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|
*DECK SYBHTK
SUBROUTINE SYBHTK (NA,NX,NREG,SIDE,RAYRE,ILIGN,INORM,IQW,LR,Z,LI,
1 IZ,PREC)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Compute the tracking information related to an hexagonal heterogeneous
* cell.
*
*Copyright:
* Copyright (C) 2008 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): A. Hebert
*
*Parameters: input
* NA number of angles in (0,$\\pi$/6).
* NX number of tracks in each sub domain for a given angle.
* NREG number of regions in the cell.
* SIDE side of an hexagon.
* RAYRE radius of each cylinder (RAYRE(1)=0.0).
* ILIGN tracking print flag (=1 to print the tracking).
* INORM track normalization flag (=1 to avoid track normalization).
* IQW equal weight quadrature flag (=1 to use equal weight
* quadratures in angle and space).
*
*Parameters: output
* LR exact size of array Z with
* L.LE.4+3*NA*(13+2*(NREG+1)*NX*NREG).
* Z real tracking information.
* Z(1) to Z(4) contain the numerical orthonormalization
* factors.
* LI size of array IZ with
* L.LE.NREG+4+3*NA*(2+(NREG+1)*(3+2*NREG)).
* IZ integer tracking information.
* IZ(1)=5, IZ(2)=NREG+1 and IZ(3)=3 for an hexagonal cell.
* PREC accuracy obtained if the non-normalized tracks are used
* to integrate the volumes.
*
*-----------------------------------------------------------------------
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER NA,NX,NREG,ILIGN,INORM,IQW,LR,LI,IZ(*)
REAL SIDE,RAYRE(NREG),Z(*),PREC
*----
* LOCAL VARIABLES
*----
PARAMETER (PIO2=1.570796327,PI=3.14159265358979,SQ3=1.73205080757)
REAL ZX(64),WX(64),ZA(64),WA(64),ZXJ(64),WXJ(64)
REAL, ALLOCATABLE, DIMENSION(:) :: VAP
*----
* SCRATCH STORAGE ALLOCATION
*----
ALLOCATE(VAP(NREG))
*
NA3=3*NA
IF(NX.GT.10) CALL XABORT('SYBHTK: NX IS GREATER THAN 10.')
IF(NA.GT.64) CALL XABORT('SYBHTK: NA IS GREATER THAN 64.')
IF(2.0*RAYRE(NREG).GT.SQ3*SIDE) CALL XABORT('SYBHTK: A RADIUS IS'
1 //' GREATER THAN HALF A SIDE.')
*----
* COMPUTE VOLUMES
*----
VOL=1.5*SQ3*SIDE**2
DO 10 IR=NREG,1,-1
R2=PI*RAYRE(IR)**2
Z(IR)=VOL-R2
VOL=R2
10 CONTINUE
*
IF(IQW.EQ.0) THEN
* GAUSS-LEGENDRE AND GAUSS-JACOBI INTEGRATION POINTS.
CALL ALGPT(NX,-1.,1.,ZX(1),WX(1))
CALL ALGJP(NX,ZXJ,WXJ)
CALL ALGPT(NA,-1.,-1./3.,ZA(1),WA(1))
CALL ALGPT(NA,-1./3.,1./3.,ZA(NA+1),WA(NA+1))
CALL ALGPT(NA,1./3.,1.,ZA(2*NA+1),WA(2*NA+1))
ELSE
* EQUAL WEIGHT INTEGRATION POINTS.
DO 15 I=1,NX
ZX(I)=(2.0*REAL(I)-1.0)/REAL(NX)-1.0
WX(I)=2.0/REAL(NX)
ZXJ(I)=0.5*(2.0*REAL(I)-1.0)/REAL(NX)
WXJ(I)=ZXJ(I)/REAL(NX)
15 CONTINUE
DO 20 I=1,NA3
ZA(I)=(2.0*REAL(I)-1.0)/REAL(NA3)-1.0
WA(I)=2.0/REAL(NA3)
20 CONTINUE
ENDIF
IZ(1)=5
IZ(2)=NREG+1
IZ(3)=3
IZ(4)=NA3
PREC=0.0
LI=4
LR=NREG+4
*----
* INTEGRATION IN ANGLE FROM 0 TO PI/2
*----
ZN1=0.0
ZN2=0.0
ZN3=0.0
DO 350 IA=1,NA3
PHI=0.5*PIO2*(ZA(IA)+1.0)
SI=SIN(PHI)
CO=COS(PHI)
TA=SI/CO
FACT1=(SQ3/TA)/(SQ3/TA-1.0)
FACT2=(SQ3/TA)/(SQ3/TA+1.0)
ZN1=ZN1+SI*WA(IA)
ZN2=ZN2+SI*SI*WA(IA)
ZN3=ZN3+SI*SI*SI*WA(IA)
Z(LR+1:LR+6)=0.0
Z(LR+9)=SI
Z(LR+10)=CO
IF(PHI.LT.PI/6.) THEN
Z(LR+11)=COS(PHI+PI/6.)
Z(LR+12)=SIN(PHI+PI/6.)
ELSE IF(PHI.LT.PI/3.) THEN
Z(LR+1)=COS(PHI-PI/6.)
Z(LR+2)=SIN(PHI-PI/6.)
ELSE
Z(LR+3)=SI
Z(LR+4)=CO
ENDIF
Z(LR+13)=WA(IA)
LR=LR+13
*----
* FIRST ANGULAR DOMAIN (0 TO PI/6)
*----
L4=LI+1
IZ(LI+1)=0
IZ(LI+2)=0
LI=LI+2
IF(PHI.GT.PIO2/3.0) GO TO 120
X1=0.0
XLIM=MIN(SIDE,0.5*SIDE*(SQ3/TA-1.0))
DLIM=0.5*SIDE*SQ3*CO+(0.5*SIDE-XLIM)*SI
DO 100 K0=NREG,1,-1
KMAX=NREG-K0+1
X2=MIN(XLIM,XLIM-(RAYRE(K0)-DLIM)/SI)
L3=LR+1
L5=LI+1
LI=LI+3
VAP(:NREG)=0.0
DO 50 IX=1,NX
IF(K0.EQ.NREG) THEN
S=0.5*(X2-X1)*SI*WX(IX)
X=X1+0.5*(X2-X1)*(1.0+ZX(IX))
ELSE
* FLURIG CHANGE OF VARIABLE.
S=2.0*(X2-X1)*SI*WXJ(IX)
X=X1+(X2-X1)*ZXJ(IX)**2
ENDIF
Z(LR+1)=S*WA(IA)
LR=LR+1
C=0.5*SIDE*SQ3*SI-(0.5*SIDE-X)*CO
D=0.5*SIDE*SQ3*CO+(0.5*SIDE-X)*SI
D=D*D
SUM=0.0
CORDE=0.0
DO 30 K=NREG,K0+1,-1
RR=RAYRE(K)**2-D
CORDE=SQRT(RR)
DEL=C-CORDE
SUM=SUM+DEL
Z(LR+NREG-K+1)=DEL
VAP(K)=VAP(K)+DEL*S
C=CORDE
30 CONTINUE
IF(KMAX.NE.1) THEN
DEL=2.0*CORDE
SUM=SUM+DEL
Z(LR+KMAX)=DEL
VAP(K)=VAP(K)+DEL*S
DO 40 I=1,KMAX-2
DEL=Z(LR+KMAX-I)
SUM=SUM+DEL
Z(LR+KMAX+I)=DEL
VAP(K+I)=VAP(K+I)+DEL*S
40 CONTINUE
ENDIF
LR=LR+2*KMAX-1
DEL=X*FACT1/CO-SUM
Z(LR)=DEL
VAP(NREG)=VAP(NREG)+DEL*S
50 CONTINUE
DO 60 K=KMAX-1,1-KMAX,-1
IZ(LI+K+KMAX)=5+ABS(K)+1+NREG-KMAX
60 CONTINUE
LI=LI+2*KMAX
IZ(L5)=2*KMAX-1
IZ(L5+1)=NX
IZ(L5+2)=4 ! ISURF
IZ(LI)=5 ! JSURF
*----
* VOLUME NORMALIZATION
*----
IF((INORM.EQ.0).AND.(K0.LT.NREG)) THEN
DLIM1=0.5*SIDE*SQ3*CO+(0.5*SIDE-X2)*SI
DLIM2=0.5*SIDE*SQ3*CO+(0.5*SIDE-X1)*SI
VW1=0.0
SUMVAP=0.0
DO 70 I=K0,NREG-1
SUMVAP=SUMVAP+VAP(I)
RW=RAYRE(I+1)
VEX1=RW*RW*ACOS(DLIM1/RW)-DLIM1*SQRT(RW*RW-DLIM1*DLIM1)
IF(RW.GT.DLIM2)
1 VEX1=VEX1-(RW*RW*ACOS(DLIM2/RW)-DLIM2*SQRT(RW*RW-DLIM2*DLIM2))
SUM=(VEX1-VW1)/VAP(I)
PREC=MAX(PREC,ABS(1.0-SUM)*(VEX1-VW1)/(1.5*SQ3*SIDE**2))
VW1=VEX1
VAP(I)=SUM
70 CONTINUE
VEX1=0.5*(SIDE*SQ3*SI-(SIDE-X1-X2)*CO)*(X2-X1)*SI
VEX2=0.5*FACT1*TA*(X2*X2-X1*X1)-VEX1
SUM=(VEX1-0.5*VW1)/(VEX1-0.5*SUMVAP)
PREC=MAX(PREC,ABS(1.0-SUM)*(VEX1-0.5*VW1)/(1.5*SQ3*SIDE**2))
VEX1=SUM
SUM=(VEX2-0.5*VW1)/(VEX2-0.5*SUMVAP)
PREC=MAX(PREC,ABS(1.0-SUM)*(VEX2-0.5*VW1)/(1.5*SQ3*SIDE**2))
VEX2=SUM
DO 90 IX=1,NX
KMAX=(IZ(L5)+1)/2
Z(L3+KMAX)=Z(L3+KMAX)*VAP(K0)
DO 80 I=1,KMAX-2
Z(L3+KMAX-I)=Z(L3+KMAX-I)*VAP(K0+I)
Z(L3+KMAX+I)=Z(L3+KMAX+I)*VAP(K0+I)
80 CONTINUE
Z(L3+1)=Z(L3+1)*VEX1
Z(L3+2*KMAX-1)=Z(L3+2*KMAX-1)*VEX2
L3=L3+2*KMAX
90 CONTINUE
ENDIF
IZ(L4)=IZ(L4)+1
IF(X2.GE.XLIM) GO TO 120
X1=X2
100 CONTINUE
*----
* SECOND ANGULAR DOMAIN (PI/6 TO PI/3)
*----
120 IF((PHI.LE.PI/6.0).OR.(PHI.GT.2.0*PIO2/3.0)) GO TO 240
X1=0.5*SIDE*(SQ3/TA-1.0)
XLIM=SIDE
DLIM=0.5*SIDE*SQ3*CO+(0.5*SIDE-XLIM)*SI
DO 230 K0=NREG,1,-1
KMAX=NREG-K0+1
X2=MIN(XLIM,XLIM-(RAYRE(K0)-DLIM)/SI)
IF(X2.LE.X1) GO TO 230
L3=LR+1
L5=LI+1
LI=LI+3
VAP(:NREG)=0.0
DO 150 IX=1,NX
IF(K0.EQ.NREG) THEN
S=0.5*(X2-X1)*SI*WX(IX)
X=X1+0.5*(X2-X1)*(1.0+ZX(IX))
ELSE
* FLURIG CHANGE OF VARIABLE.
S=2.0*(X2-X1)*SI*WXJ(IX)
X=X1+(X2-X1)*ZXJ(IX)**2
ENDIF
Z(LR+1)=S*WA(IA)
LR=LR+1
C=0.5*SIDE*SQ3*SI-(0.5*SIDE-X)*CO
D=0.5*SIDE*SQ3*CO+(0.5*SIDE-X)*SI
D=D*D
SUM=0.0
CORDE=0.0
DO 130 K=NREG,K0+1,-1
RR=RAYRE(K)**2-D
CORDE=SQRT(RR)
DEL=C-CORDE
SUM=SUM+DEL
Z(LR+NREG-K+1)=DEL
VAP(K)=VAP(K)+DEL*S
C=CORDE
130 CONTINUE
IF(KMAX.NE.1) THEN
DEL=2.0*CORDE
SUM=SUM+DEL
Z(LR+KMAX)=DEL
VAP(K)=VAP(K)+DEL*S
DO 140 I=1,KMAX-2
DEL=Z(LR+KMAX-I)
SUM=SUM+DEL
Z(LR+KMAX+I)=DEL
VAP(K+I)=VAP(K+I)+DEL*S
140 CONTINUE
ENDIF
LR=LR+2*KMAX-1
DEL=(X+SIDE)*FACT2/CO-SUM
Z(LR)=DEL
VAP(NREG)=VAP(NREG)+DEL*S
150 CONTINUE
DO 160 K=KMAX-1,1-KMAX,-1
IZ(LI+K+KMAX)=5+ABS(K)+1+NREG-KMAX
160 CONTINUE
LI=LI+2*KMAX
IZ(L5)=2*KMAX-1
IZ(L5+1)=NX
IZ(L5+2)=4 ! ISURF
IZ(LI)=0 ! JSURF
*----
* VOLUME NORMALIZATION
*----
IF((INORM.EQ.0).AND.(K0.LT.NREG)) THEN
DLIM1=0.5*SIDE*SQ3*CO+(0.5*SIDE-X2)*SI
DLIM2=0.5*SIDE*SQ3*CO+(0.5*SIDE-X1)*SI
VW1=0.0
SUMVAP=0.0
DO 200 I=K0,NREG-1
SUMVAP=SUMVAP+VAP(I)
RW=RAYRE(I+1)
VEX1=RW*RW*ACOS(DLIM1/RW)-DLIM1*SQRT(RW*RW-DLIM1*DLIM1)
IF(RW.GT.DLIM2)
1 VEX1=VEX1-(RW*RW*ACOS(DLIM2/RW)-DLIM2*SQRT(RW*RW-DLIM2*DLIM2))
SUM=(VEX1-VW1)/VAP(I)
PREC=MAX(PREC,ABS(1.0-SUM)*(VEX1-VW1)/(1.5*SQ3*SIDE**2))
VW1=VEX1
VAP(I)=SUM
200 CONTINUE
VEX1=0.5*(SIDE*SQ3*SI-(SIDE-X1-X2)*CO)*(X2-X1)*SI
VEX2=0.5*FACT2*TA*(X2-X1)*(X1+X2+2.0*SIDE)-VEX1
SUM=(VEX1-0.5*VW1)/(VEX1-0.5*SUMVAP)
PREC=MAX(PREC,ABS(1.0-SUM)*(VEX1-0.5*VW1)/(1.5*SQ3*SIDE**2))
VEX1=SUM
SUM=(VEX2-0.5*VW1)/(VEX2-0.5*SUMVAP)
PREC=MAX(PREC,ABS(1.0-SUM)*(VEX2-0.5*VW1)/(1.5*SQ3*SIDE**2))
VEX2=SUM
DO 220 IX=1,NX
KMAX=(IZ(L5)+1)/2
Z(L3+KMAX)=Z(L3+KMAX)*VAP(K0)
DO 210 I=1,KMAX-2
Z(L3+KMAX-I)=Z(L3+KMAX-I)*VAP(K0+I)
Z(L3+KMAX+I)=Z(L3+KMAX+I)*VAP(K0+I)
210 CONTINUE
Z(L3+1)=Z(L3+1)*VEX1
Z(L3+2*KMAX-1)=Z(L3+2*KMAX-1)*VEX2
L3=L3+2*KMAX
220 CONTINUE
ENDIF
IZ(L4)=IZ(L4)+1
X1=X2
230 CONTINUE
*----
* THIRD ANGULAR DOMAIN (PI/3 TO PI/2)
*----
240 IF(PHI.LE.2.0*PIO2/3.0) GO TO 350
X1=SQ3*SIDE/TA
XLIM=0.5*(SIDE+X1)
DO 340 K0=NREG,1,-1
KMAX=NREG-K0+1
X2=XLIM-RAYRE(K0)/SI
IF(X2.LE.X1) GO TO 340
L3=LR+1
L5=LI+1
LI=LI+3
VAP(:NREG)=0.0
DO 270 IX=1,NX
IF(K0.EQ.NREG) THEN
S=0.5*(X2-X1)*SI*WX(IX)
X=X1+0.5*(X2-X1)*(1.0+ZX(IX))
ELSE
* FLURIG CHANGE OF VARIABLE.
S=2.0*(X2-X1)*SI*WXJ(IX)
X=X1+(X2-X1)*ZXJ(IX)**2
ENDIF
Z(LR+1)=S*WA(IA)
LR=LR+1
C=0.5*SIDE*SQ3*SI-(0.5*SIDE-X)*CO
D=0.5*SIDE*SQ3*CO+(0.5*SIDE-X)*SI
D=D*D
SUM=0.0
CORDE=0.0
DO 250 K=NREG,K0+1,-1
RR=RAYRE(K)**2-D
CORDE=SQRT(RR)
DEL=C-CORDE
SUM=SUM+DEL
Z(LR+NREG-K+1)=DEL
VAP(K)=VAP(K)+DEL*S
C=CORDE
250 CONTINUE
IF(KMAX.NE.1) THEN
DEL=2.0*CORDE
SUM=SUM+DEL
Z(LR+KMAX)=DEL
VAP(K)=VAP(K)+DEL*S
DO 260 I=1,KMAX-2
DEL=Z(LR+KMAX-I)
SUM=SUM+DEL
Z(LR+KMAX+I)=DEL
VAP(K+I)=VAP(K+I)+DEL*S
260 CONTINUE
ENDIF
IF(KMAX.NE.KMAX) CALL XABORT('BUG')
LR=LR+2*KMAX-1
DEL=SQ3*SIDE/SI-SUM
Z(LR)=DEL
VAP(NREG)=VAP(NREG)+DEL*S
270 CONTINUE
DO 280 K=KMAX-1,1-KMAX,-1
IZ(LI+K+KMAX)=5+ABS(K)+1+NREG-KMAX
280 CONTINUE
LI=LI+2*KMAX
IZ(L5)=2*KMAX-1
IZ(L5+1)=NX
IZ(L5+2)=4 ! ISURF
IZ(LI)=1 ! JSURF
*----
* VOLUME NORMALIZATION
*----
IF((INORM.EQ.0).AND.(K0.LT.NREG)) THEN
DLIM1=0.5*SIDE*SQ3*CO+(0.5*SIDE-X2)*SI
DLIM2=0.5*SIDE*SQ3*CO+(0.5*SIDE-X1)*SI
VW1=0.0
SUMVAP=0.0
DO 310 I=K0,NREG-1
SUMVAP=SUMVAP+VAP(I)
RW=RAYRE(I+1)
VEX1=RW*RW*ACOS(DLIM1/RW)-DLIM1*SQRT(RW*RW-DLIM1*DLIM1)
IF(RW.GT.DLIM2)
1 VEX1=VEX1-(RW*RW*ACOS(DLIM2/RW)-DLIM2*SQRT(RW*RW-DLIM2*DLIM2))
SUM=(VEX1-VW1)/VAP(I)
PREC=MAX(PREC,ABS(1.0-SUM)*(VEX1-VW1)/(1.5*SQ3*SIDE**2))
VW1=VEX1
VAP(I)=SUM
310 CONTINUE
VEX1=0.5*(SIDE*SQ3*SI-(SIDE-X1-X2)*CO)*(X2-X1)*SI
VEX2=(X2-X1)*SQ3*SIDE-VEX1
SUM=(VEX1-0.5*VW1)/(VEX1-0.5*SUMVAP)
PREC=MAX(PREC,ABS(1.0-SUM)*(VEX1-0.5*VW1)/(1.5*SQ3*SIDE**2))
VEX1=SUM
SUM=(VEX2-0.5*VW1)/(VEX2-0.5*SUMVAP)
PREC=MAX(PREC,ABS(1.0-SUM)*(VEX2-0.5*VW1)/(1.5*SQ3*SIDE**2))
VEX2=SUM
DO 330 IX=1,NX
KMAX=(IZ(L5)+1)/2
Z(L3+KMAX)=Z(L3+KMAX)*VAP(K0)
DO 320 I=1,KMAX-2
Z(L3+KMAX-I)=Z(L3+KMAX-I)*VAP(K0+I)
Z(L3+KMAX+I)=Z(L3+KMAX+I)*VAP(K0+I)
320 CONTINUE
Z(L3+1)=Z(L3+1)*VEX1
Z(L3+2*KMAX-1)=Z(L3+2*KMAX-1)*VEX2
L3=L3+2*KMAX
330 CONTINUE
ENDIF
IZ(L4)=IZ(L4)+1
X1=X2
340 CONTINUE
350 CONTINUE
ZN1=0.5*ZN1*PIO2
ZN2=0.5*ZN2*PIO2
ZN3=0.5*ZN3*PIO2
Z(NREG+1)=1.0/SQRT(ZN1)
Z(NREG+2)=1.0/SQRT(0.75*ZN3-0.7205061948*ZN2*ZN2/ZN1)
Z(NREG+3)=Z(NREG+2)*0.8488263632*ZN2/ZN1
Z(NREG+4)=2.0/SQRT(3.0*(ZN1-ZN3))
*----
* TRACKING INFORMATION OUTPUT
*----
IF(ILIGN.EQ.1) THEN
L1I=IZ(1)-1
L1R=IZ(2)-1
WRITE(6,500) (Z(L1R+I),I=1,4)
L1R=L1R+4
L2=0
DO 375 IA=1,NA3
MNT=IZ(L1I+1)
L1I=L1I+2
ZSIN=Z(L1R+9)
ZCOS=Z(L1R+10)
L1R=L1R+13
DO 370 IMNT=1,MNT
NH=IZ(L1I+1)
NX=IZ(L1I+2)
L1I=L1I+3
DO 360 IX=1,NX
L2=L2+1
IF((IMNT.EQ.1).AND.(IX.EQ.1)) THEN
WRITE(6,510) L2,ZSIN,ZCOS,Z(L1R+1),NH,(Z(L1R+I+1),I=1,NH)
ELSE
WRITE(6,520) L2,Z(L1R+1),NH,(Z(L1R+I+1),I=1,NH)
ENDIF
L1R=L1R+NH+1
360 CONTINUE
L1I=L1I+NH+1
370 CONTINUE
375 CONTINUE
ENDIF
*----
* SCRATCH STORAGE DEALLOCATION
*----
DEALLOCATE(VAP)
RETURN
*
500 FORMAT (1H1//30H TRACKING INFORMATION LISTING.//12H NUMERICAL O,
1 27HRTHONORMALIZATION FACTORS =,1P,4E12.4//6H TRACK)
510 FORMAT (1X,I5,7H SIN =,1P,E10.3,7H COS =,E10.3,9H WEIGHT =,
1 E10.3,6H NH =,I3,12H SEGMENTS =,5E10.3:/(80X,5E10.3))
520 FORMAT (1X,I5,34X,9H WEIGHT =,1P,E10.3,6H NH =,I3,10H SEGMENTS,
1 2H =,5E10.3:/(80X,5E10.3))
END
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