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+*DECK SYB002
+ SUBROUTINE SYB002 (NGEN,NPIJ,NPIS,SIGT2,SIGW2,IMPX,NCOUR,IWIGN,
+ 1 IQUAD,XX,YY,NMC,RAYRE,MAIL,RZMAIL,PIJW,PISW,PSJW,PSSW)
+*
+*-----------------------------------------------------------------------
+*
+*Purpose:
+* Compute the cellwise scattering-reduced collision, escape and
+* transmission probabilities in a 2-D Cartesian or hexagonal assembly
+* with Roth approximation.
+*
+*Copyright:
+* Copyright (C) 2002 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
+* NGEN total number of generating cells.
+* NPIJ length of cellwise scattering-reduced collision probability
+* matrices.
+* NPIS length of cellwise scattering-reduced escape probability
+* matrices (NPIS=NMC(NGEN+1)).
+* SIGT2 total macroscopic cross sections.
+* SIGW2 P0 within-group scattering macroscopic cross sections.
+* IMPX print flag (equal to 0 for no print).
+* NCOUR number of currents surrounding the cells (=4 Cartesian
+* lattice; =6 hexagonal lattice).
+* IWIGN type of cylinderization.
+* IQUAD quadrature parameters.
+* XX X-thickness of the generating cells.
+* YY Y-thickness of the generating cells.
+* NMC offset of the first volume in each generating cell.
+* RAYRE radius of the tubes in each generating cell.
+* MAIL offset of the first tracking information in each generating
+* cell.
+* RZMAIL real tracking information.
+*
+*Parameters: output
+* PIJW cellwise scattering-reduced collision probability matrices.
+* PISW cellwise scattering-reduced escape probability matrices.
+* PSJW cellwise scattering-reduced collision probability matrices
+* for incoming neutrons.
+* PSSW cellwise scattering-reduced transmission probability
+* matrices.
+*
+*-----------------------------------------------------------------------
+*
+*----
+* SUBROUTINE ARGUMENTS
+*----
+ INTEGER NGEN,NPIJ,NPIS,IMPX,NCOUR,IWIGN,IQUAD(4),NMC(NGEN+1),
+ 1 MAIL(2,NGEN)
+ REAL SIGT2(NPIS),SIGW2(NPIS),XX(NGEN),YY(NGEN),RAYRE(NPIS),
+ 1 RZMAIL(*),PIJW(NPIJ),PISW(NPIS),PSJW(NPIS),PSSW(NGEN)
+*----
+* LOCAL VARIABLES
+*----
+ PARAMETER (PI=3.141592654)
+ LOGICAL LSKIP
+ REAL, ALLOCATABLE, DIMENSION(:) :: PIS,PSJ,RAYR2,WORK
+ REAL, ALLOCATABLE, DIMENSION(:,:) :: PP
+*----
+* SCRATCH STORAGE ALLOCATION
+*----
+ ALLOCATE(PIS(NPIS),PSJ(NPIS))
+*
+ MR=IQUAD(4)
+ IPIJ=0
+ DO 220 JKG=1,NGEN
+ J1=NMC(JKG)
+ J2=NMC(JKG+1)-J1
+*----
+* CYLINDERIZATION OPTIONS
+*----
+ A=XX(JKG)
+ B=YY(JKG)
+ IB=MAIL(2,JKG)
+ RJ1=RAYRE(NMC(JKG+1))
+ SCALE1=1.0
+ SCALE2=1.0
+ ROUT=0.0
+ IF((NCOUR.EQ.4).AND.(IWIGN.EQ.1)) THEN
+* ASKEW CYLINDERIZATION CARTESIAN.
+ RJ2=(A+B)/PI
+ SCALE1=(A*B-PI*RJ1**2)/(PI*RJ2**2-PI*RJ1**2)
+ ROUT=RJ2
+ ELSE IF((NCOUR.EQ.4).AND.(IWIGN.EQ.2)) THEN
+* WIGNER CYLINDERIZATION CARTESIAN.
+ ROUT=SQRT(A*B/PI)
+ ELSE IF((NCOUR.EQ.4).AND.(IWIGN.EQ.3)) THEN
+* SANCHEZ CYLINDERIZATION CARTESIAN.
+ SCALE2=SQRT(PI*A*B)/(A+B)
+ ROUT=SQRT(A*B/PI)
+ ELSE IF(IWIGN.EQ.1) THEN
+* ASKEW CYLINDERIZATION HEXAGONAL.
+ RJ2=3.0*A/PI
+ SCALE1=(1.5*SQRT(3.0)*A*A-PI*RJ1**2)/(PI*RJ2**2-PI*RJ1**2)
+ ROUT=RJ2
+ ELSE IF(IWIGN.EQ.2) THEN
+* WIGNER CYLINDERIZATION HEXAGONAL.
+ ROUT=SQRT(1.5*SQRT(3.0)/PI)*A
+ ELSE IF(IWIGN.EQ.3) THEN
+* SANCHEZ CYLINDERIZATION HEXAGONAL.
+ SCALE2=SQRT(PI*SQRT(3.0)/6.0)
+ ROUT=SQRT(1.5*SQRT(3.0)/PI)*A
+ ENDIF
+ IF(ROUT.LE.RJ1) CALL XABORT('SYB002: CYLINDERIZATION ERROR.')
+*----
+* COMPUTE THE REDUCED COLLISION PROBABILITY MATRIX
+*----
+ SURFA=0.5*PI*ROUT
+ ALLOCATE(PP(J2,J2),RAYR2(J2+1))
+ DO 10 I=1,J2
+ RAYR2(I)=RAYRE(J1+I)
+ 10 CONTINUE
+ RAYR2(J2+1)=ROUT
+ SIGT2(J1+J2)=SIGT2(J1+J2)*SCALE1
+ CALL SYBALC(J2,J2,RAYR2,SIGT2(J1+1),MR,0.0,RZMAIL(IB),PP)
+ PSS=0.0
+ RJ1=0.0
+ DO 30 I=1,J2
+ PIS(I)=1.0
+ RJ2=RAYR2(I+1)**2
+ VV=PI*(RJ2-RJ1)
+ DO 20 J=1,J2
+ PIS(I)=PIS(I)-PP(I,J)*SIGT2(J1+J)
+ 20 CONTINUE
+ PSS=PSS+PIS(I)*SIGT2(J1+I)*VV/SURFA
+ RJ1=RJ2
+ 30 CONTINUE
+ DEALLOCATE(RAYR2)
+ PSS=1.0-SCALE2*PSS
+*----
+* COMPUTE THE REDUCED COLLISION PROBABILITY MATRIX FOR INCOMING
+* NEUTRONS
+*----
+ SURFA=(0.5*PI*ROUT)/SCALE2
+ RJ1=0.0
+ DO 40 I=1,J2-1
+ RJ2=PI*RAYRE(J1+I+1)**2
+ PSJ(I)=PIS(I)*(RJ2-RJ1)/SURFA
+ RJ1=RJ2
+ 40 CONTINUE
+ RJ2=PI*ROUT**2
+ PSJ(J2)=PIS(J2)*(RJ2-RJ1)*SCALE1/SURFA
+ SIGT2(J1+J2)=SIGT2(J1+J2)/SCALE1
+ IF(IMPX.GE.8) THEN
+ CALL SYBPRX(1,1,J2,JKG,SIGT2(J1+1),SIGW2(J1+1),PP(1,1),PIS(1),
+ 1 PSJ(1),PSS)
+ ENDIF
+*----
+* CHECK IF SCATTERING REDUCTION IS REQUIRED
+*----
+ LSKIP=.TRUE.
+ DO 70 I=1,J2
+ LSKIP=LSKIP.AND.(SIGW2(J1+I).EQ.0.0)
+ 70 CONTINUE
+*----
+* SCATTERING REDUCTION IF LSKIP=.FALSE.
+*----
+ IF(LSKIP) THEN
+* DO NOT PERFORM SCATTERING REDUCTION.
+ DO 90 I=1,J2
+ DO 80 J=1,J2-1
+ PIJW(IPIJ+(J-1)*J2+I)=PP(I,J)
+ 80 CONTINUE
+ PIJW(IPIJ+(J2-1)*J2+I)=PP(I,J2)*SCALE1
+ 90 CONTINUE
+ DO 100 I=1,J2
+ PISW(J1+I)=PIS(I)
+ PSJW(J1+I)=PSJ(I)
+ 100 CONTINUE
+ PSSW(JKG)=PSS
+ ELSE
+* COMPUTE THE SCATTERING-REDUCED COLLISION AND ESCAPE MATRICES.
+ DO 120 I=1,J2
+ DO 110 J=1,J2-1
+ PIJW(IPIJ+(J-1)*J2+I)=-PP(I,J)*SIGW2(J1+J)
+ 110 CONTINUE
+ PIJW(IPIJ+(J2-1)*J2+I)=-PP(I,J2)*SIGW2(J1+J2)*SCALE1
+ PIJW(IPIJ+(I-1)*J2+I)=1.0+PIJW(IPIJ+(I-1)*J2+I)
+ 120 CONTINUE
+ CALL ALINV(J2,PIJW(IPIJ+1),J2,IER)
+ IF(IER.NE.0) CALL XABORT('SYB002: SINGULAR MATRIX.')
+ ALLOCATE(WORK(J2))
+ DO 170 I=1,J2
+ DO 130 K=1,J2
+ WORK(K)=PIJW(IPIJ+(K-1)*J2+I)
+ 130 CONTINUE
+ DO 150 J=1,J2-1
+ WGAR=0.0
+ DO 140 K=1,J2
+ WGAR=WGAR+WORK(K)*PP(K,J)
+ 140 CONTINUE
+ PIJW(IPIJ+(J-1)*J2+I)=WGAR
+ 150 CONTINUE
+ WGAR=0.0
+ DO 155 K=1,J2
+ WGAR=WGAR+WORK(K)*PP(K,J2)
+ 155 CONTINUE
+ PIJW(IPIJ+(J2-1)*J2+I)=WGAR*SCALE1
+ WGAR=0.0
+ DO 160 K=1,J2
+ WGAR=WGAR+WORK(K)*PIS(K)
+ 160 CONTINUE
+ PISW(J1+I)=WGAR
+ 170 CONTINUE
+ DEALLOCATE(WORK)
+*
+* COMPUTE THE SCATTERING-REDUCED COLLISION PROBABILITY MATRIX
+* FOR INCOMING NEUTRONS.
+ DO 190 J=1,J2
+ WGAR=PSJ(J)
+ DO 180 K=1,J2
+ WGAR=WGAR+PSJ(K)*SIGW2(J1+K)*PIJW(IPIJ+(J-1)*J2+K)
+ 180 CONTINUE
+ PSJW(J1+J)=WGAR
+ 190 CONTINUE
+*
+* COMPUTE THE SCATTERING-REDUCED TRANSMISSION PROBABILITY MATRIX.
+ WGAR=PSS
+ DO 200 K=1,J2
+ WGAR=WGAR+PSJ(K)*SIGW2(J1+K)*PISW(J1+K)
+ 200 CONTINUE
+ PSSW(JKG)=WGAR
+ ENDIF
+ DEALLOCATE(PP)
+ IF(IMPX.GE.10) THEN
+ CALL SYBPRX(2,1,J2,JKG,SIGT2(J1+1),SIGW2(J1+1),PIJW(IPIJ+1),
+ 1 PISW(J1+1),PSJW(J1+1),PSSW(JKG))
+ ENDIF
+ IPIJ=IPIJ+J2*J2
+ 220 CONTINUE
+*----
+* SCRATCH STORAGE DEALLOCATION
+*----
+ DEALLOCATE(PSJ,PIS)
+ RETURN
+ END