUTINE FNDIAM
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!
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SUBROUTINE TREE(IROOT, NDSTK, NR, LVL, IWK, NDEG, LVLWTH, LVLBOT, LVLN, MAXLW, IBORT)
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! TREE DROPS A TREE IN NDSTK FROM IROOT
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! LVL- ARRAY INDICATING AVAILABLE NODES IN NDSTK WITH ZERO
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! ENTRIES. TREE ENTERS LEVEL NUMBERS ASSIGNED
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! DURING EXECUTION OF THIS PROCEDURE
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! IWK- ON OUTPUT CONTAINS NODE NUMBERS USED IN TREE
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! ARRANGED BY LEVELS (IWK(LVLN) CONTAINS IROOT
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! AND IWK(LVLBOT+LVLWTH-1) CONTAINS LAST NODE ENTERED)
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! LVLWTH- ON OUTPUT CONTAINS WIDTH OF LAST LEVEL
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! LVLBOT- ON OUTPUT CONTAINS INDEX INTO IWK OF FIRST
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! NODE IN LAST LEVEL
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! MAXLW- ON OUTPUT CONTAINS THE MAXIMUM LEVEL WIDTH
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! LVLN- ON INPUT THE FIRST AVAILABLE LOCATION IN IWK
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! USUALLY ONE BUT IF IWK IS USED TO STORE PREVIOUS
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! CONNECTED COMPONENTS, LVLN IS NEXT AVAILABLE LOCATION.
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! ON OUTPUT THE TOTAL NUMBER OF LEVELS + 1
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! IBORT- INPUT PARAM WHICH TRIGGERS EARLY RETURN IF
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! MAXLW BECOMES >= IBORT
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! USE INTEGER*2 NDSTK WITH AN IBM 360 OR 370.
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implicit none
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integer(psb_ipk_) :: IROOT, NR, NDSTK(NR,*), LVL(*), IWK(*), NDEG(*)
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integer(psb_ipk_) :: LVLWTH, LVLBOT, LVLN, MAXLW, IBORT
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integer(psb_ipk_) :: itest, iwknow, itop, lvltop,j , inow, ndrow
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MAXLW = 0
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ITOP = LVLN
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INOW = LVLN
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LVLBOT = LVLN
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LVLTOP = LVLN + 1
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LVLN = 1
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LVL(IROOT) = 1
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IWK(ITOP) = IROOT
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10 LVLN = LVLN + 1
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20 IWKNOW = IWK(INOW)
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NDROW = NDEG(IWKNOW)
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DO 30 J=1,NDROW
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ITEST = NDSTK(IWKNOW,J)
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IF (LVL(ITEST) /= 0) CYCLE
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LVL(ITEST) = LVLN
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ITOP = ITOP + 1
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IWK(ITOP) = ITEST
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30 END DO
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INOW = INOW + 1
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IF (INOW < LVLTOP) GO TO 20
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LVLWTH = LVLTOP - LVLBOT
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IF (MAXLW < LVLWTH) MAXLW = LVLWTH
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IF (MAXLW >= IBORT) RETURN
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IF (ITOP < LVLTOP) RETURN
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LVLBOT = INOW
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LVLTOP = ITOP + 1
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GO TO 10
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END SUBROUTINE TREE
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!
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SUBROUTINE SORTDG(STK1, STK2, X1, X2, NDEG)
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! SORTDG SORTS STK2 BY DEGREE OF THE NODE AND ADDS IT TO THE END
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! OF STK1 IN ORDER OF LOWEST TO HIGHEST DEGREE. X1 AND X2 ARE THE
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! NUMBER OF NODES IN STK1 AND STK2 RESPECTIVELY.
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implicit none
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INTEGER(psb_ipk_) :: X1, X2, STK1, STK2, TEMP,NDEG
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|
! COMMON /GRA/ N, IDPTH, IDEG
|
|
DIMENSION NDEG(N), STK1(X1+X2), STK2(X2)
|
|
integer(psb_ipk_) :: ind,itest,i,j,istk2,jstk2
|
|
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)
|
|
use psb_base_mod
|
|
implicit none
|
|
integer(psb_ipk_) :: LVL(N), LVLS1(N), LVLS2(N)
|
|
integer(psb_ipk_) :: SZ,i,itemp
|
|
!-----------------------------------------------------
|
|
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
|
|
!
|
|
FUNCTION SORT2() result(val)
|
|
implicit none
|
|
INTEGER(psb_ipk_) :: val
|
|
! SORT2 SORTS SIZEG AND STPT INTO DESCENDING ORDER ACCORDING TO
|
|
! VALUES OF SIZEG. XCC=NUMBER OF ENTRIES IN EACH ARRAY
|
|
INTEGER(psb_ipk_) :: TEMP,ind,itest,i,j
|
|
! IT IS ASSUMED THAT THE GRAPH HAS AT MOST 50 CONNECTED COMPONENTS.
|
|
!COMMON /CC/ XCC, SIZEG(50), STPT(50)
|
|
|
|
VAL = 0
|
|
IF (XCC == 0) RETURN
|
|
VAL = 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)
|
|
use psb_base_mod
|
|
implicit none
|
|
! 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
|
|
! 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)
|
|
INTEGER(psb_ipk_) :: LVLS1(N), LVLS2(N), CCSTOR(N)
|
|
integer(psb_ipk_) :: SZ, ENDC,i,j,max1,max2,inode
|
|
integer(psb_ipk_) :: lvlnh, it, k, lvlnl,idflt,isdir
|
|
! 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)
|
|
use psb_base_mod
|
|
implicit none
|
|
! 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(psb_ipk_) :: SND, NUM, XA, XB, XC, XD, CX, ENDC, TEST, NR, ISDIR
|
|
! 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)
|
|
INTEGER(psb_ipk_) :: IPFA(N), NDSTK(NR,IDEG), LVLS2(N),&
|
|
& NDEG(N), RENUM(N+1), LVLST(N),LSTPT(N),ipf2,ibw2,nflg, nbw
|
|
integer(psb_ipk_),POINTER :: STKA(:),STKB(:),STKC(:),STKD(:)
|
|
integer(psb_ipk_) :: SZ1,SZ2,i,j,nstpt,lvln, lst, lnd, inx, max, ipro,&
|
|
& lvlnl, k, it
|
|
!
|
|
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)
|
|
use psb_base_mod
|
|
! PERFORM ON FLY REALLOCATION OF POINTER VET INCREASING
|
|
! ITS SIZE FROM SZ1 TO SZ2
|
|
IMPLICIT NONE
|
|
integer(psb_ipk_),allocatable :: VET(:)
|
|
integer(psb_ipk_) :: 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
|