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*DECK PIJRNL
SUBROUTINE PIJRNL(IPRT,NREG,NSOUT,SIGTAL,PROB)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Non-linear type normalization of collision probs (CP).
*
*Copyright:
* Copyright (C) 1994 Ecole Polytechnique de Montreal
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version
*
*Author(s): R. Roy, G. Marleau
*
*Parameters: input
* IPRT print level.
* NREG number of zones for geometry.
* NSOUT number of surfaces for geometry.
* SIGTAL albedo-sigt vector.
*
*Parameters: input/output
* PROB CP matrix for all types.
*
*References:
* R. Roy and G. Marleau,
* Normalization Techniques for CP Matrices,
* CONF/PHYSOR-90, Marseille/France, V 2, P IX-40 (1990).
*
*-----------------------------------------------------------------------
*
IMPLICIT NONE
INTEGER IPRT,NREG,NSOUT,IUNOUT,NITMAX,NIT,
> NUNKNO,IPRB,IPRF,IVOL,IDIA,IUNK,JUNK,IR,JR,
> NSURC,NSURM,NVOLC,NVOLM,IP,NPR
REAL SIGTAL(-NSOUT:NREG)
DOUBLE PRECISION PROB(*),EPSCON,TOTCON,WFSPAD
PARAMETER (IUNOUT=6, EPSCON=1.0E-8, NITMAX=10)
INTEGER, ALLOCATABLE, DIMENSION(:) :: IDL
DOUBLE PRECISION, ALLOCATABLE, DIMENSION(:) :: CIJ,WSPACE,WFSP,
> WEIG
C----
C SCRATCH STORAGE ALLOCATION
C CIJ : MODIFIED CP PROB MATRIX
C WSPACE: NON-LINEAR SYSTEM MATRIX
C WFSP : NON LINEAR SYSTEM SOLUTION
C IDL : WSPACE DIAGONAL LOCATION
C WEIG : NON-LINEAR WEIGHT
C----
NPR=(NSOUT+NREG+1)*(NSOUT+NREG+2)/2
ALLOCATE(IDL(NSOUT+NREG+1))
ALLOCATE(CIJ(NPR),WSPACE(NPR),WFSP(-NSOUT:NREG),WEIG(-NSOUT:NREG))
C
C CHARGE MATRIX "CIJ"
NUNKNO=NREG+NSOUT+1
IPRB= 0
IUNK= 0
IVOL= NSOUT*(NSOUT+1)/2
DO 20 IR = -NSOUT, NREG
IUNK= IUNK+1
IF( IR.LT.0.OR.SIGTAL(IR).GT.0.0 )THEN
DO 10 JR= -NSOUT, IR-1
IPRB= IPRB+1
IF( JR.LT.0.OR.SIGTAL(JR).GT.0.0 )THEN
CIJ(IPRB)= PROB(IPRB)
ELSE
CIJ(IPRB)= 0.0D0
ENDIF
10 CONTINUE
ELSE
DO 15 JR= -NSOUT, IR-1
IPRB= IPRB+1
CIJ(IPRB)= 0.0D0
15 CONTINUE
ENDIF
IPRB= IPRB+1
IDL(IUNK)= IPRB
IF( IR.LT.0 )THEN
IVOL= IVOL+1
CIJ(IPRB)= PROB(IPRB)
ELSEIF( IR.GT.0 )THEN
IVOL= IVOL+IUNK-1
IF( SIGTAL(IR).GT.0.0 )THEN
CIJ(IPRB)= PROB(IPRB)
ELSE
CIJ(IPRB)= PROB(IVOL)
ENDIF
ELSE
IVOL= IVOL+1
CIJ(IPRB)= 1.0D0
ENDIF
20 CONTINUE
C
C COPY MATRIX "CIJ" IN THE "WSPACE" ARRAY FOR INVERSION
C AND ADD TO THE DIAGONAL ALL TERMS OF A LINE
IPRB= 0
IUNK= 0
IDIA= 0
DO 50 IR = -NSOUT, NREG
IUNK= IUNK+1
IDIA= IDIA+IUNK
WSPACE(IDIA)= CIJ(IDIA) + CIJ(IDIA)
DO 30 JR= -NSOUT, IR-1
IPRB= IPRB+1
WSPACE(IPRB)= CIJ(IPRB)
WSPACE(IDIA)= WSPACE(IDIA) + CIJ(IPRB)
30 CONTINUE
IPRB= IPRB+1
IPRF= IPRB
JUNK= IUNK
DO 40 JR= IR+1 , NREG
IPRF= IPRF+JUNK
JUNK= JUNK+1
WSPACE(IDIA)= WSPACE(IDIA) + CIJ(IPRF)
40 CONTINUE
50 CONTINUE
IF( IPRT.GT.100 )THEN
WRITE(IUNOUT,8002)
IPRB= 0
DO 55 IR= -NSOUT, NREG
DO 52 JR= -NSOUT, IR
IPRB= IPRB+1
WRITE(IUNOUT,8003) IR, JR, CIJ(IPRB),
> WSPACE(IPRB),PROB(IPRB)
52 CONTINUE
55 CONTINUE
ENDIF
C
C INVERSION OF THE INITIAL SYSTEM JACOBIAN MATRIX
CALL ALDDLF(NUNKNO,WSPACE,IDL)
C
C INITIALISATION OF WEIGHTS
DO 60 IR=-NSOUT, NREG
WEIG(IR)=1.0D0
60 CONTINUE
WEIG(0)= 0.0D0
C
C THE NON-LINEAR SYSTEM FOR WEIGHTS IS:
C F1(W1, W2, ... WN)= W1*(W1*C11+W2*C12+ ... +WN*C1N) - TRUE1
C F2(W1, W2, ... WN)= W2*(W1*C21+W2*C22+ ... +WN*C2N) - TRUE2
C ...
C FN(W1, W2, ... WN)= WN*(W1*CN1+W2*CN2+ ... +WN*CNN) - TRUEN
C FORMING THE SYSTEM USING WEIGHTS "WEIG" & CONTRIBUTIONS "CIJ"
C
C MAIN ITERATION LOOP
DO 110 NIT=1,NITMAX
C
IPRB= 0
IUNK= 0
IVOL= NSOUT*(NSOUT+1)/2
DO 90 IR=-NSOUT, NREG
IF( IR.LE.0 )THEN
IVOL= IVOL+1
ELSE
IVOL= IVOL+IUNK
ENDIF
IUNK= IUNK+1
WFSPAD= 0.0D0
DO 70 JR=-NSOUT, IR
IPRB= IPRB+1
WFSPAD=WFSPAD+WEIG(JR)*CIJ(IPRB)
70 CONTINUE
IPRF= IPRB
JUNK= IUNK
DO 80 JR= IR+1 , NREG
IPRF= IPRF+JUNK
JUNK= JUNK+1
WFSPAD=WFSPAD+WEIG(JR)*CIJ(IPRF)
80 CONTINUE
WFSP(IR)=WEIG(IR)*WFSPAD-PROB(IVOL)
90 CONTINUE
IF( IPRT.GT.100 )THEN
WRITE(IUNOUT,9000)
DO 92 IR= -NSOUT, NREG
WRITE(IUNOUT,9001) IR, WFSP(IR)
92 CONTINUE
ENDIF
CALL ALDDLS(NUNKNO,IDL,WSPACE,WFSP)
C
C CALCULATIONS OF SQUARE DISTANCE BETWEEN 2 ITERATIONS
C AND UPDATING THE SOLUTION
TOTCON = 0.0D0
DO 100 IR=-NSOUT, NREG
TOTCON= TOTCON + WFSP(IR)**2
WEIG(IR)= WEIG(IR) - WFSP(IR)
100 CONTINUE
IF( IPRT.GT.100 )THEN
WRITE(IUNOUT,9004)
DO 102 IR= -NSOUT, NREG
WRITE(IUNOUT,9005) IR, WEIG(IR)
102 CONTINUE
WRITE(IUNOUT,'( 8H TOTCON: ,E15.7)') TOTCON
ENDIF
C
C CONVERGENCE TEST
IF( TOTCON.LT.EPSCON )GO TO 120
C
110 CONTINUE
WRITE(IUNOUT,'(35H PIJRNL: WEIGHTS NOT CONVERGED )')
120 CONTINUE
C
C RECOMPUTE WEIGHTS FOR VOID REGIONS
IPRB= (NSOUT+1)*(NSOUT+2)/2
IVOL= IPRB
IUNK= NSOUT+1
DO 220 IR= 1, NREG
IVOL= IVOL+IUNK
IUNK= IUNK+1
IF( SIGTAL(IR).EQ.0.0 )THEN
WFSPAD= 0.0D0
DO 200 JR=-NSOUT, IR
IPRB= IPRB+1
IF( JR.LT.0.OR.SIGTAL(JR).GT.0.0 )THEN
WFSPAD=WFSPAD+WEIG(JR)*PROB(IPRB)
ENDIF
200 CONTINUE
IPRF= IPRB
JUNK= IUNK
DO 210 JR= IR+1 , NREG
IPRF= IPRF+JUNK
JUNK= JUNK+1
IF( JR.LT.0.OR.SIGTAL(JR).GT.0.0 )THEN
WFSPAD=WFSPAD+WEIG(JR)*PROB(IPRF)
ENDIF
210 CONTINUE
WEIG(IR)=PROB(IVOL)/WFSPAD
ELSE
IPRB= IPRB+IUNK
ENDIF
220 CONTINUE
C
C RENORMALIZE "PIJ" SYMMETRIC MATRIX
IPRB = 0
DO 240 IR = -NSOUT, NREG
DO 230 JR= -NSOUT, IR
IPRB= IPRB+1
IF( IR.NE.0.AND.JR.NE.0 )THEN
PROB(IPRB)=PROB(IPRB)*WEIG(IR)*WEIG(JR)
ENDIF
230 CONTINUE
240 CONTINUE
C
C PRINT WEIGHT FACTORS IF REQUESTED
IF( IPRT .GE. 100 )THEN
WRITE(IUNOUT,'(30H0 SURFACE WEIGHTS FACTORS /)')
NSURC = -1
DO 300 IP = 1, (9 +NSOUT) / 10
NSURM= MAX( -NSOUT, NSURC-9 )
WRITE(IUNOUT,'(10X,10( A5, I6)/)')
> (' SUR ',-IR,IR= NSURC, NSURM, -1)
WRITE(IUNOUT,'(10H WEIGHT ,10F11.5)')
> (WEIG(IR),IR=NSURC,NSURM,-1)
NSURC = NSURC - 10
300 CONTINUE
WRITE(IUNOUT,'(30H0 VOLUME WEIGHTS FACTORS /)')
NVOLC = 1
DO 310 IP = 1, (9 + NREG) / 10
NVOLM= MIN( NREG, NVOLC+9 )
WRITE(IUNOUT,'(10X,10( A5 , I6)/)')
> (' VOL ',IR,IR=NVOLC,NVOLM, 1)
WRITE(IUNOUT,'(10H WEIGHT ,10F11.5)')
> (WEIG(IR),IR=NVOLC,NVOLM, 1)
NVOLC = NVOLC + 10
310 CONTINUE
ENDIF
C----
C SCRATCH STORAGE DEALLOCATION
C----
DEALLOCATE(WEIG,WFSP,WSPACE,CIJ)
DEALLOCATE(IDL)
RETURN
C
8002 FORMAT(//' S U R F / S U R F C O N T R I B U T I O N S'//
>9X,'BEGIN S',6X,'END S ',11X,'CIJ. ',11X, 'WSPACE ',
> 11X,'PROBS. ')
8003 FORMAT(6X,I10,5X,I10,5X,1P,E15.7,5X,E15.7,5X,E15.7 )
9000 FORMAT(//' F U N C T I O N V A L U E S'//
>9X,'VOL/SUR',6X,'VALUE')
9001 FORMAT(6X,I10,5X,F10.4)
9004 FORMAT(//' W E I G H T E D V A L U E S'//
>9X,'VOL/SUR',6X,'VALUE')
9005 FORMAT(6X,I10,5X,F10.4)
END
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