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+*DECK SYBALC
+ SUBROUTINE SYBALC(NPIJ,MAXPTS,RAYRE,SIG,NGAUSS,ALBEDO,Z,PIJ)
+*
+*-----------------------------------------------------------------------
+*
+*Purpose:
+* Pij calculation in 1D cylindrical geometry. The tracking is computed
+* by subroutine SYBT1D.
+*
+*Copyright:
+* Copyright (C) 2005 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
+* NPIJ number of regions.
+* MAXPTS first dimension of matrix PIJ.
+* RAYRE radius of regions array.
+* SIG total cross section array.
+* NGAUSS number of Gauss points.
+* ALBEDO outside albedo.
+* Z tracking information.
+*
+*Parameters: output
+* PIJ reduced collision probability matrix.
+*
+*Reference:
+* A. Kavenoky, 'Calcul et utilisation des probabilites de premiere
+* collision pour les milieux heterogenes a une dimension: Les programmes
+* ALCOLL et CORTINA', note CEA-N-1077, Commissariat a l'energie
+* atomique, mars 1969.
+*
+*----
+* SUBROUTINE ARGUMENTS
+*----
+ INTEGER NPIJ,MAXPTS,NGAUSS
+ REAL RAYRE(NPIJ+1),SIG(NPIJ),PIJ(MAXPTS,NPIJ),ALBEDO,Z(*)
+*----
+* LOCAL VARIABLES
+*----
+ PARAMETER (MKI3=600,PI=3.1415926535,ZI30=0.785398164)
+ LOGICAL LGEMPT
+ REAL, ALLOCATABLE, DIMENSION(:,:) :: AUXI
+ COMMON /BICKL3/BI3(0:MKI3),BI31(0:MKI3),BI32(0:MKI3),PAS3,XLIM3,L3
+*----
+* SCRATCH STORAGE ALLOCATION
+*----
+ ALLOCATE(AUXI(NPIJ,3))
+*----
+* TEST FOR VOIDED REGIONS
+*----
+ LGEMPT=.FALSE.
+ VOLI=PI*RAYRE(1)**2
+ DO 10 IP=1,NPIJ
+ LGEMPT=LGEMPT.OR.(2.0*(RAYRE(IP+1)-RAYRE(IP))*SIG(IP).LE.0.004)
+ AUXI(IP,1)=PI*RAYRE(IP+1)**2-VOLI
+ AUXI(IP,2)=MAX(1.0E-10,SIG(IP))
+ VOLI=PI*RAYRE(IP+1)**2
+ 10 CONTINUE
+ SURF=2.0*PI*RAYRE(NPIJ+1)
+ PIJ(:MAXPTS,:NPIJ)=0.0
+ IZ=1
+ IF(.NOT.LGEMPT) THEN
+* NO VOIDED REGIONS DETECTED.
+ DO 42 IX=1,NPIJ
+ DO 41 I=1,NGAUSS
+ IZ=IZ+2
+ W=Z(IZ)
+ DO 20 ITR=IX,NPIJ
+ IZ=IZ+1
+ AUXI(ITR,3)=AUXI(ITR,2)*Z(IZ)
+ 20 CONTINUE
+ AUX0=2.0*AUXI(IX,3)
+ DII=AUX0-ZI30+TABKI(3,AUX0)
+ PIJ(IX,IX)=PIJ(IX,IX)+W*DII/AUXI(IX,2)**2
+ TAU=AUX0
+ TAU1J=0.0
+ DO 40 IP=IX+1,NPIJ
+ AUX1=AUXI(IP,3)
+ AUX2=TAU+2.0*AUXI(IP,3)
+ DII=AUX1-ZI30+TABKI(3,AUX1)
+ TAB0=TABKI(3,TAU)
+ TAB1=TABKI(3,TAU+AUX1)
+ TAB2=TABKI(3,AUX2)
+ CII=TAB0-2.0*TAB1+TAB2
+ TAB0=TABKI(3,TAU1J)
+ TAB1=TABKI(3,TAU1J+AUX0)
+ TAB2=TABKI(3,TAU1J+AUX1)
+ TAB3=TABKI(3,TAU1J+AUX0+AUX1)
+ CIJ1=TAB0-TAB1-TAB2+TAB3
+ PIJ(IP,IP)=PIJ(IP,IP)+W*(2.0*DII+CII)/AUXI(IP,2)**2
+ PIJ(IX,IP)=PIJ(IX,IP)+W*CIJ1/(AUXI(IX,2)*AUXI(IP,2))
+ TAUIJ=0.0
+ DO 30 JP=IP+1,NPIJ
+ AUX3=AUXI(JP,3)
+ IF(TAUIJ+AUX1+AUX3.GE.XLIM3) THEN
+ TAB0=TABKI(3,TAUIJ)
+ TAB1=TABKI(3,TAUIJ+AUX1)
+ TAB2=TABKI(3,TAUIJ+AUX3)
+ TAB3=TABKI(3,TAUIJ+AUX1+AUX3)
+ ELSE
+ K=NINT(TAUIJ*PAS3)
+ TAB0=BI3(K)+TAUIJ*(BI31(K)+TAUIJ*BI32(K))
+ TAUX=TAUIJ+AUX1
+ K=NINT(TAUX*PAS3)
+ TAB1=BI3(K)+TAUX*(BI31(K)+TAUX*BI32(K))
+ TAUX=TAUIJ+AUX3
+ K=NINT(TAUX*PAS3)
+ TAB2=BI3(K)+TAUX*(BI31(K)+TAUX*BI32(K))
+ TAUX=TAUIJ+AUX1+AUX3
+ K=NINT(TAUX*PAS3)
+ TAB3=BI3(K)+TAUX*(BI31(K)+TAUX*BI32(K))
+ ENDIF
+ CIJ2=TAB0-TAB1-TAB2+TAB3
+ IF(TAUIJ+AUX2+AUX3.GE.XLIM3) THEN
+ TAB0=TABKI(3,TAUIJ+TAU+AUX1)
+ TAB1=TABKI(3,TAUIJ+AUX2)
+ TAB2=TABKI(3,TAUIJ+TAU+AUX1+AUX3)
+ TAB3=TABKI(3,TAUIJ+AUX2+AUX3)
+ ELSE
+ TAUX=TAUIJ+TAU+AUX1
+ K=NINT(TAUX*PAS3)
+ TAB0=BI3(K)+TAUX*(BI31(K)+TAUX*BI32(K))
+ TAUX=TAUIJ+AUX2
+ K=NINT(TAUX*PAS3)
+ TAB1=BI3(K)+TAUX*(BI31(K)+TAUX*BI32(K))
+ TAUX=TAUIJ+TAU+AUX1+AUX3
+ K=NINT(TAUX*PAS3)
+ TAB2=BI3(K)+TAUX*(BI31(K)+TAUX*BI32(K))
+ TAUX=TAUIJ+AUX2+AUX3
+ K=NINT(TAUX*PAS3)
+ TAB3=BI3(K)+TAUX*(BI31(K)+TAUX*BI32(K))
+ ENDIF
+ CIJ3=TAB0-TAB1-TAB2+TAB3
+ PIJ(IP,JP)=PIJ(IP,JP)+W*(CIJ2+CIJ3)/(AUXI(IP,2)*AUXI(JP,2))
+ TAUIJ=TAUIJ+AUX3
+ 30 CONTINUE
+ TAU=AUX2
+ TAU1J=TAU1J+AUX1
+ 40 CONTINUE
+ 41 CONTINUE
+ 42 CONTINUE
+ ELSE
+ DO 72 IX=1,NPIJ
+ DO 71 I=1,NGAUSS
+ IZ=IZ+2
+ W=Z(IZ)
+ DO 50 ITR=IX,NPIJ
+ IZ=IZ+1
+ AUXI(ITR,3)=AUXI(ITR,2)*Z(IZ)
+ 50 CONTINUE
+ CALL SYB33C(DII,2.0*AUXI(IX,3))
+ PIJ(IX,IX)=PIJ(IX,IX)+W*DII/AUXI(IX,2)**2
+ TAU=2.0*AUXI(IX,3)
+ TAU1J=0.0
+ DO 70 IP=IX+1,NPIJ
+ CALL SYB33C(DII,AUXI(IP,3))
+ CALL SYB31C(CII,TAU,AUXI(IP,3),AUXI(IP,3))
+ CALL SYB31C(CIJ1,TAU1J,2.0*AUXI(IX,3),AUXI(IP,3))
+ PIJ(IP,IP)=PIJ(IP,IP)+W*(2.0*DII+CII)/AUXI(IP,2)**2
+ PIJ(IX,IP)=PIJ(IX,IP)+W*CIJ1/(AUXI(IX,2)*AUXI(IP,2))
+ TAUIJ=0.0
+ DO 60 JP=IP+1,NPIJ
+ CALL SYB31C(CIJ2,TAUIJ,AUXI(IP,3),AUXI(JP,3))
+ CALL SYB31C(CIJ3,TAUIJ+TAU+AUXI(IP,3),AUXI(IP,3),AUXI(JP,3))
+ PIJ(IP,JP)=PIJ(IP,JP)+W*(CIJ2+CIJ3)/(AUXI(IP,2)*AUXI(JP,2))
+ TAUIJ=TAUIJ+AUXI(JP,3)
+ 60 CONTINUE
+ TAU=TAU+2*AUXI(IP,3)
+ TAU1J=TAU1J+AUXI(IP,3)
+ 70 CONTINUE
+ 71 CONTINUE
+ 72 CONTINUE
+ ENDIF
+*
+ DO 85 I=1,NPIJ
+ DO 80 J=I,NPIJ
+ VAL=PIJ(I,J)
+ PIJ(I,J)=VAL/AUXI(I,1)
+ PIJ(J,I)=VAL/AUXI(J,1)
+ 80 CONTINUE
+ 85 CONTINUE
+*----
+* COMPUTING REFLECTED PROBABILITIES ASSUMING WHITE BOUNDARY CONDITION.
+*----
+ IF(ALBEDO.NE.0.0) THEN
+ PSS=1.0
+ DO 100 IK=1,NPIJ
+ AUXI(IK,3)=1.0
+ DO 90 JK=1,NPIJ
+ AUXI(IK,3)=AUXI(IK,3)-PIJ(IK,JK)*AUXI(JK,2)
+ 90 CONTINUE
+ PSS=PSS-4.0*AUXI(IK,1)*AUXI(IK,2)*AUXI(IK,3)/SURF
+ 100 CONTINUE
+ AUX0=ALBEDO/(1.0-ALBEDO*PSS)
+ DO 120 JK=1,NPIJ
+ AUX1=AUX0*(4.0*AUXI(JK,1)/SURF)*AUXI(JK,3)
+ DO 110 IK=1,NPIJ
+ PIJ(IK,JK)=PIJ(IK,JK)+AUXI(IK,3)*AUX1
+ 110 CONTINUE
+ 120 CONTINUE
+ ENDIF
+*----
+* SCRATCH STORAGE DEALLOCATION
+*----
+ DEALLOCATE(AUXI)
+ RETURN
+ END