C The code was originally developed by Michael Mishchenko at the NASA C Goddard Institute for Space Studies, New York. This research C was funded by the NASA Radiation Science Program. C The code can be used without limitations in any not-for- C profit scientific research. The only request is that in any C publication using the code the source of the code be acknowledged C and relevant references be made. C This version code has been modified by Cory Davis (University C of Edinburgh) for inclusion in the the PyARTS atmospheric radiative C transfer package SUBROUTINE TMQ(RAT,NDISTR,AXMAX,NPNAX,B,GAM,NKMAX,DEPS,NP,DLAM, & DMRR,DMRI,DDELT,NPNA,NDGS,R1RAT,R2RAT,QUIET,REFF,VEFF,CEXT, & CSCA,WALB,ASYMM,F11,F22,F33,F44,F12,F34,ERRMSG) IMPLICIT REAL*8 (A-H,O-Z) INCLUDE 'tmq.par.f' REAL*16 LAM,MRR,MRI,X(NPNG2),W(NPNG2),S(NPNG2),SS(NPNG2), * AN(NPN1),R(NPNG2),DR(NPNG2),PPI,PIR,PII,P,EPS,A, * DDR(NPNG2),DRR(NPNG2),DRI(NPNG2),ANN(NPN1,NPN1) REAL*8 XG(1000),WG(1000),TR1(NPN2,NPN2),TI1(NPN2,NPN2), & ALPH1(NPL),ALPH2(NPL),ALPH3(NPL),ALPH4(NPL),BET1(NPL), & BET2(NPL),XG1(2000),WG1(2000), & AL1(NPL),AL2(NPL),AL3(NPL),AL4(NPL),BE1(NPL),BE2(NPL) REAL*4 & RT11(NPN6,NPN4,NPN4),RT12(NPN6,NPN4,NPN4), & RT21(NPN6,NPN4,NPN4),RT22(NPN6,NPN4,NPN4), & IT11(NPN6,NPN4,NPN4),IT12(NPN6,NPN4,NPN4), & IT21(NPN6,NPN4,NPN4),IT22(NPN6,NPN4,NPN4) INTEGER QUIET CHARACTER ERRMSG*100 Cf2py intent(out) REFF,VEFF,CEXT,CSCA,WALB,ASYMM,F11,F22,F33,F44,F12,F34,ERRMSG Cf2py depend(npna) F11,F22,F33,F44,F12,F34 COMMON /CT/ TR1,TI1 COMMON /TMAT/ RT11,RT12,RT21,RT22,IT11,IT12,IT21,IT22 COMMON /CHOICE/ ICHOICE P=QACOS(-1Q0) !changed qarcos to qacos PIN=P C Get quad versions of double inputs LAM=DLAM MRR=DMRR MRI=DMRI EPS=DEPS C OPEN FILES ******************************************************* c OPEN (6,FILE='test') c OPEN (10,FILE='tmatr.write') C INPUT DATA ******************************************************** C RAT=0.5D0 C NDISTR=3 C AXMAX=1D0 C NPNAX=2 C B=1D-1 C GAM=0.5D0 C NKMAX=5 C EPS=2D0 C NP=-1 C LAM=0.5D0 C MRR=1.33D0 C MRI=0.001D0 C DDELT=0.001D0 C NPNA=19 C NDGS=2 ICHOICE=1 NCHECK=0 IF (NP.EQ.-1.OR.NP.EQ.-2) NCHECK=1 IF (NP.GT.0.AND.(-1)**NP.EQ.1) NCHECK=1 C WRITE (6,5454) ICHOICE,NCHECK 5454 FORMAT ('ICHOICE=',I1,' NCHECK=',I1) DAX=AXMAX/NPNAX C DLAM=LAM C DMRR=MRR C DMRI=MRI C DEPS=EPS IF (DABS(RAT-1D0).GT.1D-8.AND.NP.EQ.-1) CALL SAREA (DEPS,RAT) IF (DABS(RAT-1D0).GT.1D-8.AND.NP.GE.0) CALL SURFCH(NP,DEPS,RAT) IF (DABS(RAT-1D0).GT.1D-8.AND.NP.EQ.-2) CALL SAREAC (DEPS,RAT) C PRINT 8000, RAT 8000 FORMAT ('RAT=',F8.6) IF(QUIET.EQ.0) THEN IF(NP.EQ.-1.AND.EPS.GE.1D0) PRINT 7000,EPS IF(NP.EQ.-1.AND.EPS.LT.1D0) PRINT 7001,EPS IF(NP.GE.0) PRINT 7100,NP,EPS IF(NP.EQ.-2.AND.EPS.GE.1D0) PRINT 7150,EPS IF(NP.EQ.-2.AND.EPS.LT.1D0) PRINT 7151,EPS PRINT 7400, LAM,MRR,MRI PRINT 7200,DDELT ENDIF 7000 FORMAT('RANDOMLY ORIENTED OBLATE SPHEROIDS, A/B=',F11.7) 7001 FORMAT('RANDOMLY ORIENTED PROLATE SPHEROIDS, A/B=',F11.7) 7100 FORMAT('RANDOMLY ORIENTED CHEBYSHEV PARTICLES, T', & I1,'(',F5.2,')') 7150 FORMAT('RANDOMLY ORIENTED OBLATE CYLINDERS, D/L=',F11.7) 7151 FORMAT('RANDOMLY ORIENTED PROLATE CYLINDERS, D/L=',F11.7) 7200 format ('ACCURACY OF COMPUTATIONS DDELT = ',d8.2) 7400 FORMAT('LAM=',F10.6,3X,'MRR=',D10.4,3X,'MRI=',D10.4) DDELT=0.1D0*DDELT DO 600 IAX=1,NPNAX AXI=AXMAX-DAX*DFLOAT(IAX-1) R1=R1RAT*AXI !0.89031D0*AXI R2=R2RAT*AXI !1.56538D0*AXI NK=MAX(IDINT(AXI*NKMAX/AXMAX+2),1) !MAX call added by Cory to avoid occasional IF (NK.GT.1000) THEN !problems with nkmax=-1 WRITE (ERRMSG,8001) NK PRINT *,ERRMSG RETURN ENDIF IF (NDISTR.EQ.3) CALL POWER (AXI,B,R1,R2) 8001 FORMAT ('NK=',I4,' I.E., IS GREATER THAN 1000. ', & 'EXECUTION TERMINATED.') CALL GAUSS (NK,0,0,XG,WG) Z1=(R2-R1)*0.5D0 Z2=(R1+R2)*0.5D0 Z3=R1*0.5D0 IF (NDISTR.EQ.5) GO TO 3 DO I=1,NK XG1(I)=Z1*XG(I)+Z2 WG1(I)=WG(I)*Z1 ENDDO GO TO 4 3 DO I=1,NK XG1(I)=Z3*XG(I)+Z3 WG1(I)=WG(I)*Z3 ENDDO DO I=NK+1,2*NK II=I-NK XG1(I)=Z1*XG(II)+Z2 WG1(I)=WG(II)*Z1 ENDDO NK=NK*2 4 CALL DISTRB (NK,XG1,WG1,NDISTR,AXI,B,GAM,R1,R2, & QUIET,REFF,VEFF,P) IF (QUIET.EQ.0) THEN PRINT 8002,R1,R2 8002 FORMAT('R1=',F10.6,' R2=',F10.6) IF (DABS(RAT-1D0).LE.1D-6) PRINT 8003, REFF,VEFF IF (DABS(RAT-1D0).GT.1D-6) PRINT 8004, REFF,VEFF 8003 FORMAT('EQUAL-VOLUME-SPHERE REFF=',F8.4,' VEFF=',F7.4) 8004 FORMAT('EQUAL-SURFACE-AREA-SPHERE REFF=',F8.4, & ' VEFF=',F7.4) PRINT 7250,NK 7250 FORMAT('NUMBER OF GAUSSIAN QUADRATURE POINTS ', & 'IN SIZE AVERAGING =',I4) ENDIF DO I=1,NPL ALPH1(I)=0D0 ALPH2(I)=0D0 ALPH3(I)=0D0 ALPH4(I)=0D0 BET1(I)=0D0 BET2(I)=0D0 ENDDO CSCAT=0D0 CEXTIN=0D0 L1MAX=0 DO 500 INK=1,NK I=NK-INK+1 A=RAT*XG1(I) XEV=2D0*PIN*A/DLAM IXXX=XEV+4.05D0*XEV**0.333333D0 INM1=MAX0(4,IXXX) IF (INM1.GE.NPN1) THEN WRITE (ERRMSG,7333) NPN1 PRINT *,ERRMSG RETURN END IF 7333 FORMAT('CONVERGENCE IS NOT OBTAINED FOR NPN1=',I3, & '. EXECUTION TERMINATED') QEXT1=0D0 QSCA1=0D0 DO 50 NMA=INM1,NPN1 NMAX=NMA MMAX=1 NGAUSS=NMAX*NDGS IF (NGAUSS.GT.NPNG1) THEN WRITE (ERRMSG,7340) NGAUSS PRINT *,ERRMSG RETURN END IF 7340 FORMAT('NGAUSS =',I3,' I.E. IS GREATER THAN NPNG1.', & ' EXECUTION TERMINATED') 7334 FORMAT(' NMAX =', I3,' DC2=',D8.2,' DC1=',D8.2) 7335 FORMAT(' NMAX1 =', I3,' DC2=',D8.2, & ' DC1=',D8.2) CALL CONSTQ(NGAUSS,NMAX,MMAX,P,X,W,AN,ANN,S,SS,NP,EPS) CALL VARYQ(LAM,MRR,MRI,A,EPS,NP,NGAUSS,X,P,PPI,PIR,PII,R, & DR,DDR,DRR,DRI,NMAX) CALL TMATR0Q (NGAUSS,X,W,AN,ANN,S,SS,PPI,PIR,PII,R,DR, & DDR,DRR,DRI,NMAX,NCHECK) QEXT=0D0 QSCA=0D0 DO N=1,NMAX N1=N+NMAX TR1NN=TR1(N,N) TI1NN=TI1(N,N) TR1NN1=TR1(N1,N1) TI1NN1=TI1(N1,N1) DN1=DFLOAT(2*N+1) QSCA=QSCA+DN1*(TR1NN*TR1NN+TI1NN*TI1NN & +TR1NN1*TR1NN1+TI1NN1*TI1NN1) QEXT=QEXT+(TR1NN+TR1NN1)*DN1 ENDDO DSCA=DABS((QSCA1-QSCA)/QSCA) DEXT=DABS((QEXT1-QEXT)/QEXT) C PRINT 7334, NMAX,DSCA,DEXT QEXT1=QEXT QSCA1=QSCA NMIN=DFLOAT(NMAX)/2D0+1D0 DO 10 N=NMIN,NMAX N1=N+NMAX TR1NN=TR1(N,N) TI1NN=TI1(N,N) TR1NN1=TR1(N1,N1) TI1NN1=TI1(N1,N1) DN1=DFLOAT(2*N+1) DQSCA=DN1*(TR1NN*TR1NN+TI1NN*TI1NN & +TR1NN1*TR1NN1+TI1NN1*TI1NN1) DQEXT=(TR1NN+TR1NN1)*DN1 DQSCA=DABS(DQSCA/QSCA) DQEXT=DABS(DQEXT/QEXT) NMAX1=N IF (DQSCA.LE.DDELT.AND.DQEXT.LE.DDELT) GO TO 12 10 CONTINUE 12 CONTINUE c PRINT 7335, NMAX1,DQSCA,DQEXT IF(DSCA.LE.DDELT.AND.DEXT.LE.DDELT) GO TO 55 IF (NMA.EQ.NPN1) THEN WRITE (ERRMSG,7333) NPN1 PRINT *,ERRMSG RETURN END IF 50 CONTINUE 55 NNNGGG=NGAUSS+1 IF (NGAUSS.EQ.NPNG1) PRINT 7336 MMAX=NMAX1 DO 150 NGAUS=NNNGGG,NPNG1 NGAUSS=NGAUS NGGG=2*NGAUSS 7336 FORMAT('WARNING: NGAUSS=NPNG1') 7337 FORMAT(' NG=',I3,' DC2=',D8.2,' DC1=',D8.2) CALL CONSTQ(NGAUSS,NMAX,MMAX,P,X,W,AN,ANN,S,SS,NP,EPS) CALL VARYQ(LAM,MRR,MRI,A,EPS,NP,NGAUSS,X,P,PPI,PIR,PII,R, & DR,DDR,DRR,DRI,NMAX) CALL TMATR0Q (NGAUSS,X,W,AN,ANN,S,SS,PPI,PIR,PII,R,DR, & DDR,DRR,DRI,NMAX,NCHECK) QEXT=0D0 QSCA=0D0 DO 104 N=1,NMAX N1=N+NMAX TR1NN=TR1(N,N) TI1NN=TI1(N,N) TR1NN1=TR1(N1,N1) TI1NN1=TI1(N1,N1) DN1=DFLOAT(2*N+1) QSCA=QSCA+DN1*(TR1NN*TR1NN+TI1NN*TI1NN & +TR1NN1*TR1NN1+TI1NN1*TI1NN1) QEXT=QEXT+(TR1NN+TR1NN1)*DN1 104 CONTINUE DSCA=DABS((QSCA1-QSCA)/QSCA) DEXT=DABS((QEXT1-QEXT)/QEXT) c PRINT 7337, NGGG,DSCA,DEXT QEXT1=QEXT QSCA1=QSCA IF(DSCA.LE.DDELT.AND.DEXT.LE.DDELT) GO TO 155 IF (NGAUS.EQ.NPNG1) PRINT 7336 150 CONTINUE 155 CONTINUE QSCA=0D0 QEXT=0D0 NNM=NMAX*2 DO 204 N=1,NNM QEXT=QEXT+TR1(N,N) 204 CONTINUE IF (NMAX1.GT.NPN4) THEN WRITE (ERRMSG,7550) NMAX1 PRINT *,ERRMSG END IF 7550 FORMAT ('nmax1 = ',I3, ', i.e. greater than NPN4.', & ' Execution terminated') IF (NMAX1.GT.NPN4) STOP DO 213 N2=1,NMAX1 NN2=N2+NMAX DO 213 N1=1,NMAX1 NN1=N1+NMAX ZZ1=TR1(N1,N2) RT11(1,N1,N2)=ZZ1 ZZ2=TI1(N1,N2) IT11(1,N1,N2)=ZZ2 ZZ3=TR1(N1,NN2) RT12(1,N1,N2)=ZZ3 ZZ4=TI1(N1,NN2) IT12(1,N1,N2)=ZZ4 ZZ5=TR1(NN1,N2) RT21(1,N1,N2)=ZZ5 ZZ6=TI1(NN1,N2) IT21(1,N1,N2)=ZZ6 ZZ7=TR1(NN1,NN2) RT22(1,N1,N2)=ZZ7 ZZ8=TI1(NN1,NN2) IT22(1,N1,N2)=ZZ8 QSCA=QSCA+ZZ1*ZZ1+ZZ2*ZZ2+ZZ3*ZZ3+ZZ4*ZZ4 & +ZZ5*ZZ5+ZZ6*ZZ6+ZZ7*ZZ7+ZZ8*ZZ8 213 CONTINUE C PRINT 7800,0,DABS(QEXT),QSCA,NMAX DO 220 M=1,NMAX1 CALL TMATRQ(M,NGAUSS,X,W,AN,ANN,S,SS,PPI,PIR,PII,R,DR, & DDR,DRR,DRI,NMAX,NCHECK) NM=NMAX-M+1 NM1=NMAX1-M+1 M1=M+1 QSC=0D0 DO 214 N2=1,NM1 NN2=N2+M-1 N22=N2+NM DO 214 N1=1,NM1 NN1=N1+M-1 N11=N1+NM ZZ1=TR1(N1,N2) RT11(M1,NN1,NN2)=ZZ1 ZZ2=TI1(N1,N2) IT11(M1,NN1,NN2)=ZZ2 ZZ3=TR1(N1,N22) RT12(M1,NN1,NN2)=ZZ3 ZZ4=TI1(N1,N22) IT12(M1,NN1,NN2)=ZZ4 ZZ5=TR1(N11,N2) RT21(M1,NN1,NN2)=ZZ5 ZZ6=TI1(N11,N2) IT21(M1,NN1,NN2)=ZZ6 ZZ7=TR1(N11,N22) RT22(M1,NN1,NN2)=ZZ7 ZZ8=TI1(N11,N22) IT22(M1,NN1,NN2)=ZZ8 QSC=QSC+(ZZ1*ZZ1+ZZ2*ZZ2+ZZ3*ZZ3+ZZ4*ZZ4 & +ZZ5*ZZ5+ZZ6*ZZ6+ZZ7*ZZ7+ZZ8*ZZ8)*2D0 214 CONTINUE NNM=2*NM QXT=0D0 DO 215 N=1,NNM QXT=QXT+TR1(N,N)*2D0 215 CONTINUE QSCA=QSCA+QSC QEXT=QEXT+QXT C PRINT 7800,M,DABS(QXT),QSC,NMAX 7800 FORMAT(' m=',I3,' qxt=',D12.6,' qsc=',D12.6, & ' nmax=',I3) 220 CONTINUE COEFF1=LAM*LAM*0.5D0/P CSCA=QSCA*COEFF1 CEXT=-QEXT*COEFF1 c PRINT 7880, NMAX,NMAX1 7880 FORMAT ('nmax=',I3,' nmax1=',I3) CALL GSPQ (NMAX1,CSCA,LAM,AL1,AL2,AL3,AL4,BE1,BE2,LMAX) L1M=LMAX+1 L1MAX=MAX(L1MAX,L1M) WGII=WG1(I) WGI=WGII*CSCA DO 250 L1=1,L1M ALPH1(L1)=ALPH1(L1)+AL1(L1)*WGI ALPH2(L1)=ALPH2(L1)+AL2(L1)*WGI ALPH3(L1)=ALPH3(L1)+AL3(L1)*WGI ALPH4(L1)=ALPH4(L1)+AL4(L1)*WGI BET1(L1)=BET1(L1)+BE1(L1)*WGI BET2(L1)=BET2(L1)+BE2(L1)*WGI 250 CONTINUE CSCAT=CSCAT+WGI CEXTIN=CEXTIN+CEXT*WGII C PRINT 6070, I,NMAX,NMAX1,NGAUSS 6070 FORMAT(4I6) 500 CONTINUE DO 510 L1=1,L1MAX ALPH1(L1)=ALPH1(L1)/CSCAT ALPH2(L1)=ALPH2(L1)/CSCAT ALPH3(L1)=ALPH3(L1)/CSCAT ALPH4(L1)=ALPH4(L1)/CSCAT BET1(L1)=BET1(L1)/CSCAT BET2(L1)=BET2(L1)/CSCAT 510 CONTINUE WALB=CSCAT/CEXTIN CALL HOVENR(L1MAX,ALPH1,ALPH2,ALPH3,ALPH4,BET1,BET2,QUIET) ASYMM=ALPH1(2)/3D0 IF (QUIET.EQ.0) THEN PRINT 9100,CEXTIN,CSCAT,WALB,ASYMM 9100 FORMAT('CEXT=',D12.6,2X,'CSCA=',D12.6,2X, & 2X,'W=',D12.6,2X,'=',D12.6) IF (WALB.GT.1D0) PRINT 9111 9111 FORMAT ('WARNING: W IS GREATER THAN 1') ENDIF C WRITE (10,580) WALB,L1MAX C DO L=1,L1MAX C WRITE (10,575) ALPH1(L),ALPH2(L),ALPH3(L),ALPH4(L), C & BET1(L),BET2(L) C ENDDO 575 FORMAT(6D14.7) 580 FORMAT(D14.8,I8) LMAX=L1MAX-1 CALL MATRQ (ALPH1,ALPH2,ALPH3,ALPH4,BET1,BET2,LMAX,NPNA,QUIET, & F11,F22,F33,F44,F12,F34) 600 CONTINUE C ITIME=MCLOCK() C TIME=DFLOAT(ITIME)/6000D0 C PRINT 1001,TIME C 1001 FORMAT (' time =',F8.2,' min') RETURN END C********************************************************************** C * C INPUT PARAMETERS: * C * C NG = 2*NGAUSS - number of gaussian quadrature points on the * C interval (-1,1). NGAUSS.LE.NPNG1 * C NMAX,MMAX - maximum dimensions of the arrays. NMAX.LE.NPN1 * C MMAX.LE.NPN1 * C P - pi * C * C OUTPUT PARAMETERS: * C * C X,W - points and weights of the quadrature formula * C AN(N) = n*(n+1) * C ANN(N1,N2) = (1/2)*sqrt((2*n1+1)*(2*n2+1)/(n1*(n1+1)*n2*(n2+1))) * C S(I)=1/sin(arccos(x(i))) * C SS(I)=S(I)**2 * C * C********************************************************************** SUBROUTINE CONSTQ (NGAUSS,NMAX,MMAX,P,X,W,AN,ANN,S,SS,NP,EPS) IMPLICIT REAL*16 (A-H,O-Z) INCLUDE 'tmq.par.f' REAL*16 X(NPNG2),W(NPNG2),X1(NPNG1),W1(NPNG1), * X2(NPNG1),W2(NPNG1), * S(NPNG2),SS(NPNG2), * AN(NPN1),ANN(NPN1,NPN1),DD(NPN1) DO 10 N=1,NMAX NN=N*(N+1) AN(N)=QFLOAT(NN) D=QSQRT(QFLOAT(2*N+1)/QFLOAT(NN)) DD(N)=D DO 10 N1=1,N DDD=D*DD(N1)*0.5Q0 ANN(N,N1)=DDD ANN(N1,N)=DDD 10 CONTINUE NG=2*NGAUSS IF (NP.EQ.-2) GO TO 11 CALL QGAUSS(NG,0,0,X,W) GO TO 19 11 NG1=DFLOAT(NGAUSS)/2D0 NG2=NGAUSS-NG1 XX=-QCOS(QATAN(EPS)) CALL QGAUSS(NG1,0,0,X1,W1) CALL QGAUSS(NG2,0,0,X2,W2) DO 12 I=1,NG1 W(I)=0.5Q0*(XX+1Q0)*W1(I) X(I)=0.5Q0*(XX+1Q0)*X1(I)+0.5Q0*(XX-1Q0) 12 CONTINUE DO 14 I=1,NG2 W(I+NG1)=-0.5Q0*XX*W2(I) X(I+NG1)=-0.5Q0*XX*X2(I)+0.5Q0*XX 14 CONTINUE DO 16 I=1,NGAUSS W(NG-I+1)=W(I) X(NG-I+1)=-X(I) 16 CONTINUE 19 DO 20 I=1,NGAUSS Y=X(I) Y=1Q0/(1Q0-Y*Y) SS(I)=Y SS(NG-I+1)=Y Y=QSQRT(Y) S(I)=Y S(NG-I+1)=Y 20 CONTINUE RETURN END C*************************************************************** SUBROUTINE QGAUSS ( N,IND1,IND2,Z,W ) IMPLICIT REAL*16 (A-H,P-Z) REAL*16 Z(N),W(N) DATA A,B,C /1Q0,2Q0,3Q0/ IND=MOD(N,2) K=N/2+IND F=QFLOAT(N) DO 100 I=1,K M=N+1-I IF(I.EQ.1) X=A-B/((F+A)*F) IF(I.EQ.2) X=(Z(N)-A)*4Q0+Z(N) IF(I.EQ.3) X=(Z(N-1)-Z(N))*1.6Q0+Z(N-1) IF(I.GT.3) X=(Z(M+1)-Z(M+2))*C+Z(M+3) IF(I.EQ.K.AND.IND.EQ.1) X=0Q0 NITER=0 CHECK=1Q-32 10 PB=1Q0 NITER=NITER+1 IF (NITER.LE.100) GO TO 15 c PRINT 5000, CHECK CHECK=CHECK*10Q0 15 PC=X DJ=A DO 20 J=2,N DJ=DJ+A PA=PB PB=PC 20 PC=X*PB+(X*PB-PA)*(DJ-A)/DJ PA=A/((PB-X*PC)*F) PB=PA*PC*(A-X*X) X=X-PB IF(QABS(PB).GT.CHECK*QABS(X)) GO TO 10 Z(M)=X W(M)=PA*PA*(A-X*X) IF(IND1.EQ.0) W(M)=B*W(M) IF(I.EQ.K.AND.IND.EQ.1) GO TO 100 Z(I)=-Z(M) W(I)=W(M) 100 CONTINUE 5000 format ('QGAUSS DOES NOT CONVERGE, CHECK=',Q10.3) IF(IND2.NE.1) GO TO 110 PRINT 1100,N 1100 FORMAT(' *** POINTS AND WEIGHTS OF GAUSSIAN QUADRATURE FORMULA', * ' OF ',I4,'-TH ORDER') DO 105 I=1,K ZZ=-Z(I) 105 PRINT 1200,I,ZZ,I,W(I) 1200 FORMAT(' ',4X,'X(',I4,') = ',F17.14,5X,'W(',I4,') = ',F17.14) GO TO 115 110 CONTINUE C PRINT 1300,N 1300 FORMAT(' GAUSSIAN QUADRATURE FORMULA OF ',I4,'-TH ORDER IS USED') 115 CONTINUE IF(IND1.EQ.0) GO TO 140 DO 120 I=1,N 120 Z(I)=(A+Z(I))/B 140 CONTINUE RETURN END C********************************************************************** C * C INPUT PARAMETERS: * C * C LAM - wavelength of light * C MRR and MRI - real and imaginary parts of the refractive index * C A,EPS,NP - specify shape of the particle * C (see subroutines RSP1, RSP2, and RSP3) * C NG = NGAUSS*2 - number of gaussian quadrature points on the * C interval (-1,1) * C X - gaussian division points * C P - pi * C * C OUTPUT INFORMATION: * C * C PPI = PI**2 , where PI = (2*P)/LAM (wavenumber) * C PIR = PPI*MRR * C PII = PPI*MRI * C R and DR - see subroutines RSP1, RSP2, and RSP3 * C DDR=1/(PI*SQRT(R)) * C DRR+I*DRI=DDR/(MRR+I*MRI) * C NMAX - dimension of T(m)-matrices * C arrays J,Y,JR,JI,DJ,DY,DJR,DJI are transferred through * C COMMON /CBESS/ - see subroutine BESS * C * C********************************************************************** SUBROUTINE VARYQ (LAM,MRR,MRI,A,EPS,NP,NGAUSS,X,P,PPI,PIR,PII, * R,DR,DDR,DRR,DRI,NMAX) INCLUDE 'tmq.par.f' IMPLICIT REAL*16 (A-H,O-Z) REAL*16 X(NPNG2),R(NPNG2),DR(NPNG2),MRR,MRI,LAM, * Z(NPNG2),ZR(NPNG2),ZI(NPNG2), * J(NPNG2,NPN1),Y(NPNG2,NPN1),JR(NPNG2,NPN1), * JI(NPNG2,NPN1),DJ(NPNG2,NPN1), * DJR(NPNG2,NPN1),DJI(NPNG2,NPN1),DDR(NPNG2), * DRR(NPNG2),DRI(NPNG2), * DY(NPNG2,NPN1) COMMON /CBESS/ J,Y,JR,JI,DJ,DY,DJR,DJI NG=NGAUSS*2 IF (NP.EQ.-1) CALL RSP1Q(X,NG,NGAUSS,A,EPS,NP,R,DR) IF (NP.GE.0) CALL RSP2Q(X,NG,A,EPS,NP,R,DR) IF (NP.EQ.-2) CALL RSP3Q(X,NG,NGAUSS,A,EPS,R,DR) PI=P*2Q0/LAM PPI=PI*PI PIR=PPI*MRR PII=PPI*MRI V=1Q0/(MRR*MRR+MRI*MRI) PRR=MRR*V PRI=-MRI*V TA=0Q0 DO 10 I=1,NG VV=QSQRT(R(I)) V=VV*PI TA=MAX(TA,V) VV=1Q0/V DDR(I)=VV DRR(I)=PRR*VV DRI(I)=PRI*VV V1=V*MRR V2=V*MRI Z(I)=V ZR(I)=V1 ZI(I)=V2 10 CONTINUE IF (NMAX.GT.NPN1) PRINT 9000,NMAX,NPN1 IF (NMAX.GT.NPN1) STOP 9000 FORMAT(' NMAX = ',I2,', i.e., greater than ',I3) TB=TA*QSQRT(MRR*MRR+MRI*MRI) TB=QMAX1(TB,QFLOAT(NMAX)) NNMAX1=8.0Q0*QSQRT(QMAX1(TA,QFLOAT(NMAX)))+3Q0 NNMAX2=(TB+4Q0*(TB**0.33333Q0)+8.0Q0*QSQRT(TB)) NNMAX2=NNMAX2-NMAX+5 CALL BESSQ(Z,ZR,ZI,NG,NMAX,NNMAX1,NNMAX2) RETURN END C********************************************************************** C * C Calculation of the functions R(I)=r(y(I))**2 and * C DR(I)=((d/dy)r(y))/r(y) and horizontal semi-axis A * C for a spheroid specified by the parameters REV (equal-volume- * C sphere radius) and EPS=A/B (ratio of the semi-axes). * C Y(I)=arccos(X(I)) * C 1.LE.I.LE.NGAUSS * C X - arguments * C * C********************************************************************** SUBROUTINE RSP1Q (X,NG,NGAUSS,REV,EPS,NP,R,DR) IMPLICIT REAL*16 (A-H,O-Z) REAL*16 X(NG),R(NG),DR(NG) A=REV*EPS**(1Q0/3Q0) AA=A*A EE=EPS*EPS EE1=EE-1Q0 DO 50 I=1,NGAUSS C=X(I) CC=C*C SS=1Q0-CC S=QSQRT(SS) RR=1Q0/(SS+EE*CC) R(I)=AA*RR R(NG-I+1)=R(I) DR(I)=RR*C*S*EE1 DR(NG-I+1)=-DR(I) 50 CONTINUE RETURN END C********************************************************************** C * C Calculation of the functions R(I)=r(y(i))**2 and * C DR(I)=((d/dy)r(y))/r(y) and parameter R0 for a Chebyshev * C particle specified by the parameters REV (equal-volume-sphere * C radius), EPS, and N. * C Y(I)=arccos(X(I)) * C 1.LE.I.LE.NGAUSS * C X - arguments * C * C********************************************************************** SUBROUTINE RSP2Q (X,NG,REV,EPS,N,R,DR) IMPLICIT REAL*16 (A-H,O-Z) REAL*16 X(NG),R(NG),DR(NG) DNP=QFLOAT(N) DN=DNP*DNP DN4=DN*4Q0 EP=EPS*EPS A=1Q0+1.5Q0*EP*(DN4-2Q0)/(DN4-1Q0) I=(DNP+0.1Q0)*0.5Q0 I=2*I IF (I.EQ.N) A=A-3Q0*EPS*(1Q0+0.25Q0*EP)/ * (DN-1Q0)-0.25Q0*EP*EPS/(9Q0*DN-1Q0) R0=REV*A**(-1Q0/3Q0) DO 50 I=1,NG XI=QACOS(X(I))*DNP RI=R0*(1Q0+EPS*QCOS(XI)) R(I)=RI*RI DR(I)=-R0*EPS*DNP*QSIN(XI)/RI 50 CONTINUE RETURN END C********************************************************************** C * C Calculation of the functions R(I)=R(Y(I))**2 and * C DR(I)=((d/dy)r(y))/r(y) * C for a cylinder specified by the parameters REV (equal-volume- * C sphere radius) and EPS=A/H (ratio of radius to semi-length) * C Y(I)=arccos(X(I)) * C 1.LE.I.LE.NGAUSS * C X - arguments * C * C********************************************************************** SUBROUTINE RSP3Q (X,NG,NGAUSS,REV,EPS,R,DR) IMPLICIT REAL*16 (A-H,O-Z) REAL*16 X(NG),R(NG),DR(NG) H=REV*( (2Q0/(3Q0*EPS*EPS))**(1Q0/3Q0) ) A=H*EPS DO 50 I=1,NGAUSS CO=-X(I) SI=QSQRT(1Q0-CO*CO) IF (SI/CO.GT.A/H) GO TO 20 RAD=H/CO RTHET=H*SI/(CO*CO) GO TO 30 20 RAD=A/SI RTHET=-A*CO/(SI*SI) 30 R(I)=RAD*RAD R(NG-I+1)=R(I) DR(I)=-RTHET/RAD DR(NG-I+1)=-DR(I) 50 CONTINUE RETURN END C********************************************************************** C * C Calculation of spherical Bessel functions of the first kind * C J(I,N) = j_n(x) and second kind Y(I,N) = y_n(x) * C of real-valued argument X(I) and first kind JR(I,N)+I*JI(I,N) = * C = j_n(z) of complex argument Z(I)=XR(I)+I*XI(I), as well as * C the functions * C * C DJ(I,N) = (1/x)(d/dx)(x*j_n(x)) , * C DY(I,N) = (1/x)(d/dx)(x*y_n(x)) , * C DJR(I,N) = Re ((1/z)(d/dz)(z*j_n(x)) , * C DJI(I,N) = Im ((1/z)(d/dz)(z*j_n(x)) . * C * C 1.LE.N.LE.NMAX * C NMAX.LE.NPN1 * C X,XR,XI - arguments * C 1.LE.I.LE.NG * C Arrays J,Y,JR,JI,DJ,DY,DJR,DJI are in * C COMMON /CBESS/ * C Parameters NNMAX1 and NMAX2 determine computational accuracy * C * C********************************************************************** SUBROUTINE BESSQ (X,XR,XI,NG,NMAX,NNMAX1,NNMAX2) INCLUDE 'tmq.par.f' IMPLICIT REAL*16 (A-H,O-Z) REAL*16 X(NG),XR(NG),XI(NG), * J(NPNG2,NPN1),Y(NPNG2,NPN1),JR(NPNG2,NPN1), * JI(NPNG2,NPN1),DJ(NPNG2,NPN1),DY(NPNG2,NPN1), * DJR(NPNG2,NPN1),DJI(NPNG2,NPN1), * AJ(NPN1),AY(NPN1),AJR(NPN1),AJI(NPN1), * ADJ(NPN1),ADY(NPN1),ADJR(NPN1), * ADJI(NPN1) COMMON /CBESS/ J,Y,JR,JI,DJ,DY,DJR,DJI DO 10 I=1,NG XX=X(I) CALL RJBQ(XX,AJ,ADJ,NMAX,NNMAX1) CALL RYBQ(XX,AY,ADY,NMAX) YR=XR(I) YI=XI(I) CALL CJBQ(YR,YI,AJR,AJI,ADJR,ADJI,NMAX,NNMAX2) DO 10 N=1,NMAX J(I,N)=AJ(N) Y(I,N)=AY(N) JR(I,N)=AJR(N) JI(I,N)=AJI(N) DJ(I,N)=ADJ(N) DY(I,N)=ADY(N) DJR(I,N)=ADJR(N) DJI(I,N)=ADJI(N) 10 CONTINUE RETURN END C********************************************************************** C * C Calculation of spherical Bessel functions of the first kind j * C of real-valued argument x of orders from 1 to NMAX by using * C backward recursion. Parametr NNMAX determines numerical accuracy. * C U - function (1/x)(d/dx)(x*j(x)) * C * C********************************************************************** SUBROUTINE RJBQ(X,Y,U,NMAX,NNMAX) IMPLICIT REAL*16 (A-H,O-Z) REAL*16 Y(NMAX),U(NMAX),Z(900) L=NMAX+NNMAX XX=1Q0/X Z(L)=1Q0/(QFLOAT(2*L+1)*XX) L1=L-1 DO 5 I=1,L1 I1=L-I Z(I1)=1Q0/(QFLOAT(2*I1+1)*XX-Z(I1+1)) 5 CONTINUE Z0=1Q0/(XX-Z(1)) Y0=Z0*QCOS(X)*XX Y1=Y0*Z(1) U(1)=Y0-Y1*XX Y(1)=Y1 DO 10 I=2,NMAX YI1=Y(I-1) YI=YI1*Z(I) U(I)=YI1-QFLOAT(I)*YI*XX Y(I)=YI 10 CONTINUE RETURN END C********************************************************************** C * C Calculation of spherical Bessel functions of the second kind y * C of real-valued argument x of orders from 1 to NMAX by using upward* C recursion. V - function (1/x)(d/dx)(x*y(x)) * C * C********************************************************************** SUBROUTINE RYBQ(X,Y,V,NMAX) IMPLICIT REAL*16 (A-H,O-Z) REAL*16 Y(NMAX),V(NMAX) C=QCOS(X) S=QSIN(X) X1=1Q0/X X2=X1*X1 X3=X2*X1 Y1=-C*X2-S*X1 Y(1)=Y1 Y(2)=(-3Q0*X3+X1)*C-3Q0*X2*S NMAX1=NMAX-1 DO 5 I=2,NMAX1 5 Y(I+1)=QFLOAT(2*I+1)*X1*Y(I)-Y(I-1) V(1)=-X1*(C+Y1) DO 10 I=2,NMAX 10 V(I)=Y(I-1)-QFLOAT(I)*X1*Y(I) RETURN END C********************************************************************** C * C Calculation of spherical Bessel functions of the first kind * C j=JR+I*JI of complex argument x=XR+I*XI of orders from 1 to NMAX * C by using backward recursion. Parametr NNMAX determines numerical * C accuracy. U=UR+I*UI - function (1/x)(d/dx)(x*j(x)) * C * C********************************************************************** SUBROUTINE CJBQ (XR,XI,YR,YI,UR,UI,NMAX,NNMAX) INCLUDE 'tmq.par.f' IMPLICIT REAL*16 (A-H,O-Z) REAL*16 YR(NMAX),YI(NMAX),UR(NMAX),UI(NMAX) REAL*16 CYR(NPN1),CYI(NPN1),CZR(1200),CZI(1200), * CUR(NPN1),CUI(NPN1) L=NMAX+NNMAX XRXI=1Q0/(XR*XR+XI*XI) CXXR=XR*XRXI CXXI=-XI*XRXI QF=1Q0/QFLOAT(2*L+1) CZR(L)=XR*QF CZI(L)=XI*QF L1=L-1 DO 5 I=1,L1 I1=L-I QF=QFLOAT(2*I1+1) AR=QF*CXXR-CZR(I1+1) AI=QF*CXXI-CZI(I1+1) ARI=1Q0/(AR*AR+AI*AI) CZR(I1)=AR*ARI CZI(I1)=-AI*ARI 5 CONTINUE AR=CXXR-CZR(1) AI=CXXI-CZI(1) ARI=1Q0/(AR*AR+AI*AI) CZ0R=AR*ARI CZ0I=-AI*ARI CR=QCOS(XR)*QCOSH(XI) CI=-QSIN(XR)*QSINH(XI) AR=CZ0R*CR-CZ0I*CI AI=CZ0I*CR+CZ0R*CI CY0R=AR*CXXR-AI*CXXI CY0I=AI*CXXR+AR*CXXI CY1R=CY0R*CZR(1)-CY0I*CZI(1) CY1I=CY0I*CZR(1)+CY0R*CZI(1) AR=CY1R*CXXR-CY1I*CXXI AI=CY1I*CXXR+CY1R*CXXI CU1R=CY0R-AR CU1I=CY0I-AI CYR(1)=CY1R CYI(1)=CY1I CUR(1)=CU1R CUI(1)=CU1I YR(1)=CY1R YI(1)=CY1I UR(1)=CU1R UI(1)=CU1I DO 10 I=2,NMAX QI=QFLOAT(I) CYI1R=CYR(I-1) CYI1I=CYI(I-1) CYIR=CYI1R*CZR(I)-CYI1I*CZI(I) CYII=CYI1I*CZR(I)+CYI1R*CZI(I) AR=CYIR*CXXR-CYII*CXXI AI=CYII*CXXR+CYIR*CXXI CUIR=CYI1R-QI*AR CUII=CYI1I-QI*AI CYR(I)=CYIR CYI(I)=CYII CUR(I)=CUIR CUI(I)=CUII YR(I)=CYIR YI(I)=CYII UR(I)=CUIR UI(I)=CUII 10 CONTINUE RETURN END C********************************************************************** C * C calculation of the T(0) matrix for an axially symmetric particle * C * C Output information: * C * C Arrays TR1 and TI1 (real and imaginary parts of the * C T(0) matrix) are in COMMON /CT/ * C * C********************************************************************** SUBROUTINE TMATR0Q (NGAUSS,X,W,AN,ANN,S,SS,PPI,PIR,PII,R,DR,DDR, * DRR,DRI,NMAX,NCHECK) INCLUDE 'tmq.par.f' IMPLICIT REAL*16 (A-H,O-Z) REAL*16 X(NPNG2),W(NPNG2),AN(NPN1),S(NPNG2),SS(NPNG2), * R(NPNG2),DR(NPNG2),SIG(NPN2), * J(NPNG2,NPN1),Y(NPNG2,NPN1), * JR(NPNG2,NPN1),JI(NPNG2,NPN1),DJ(NPNG2,NPN1), * DY(NPNG2,NPN1),DJR(NPNG2,NPN1), * DJI(NPNG2,NPN1),DDR(NPNG2),DRR(NPNG2), * D1(NPNG2,NPN1),D2(NPNG2,NPN1), * DRI(NPNG2),DS(NPNG2),DSS(NPNG2),RR(NPNG2), * DV1(NPN1),DV2(NPN1) REAL*16 R11(NPN1,NPN1),R12(NPN1,NPN1), * R21(NPN1,NPN1),R22(NPN1,NPN1), * I11(NPN1,NPN1),I12(NPN1,NPN1), * I21(NPN1,NPN1),I22(NPN1,NPN1), * RG11(NPN1,NPN1),RG12(NPN1,NPN1), * RG21(NPN1,NPN1),RG22(NPN1,NPN1), * IG11(NPN1,NPN1),IG12(NPN1,NPN1), * IG21(NPN1,NPN1),IG22(NPN1,NPN1), * ANN(NPN1,NPN1), * QR(NPN2,NPN2),QI(NPN2,NPN2), * RGQR(NPN2,NPN2),RGQI(NPN2,NPN2), * TQR(NPN2,NPN2),TQI(NPN2,NPN2), * TRGQR(NPN2,NPN2),TRGQI(NPN2,NPN2) REAL*8 TR1(NPN2,NPN2),TI1(NPN2,NPN2) REAL*4 PLUS(NPN6*NPN4*NPN4*8) COMMON /TMAT/ PLUS, & R11,R12,R21,R22,I11,I12,I21,I22,RG11,RG12,RG21,RG22, & IG11,IG12,IG21,IG22 COMMON /CBESS/ J,Y,JR,JI,DJ,DY,DJR,DJI COMMON /CT/ TR1,TI1 COMMON /CTT/ QR,QI,RGQR,RGQI MM1=1 NNMAX=NMAX+NMAX NG=2*NGAUSS NGSS=NG FACTOR=1Q0 IF (NCHECK.EQ.1) THEN NGSS=NGAUSS FACTOR=2Q0 ELSE CONTINUE ENDIF SI=1Q0 DO 5 N=1,NNMAX SI=-SI SIG(N)=SI 5 CONTINUE 20 DO 25 I=1,NGAUSS I1=NGAUSS+I I2=NGAUSS-I+1 CALL VIGQ (X(I1),NMAX,0,DV1,DV2) DO 25 N=1,NMAX SI=SIG(N) DD1=DV1(N) DD2=DV2(N) D1(I1,N)=DD1 D2(I1,N)=DD2 D1(I2,N)=DD1*SI D2(I2,N)=-DD2*SI 25 CONTINUE 30 DO 40 I=1,NGSS RR(I)=W(I)*R(I) 40 CONTINUE DO 300 N1=MM1,NMAX AN1=AN(N1) DO 300 N2=MM1,NMAX AN2=AN(N2) AR12=0Q0 AR21=0Q0 AI12=0Q0 AI21=0Q0 GR12=0Q0 GR21=0Q0 GI12=0Q0 GI21=0Q0 IF (NCHECK.EQ.1.AND.SIG(N1+N2).LT.0Q0) GO TO 205 DO 200 I=1,NGSS D1N1=D1(I,N1) D2N1=D2(I,N1) D1N2=D1(I,N2) D2N2=D2(I,N2) A12=D1N1*D2N2 A21=D2N1*D1N2 A22=D2N1*D2N2 AA1=A12+A21 QJ1=J(I,N1) QY1=Y(I,N1) QJR2=JR(I,N2) QJI2=JI(I,N2) QDJR2=DJR(I,N2) QDJI2=DJI(I,N2) QDJ1=DJ(I,N1) QDY1=DY(I,N1) C1R=QJR2*QJ1 C1I=QJI2*QJ1 B1R=C1R-QJI2*QY1 B1I=C1I+QJR2*QY1 C2R=QJR2*QDJ1 C2I=QJI2*QDJ1 B2R=C2R-QJI2*QDY1 B2I=C2I+QJR2*QDY1 DDRI=DDR(I) C3R=DDRI*C1R C3I=DDRI*C1I B3R=DDRI*B1R B3I=DDRI*B1I C4R=QDJR2*QJ1 C4I=QDJI2*QJ1 B4R=C4R-QDJI2*QY1 B4I=C4I+QDJR2*QY1 DRRI=DRR(I) DRII=DRI(I) C5R=C1R*DRRI-C1I*DRII C5I=C1I*DRRI+C1R*DRII B5R=B1R*DRRI-B1I*DRII B5I=B1I*DRRI+B1R*DRII URI=DR(I) RRI=RR(I) F1=RRI*A22 F2=RRI*URI*AN1*A12 AR12=AR12+F1*B2R+F2*B3R AI12=AI12+F1*B2I+F2*B3I GR12=GR12+F1*C2R+F2*C3R GI12=GI12+F1*C2I+F2*C3I F2=RRI*URI*AN2*A21 AR21=AR21+F1*B4R+F2*B5R AI21=AI21+F1*B4I+F2*B5I GR21=GR21+F1*C4R+F2*C5R GI21=GI21+F1*C4I+F2*C5I 200 CONTINUE 205 AN12=ANN(N1,N2)*FACTOR R12(N1,N2)=AR12*AN12 R21(N1,N2)=AR21*AN12 I12(N1,N2)=AI12*AN12 I21(N1,N2)=AI21*AN12 RG12(N1,N2)=GR12*AN12 RG21(N1,N2)=GR21*AN12 IG12(N1,N2)=GI12*AN12 IG21(N1,N2)=GI21*AN12 300 CONTINUE TPIR=PIR TPII=PII TPPI=PPI NM=NMAX DO 310 N1=MM1,NMAX K1=N1-MM1+1 KK1=K1+NM DO 310 N2=MM1,NMAX K2=N2-MM1+1 KK2=K2+NM TAR12= I12(N1,N2) TAI12=-R12(N1,N2) TGR12= IG12(N1,N2) TGI12=-RG12(N1,N2) TAR21=-I21(N1,N2) TAI21= R21(N1,N2) TGR21=-IG21(N1,N2) TGI21= RG21(N1,N2) TQR(K1,K2)=TPIR*TAR21-TPII*TAI21+TPPI*TAR12 TQI(K1,K2)=TPIR*TAI21+TPII*TAR21+TPPI*TAI12 TRGQR(K1,K2)=TPIR*TGR21-TPII*TGI21+TPPI*TGR12 TRGQI(K1,K2)=TPIR*TGI21+TPII*TGR21+TPPI*TGI12 TQR(K1,KK2)=0Q0 TQI(K1,KK2)=0Q0 TRGQR(K1,KK2)=0Q0 TRGQI(K1,KK2)=0Q0 TQR(KK1,K2)=0Q0 TQI(KK1,K2)=0Q0 TRGQR(KK1,K2)=0Q0 TRGQI(KK1,K2)=0Q0 TQR(KK1,KK2)=TPIR*TAR12-TPII*TAI12+TPPI*TAR21 TQI(KK1,KK2)=TPIR*TAI12+TPII*TAR12+TPPI*TAI21 TRGQR(KK1,KK2)=TPIR*TGR12-TPII*TGI12+TPPI*TGR21 TRGQI(KK1,KK2)=TPIR*TGI12+TPII*TGR12+TPPI*TGI21 310 CONTINUE NNMAX=2*NM DO 320 N1=1,NNMAX DO 320 N2=1,NNMAX QR(N1,N2)=TQR(N1,N2) QI(N1,N2)=TQI(N1,N2) RGQR(N1,N2)=TRGQR(N1,N2) RGQI(N1,N2)=TRGQI(N1,N2) 320 CONTINUE CALL TTQ(NMAX,NCHECK) RETURN END C********************************************************************** C * C Calculation of the T(M) matrix, M.GE.1, for an axially symmetric * C particle * C * C Input parameters: * C * C M.GE.1 * C NG = NGAUSS*2 - number of gaussian division points on the * C interval (-1,1) * C W - quadrature weights * C AN,ANN - see subroutine CONST * C S,SS - see subroutine CONST * C ARRAYS DV1,DV2,DV3,DV4 are in COMMON /DV/ - * C see subroutine DVIG * C PPI,PIR,PII - see subroutine VARY * C R J DR - see subroutines RSP1 and RSP2 * C DDR,DRR,DRI - see subroutine VARY * C NMAX - dimension of the T(M) matrix * C Arrays J,Y,JR,JI,DJ,DY,DJR,DJI are in * C COMMON /CBESS/ - see subroutine BESS * C * C Output parameters: * C * C Arrays TR1,TI1 (real and imaginary parts of the T(M) matrix) * C are in COMMON /CT/ * C * C********************************************************************** SUBROUTINE TMATRQ (M,NGAUSS,X,W,AN,ANN,S,SS,PPI,PIR,PII,R,DR,DDR, * DRR,DRI,NMAX,NCHECK) INCLUDE 'tmq.par.f' IMPLICIT REAL*16 (A-H,O-Z) REAL*16 X(NPNG2),W(NPNG2),AN(NPN1),S(NPNG2),SS(NPNG2), * R(NPNG2),DR(NPNG2),SIG(NPN2), * J(NPNG2,NPN1),Y(NPNG2,NPN1), * JR(NPNG2,NPN1),JI(NPNG2,NPN1),DJ(NPNG2,NPN1), * DY(NPNG2,NPN1),DJR(NPNG2,NPN1), * DJI(NPNG2,NPN1),DDR(NPNG2),DRR(NPNG2), * D1(NPNG2,NPN1),D2(NPNG2,NPN1), * DRI(NPNG2),DS(NPNG2),DSS(NPNG2),RR(NPNG2), * DV1(NPN1),DV2(NPN1) REAL*16 R11(NPN1,NPN1),R12(NPN1,NPN1), * R21(NPN1,NPN1),R22(NPN1,NPN1), * I11(NPN1,NPN1),I12(NPN1,NPN1), * I21(NPN1,NPN1),I22(NPN1,NPN1), * RG11(NPN1,NPN1),RG12(NPN1,NPN1), * RG21(NPN1,NPN1),RG22(NPN1,NPN1), * IG11(NPN1,NPN1),IG12(NPN1,NPN1), * IG21(NPN1,NPN1),IG22(NPN1,NPN1), * ANN(NPN1,NPN1), * QR(NPN2,NPN2),QI(NPN2,NPN2), * RGQR(NPN2,NPN2),RGQI(NPN2,NPN2), * TQR(NPN2,NPN2),TQI(NPN2,NPN2), * TRGQR(NPN2,NPN2),TRGQI(NPN2,NPN2) REAL*8 TR1(NPN2,NPN2),TI1(NPN2,NPN2) REAL*4 PLUS(NPN6*NPN4*NPN4*8) COMMON /TMAT/ PLUS, & R11,R12,R21,R22,I11,I12,I21,I22,RG11,RG12,RG21,RG22, & IG11,IG12,IG21,IG22 COMMON /CBESS/ J,Y,JR,JI,DJ,DY,DJR,DJI COMMON /CT/ TR1,TI1 COMMON /CTT/ QR,QI,RGQR,RGQI MM1=M QM=QFLOAT(M) QMM=QM*QM NG=2*NGAUSS NGSS=NG FACTOR=1Q0 IF (NCHECK.EQ.1) THEN NGSS=NGAUSS FACTOR=2Q0 ELSE CONTINUE ENDIF SI=1Q0 NM=NMAX+NMAX DO 5 N=1,NM SI=-SI SIG(N)=SI 5 CONTINUE 20 DO 25 I=1,NGAUSS I1=NGAUSS+I I2=NGAUSS-I+1 CALL VIGQ (X(I1),NMAX,M,DV1,DV2) DO 25 N=1,NMAX SI=SIG(N+M) DD1=DV1(N) DD2=DV2(N) D1(I1,N)=DD1 D2(I1,N)=DD2 D1(I2,N)=DD1*SI D2(I2,N)=-DD2*SI 25 CONTINUE 30 DO 40 I=1,NGSS WR=W(I)*R(I) DS(I)=S(I)*QM*WR DSS(I)=SS(I)*QMM RR(I)=WR 40 CONTINUE DO 300 N1=MM1,NMAX AN1=AN(N1) DO 300 N2=MM1,NMAX AN2=AN(N2) AR11=0Q0 AR12=0Q0 AR21=0Q0 AR22=0Q0 AI11=0Q0 AI12=0Q0 AI21=0Q0 AI22=0Q0 GR11=0Q0 GR12=0Q0 GR21=0Q0 GR22=0Q0 GI11=0Q0 GI12=0Q0 GI21=0Q0 GI22=0Q0 SI=SIG(N1+N2) DO 200 I=1,NGSS D1N1=D1(I,N1) D2N1=D2(I,N1) D1N2=D1(I,N2) D2N2=D2(I,N2) A11=D1N1*D1N2 A12=D1N1*D2N2 A21=D2N1*D1N2 A22=D2N1*D2N2 AA1=A12+A21 AA2=A11*DSS(I)+A22 QJ1=J(I,N1) QY1=Y(I,N1) QJR2=JR(I,N2) QJI2=JI(I,N2) QDJR2=DJR(I,N2) QDJI2=DJI(I,N2) QDJ1=DJ(I,N1) QDY1=DY(I,N1) C1R=QJR2*QJ1 C1I=QJI2*QJ1 B1R=C1R-QJI2*QY1 B1I=C1I+QJR2*QY1 C2R=QJR2*QDJ1 C2I=QJI2*QDJ1 B2R=C2R-QJI2*QDY1 B2I=C2I+QJR2*QDY1 DDRI=DDR(I) C3R=DDRI*C1R C3I=DDRI*C1I B3R=DDRI*B1R B3I=DDRI*B1I C4R=QDJR2*QJ1 C4I=QDJI2*QJ1 B4R=C4R-QDJI2*QY1 B4I=C4I+QDJR2*QY1 DRRI=DRR(I) DRII=DRI(I) C5R=C1R*DRRI-C1I*DRII C5I=C1I*DRRI+C1R*DRII B5R=B1R*DRRI-B1I*DRII B5I=B1I*DRRI+B1R*DRII C6R=QDJR2*QDJ1 C6I=QDJI2*QDJ1 B6R=C6R-QDJI2*QDY1 B6I=C6I+QDJR2*QDY1 C7R=C4R*DDRI C7I=C4I*DDRI B7R=B4R*DDRI B7I=B4I*DDRI C8R=C2R*DRRI-C2I*DRII C8I=C2I*DRRI+C2R*DRII B8R=B2R*DRRI-B2I*DRII B8I=B2I*DRRI+B2R*DRII URI=DR(I) DSI=DS(I) DSSI=DSS(I) RRI=RR(I) IF (NCHECK.EQ.1.AND.SI.GT.0Q0) GO TO 150 E1=DSI*AA1 AR11=AR11+E1*B1R AI11=AI11+E1*B1I GR11=GR11+E1*C1R GI11=GI11+E1*C1I IF (NCHECK.EQ.1) GO TO 160 150 F1=RRI*AA2 F2=RRI*URI*AN1*A12 AR12=AR12+F1*B2R+F2*B3R AI12=AI12+F1*B2I+F2*B3I GR12=GR12+F1*C2R+F2*C3R GI12=GI12+F1*C2I+F2*C3I F2=RRI*URI*AN2*A21 AR21=AR21+F1*B4R+F2*B5R AI21=AI21+F1*B4I+F2*B5I GR21=GR21+F1*C4R+F2*C5R GI21=GI21+F1*C4I+F2*C5I IF (NCHECK.EQ.1) GO TO 200 160 E2=DSI*URI*A11 E3=E2*AN2 E2=E2*AN1 AR22=AR22+E1*B6R+E2*B7R+E3*B8R AI22=AI22+E1*B6I+E2*B7I+E3*B8I GR22=GR22+E1*C6R+E2*C7R+E3*C8R GI22=GI22+E1*C6I+E2*C7I+E3*C8I 200 CONTINUE AN12=ANN(N1,N2)*FACTOR R11(N1,N2)=AR11*AN12 R12(N1,N2)=AR12*AN12 R21(N1,N2)=AR21*AN12 R22(N1,N2)=AR22*AN12 I11(N1,N2)=AI11*AN12 I12(N1,N2)=AI12*AN12 I21(N1,N2)=AI21*AN12 I22(N1,N2)=AI22*AN12 RG11(N1,N2)=GR11*AN12 RG12(N1,N2)=GR12*AN12 RG21(N1,N2)=GR21*AN12 RG22(N1,N2)=GR22*AN12 IG11(N1,N2)=GI11*AN12 IG12(N1,N2)=GI12*AN12 IG21(N1,N2)=GI21*AN12 IG22(N1,N2)=GI22*AN12 300 CONTINUE TPIR=PIR TPII=PII TPPI=PPI NM=NMAX-MM1+1 DO 310 N1=MM1,NMAX K1=N1-MM1+1 KK1=K1+NM DO 310 N2=MM1,NMAX K2=N2-MM1+1 KK2=K2+NM TAR11=-R11(N1,N2) TAI11=-I11(N1,N2) TGR11=-RG11(N1,N2) TGI11=-IG11(N1,N2) TAR12= I12(N1,N2) TAI12=-R12(N1,N2) TGR12= IG12(N1,N2) TGI12=-RG12(N1,N2) TAR21=-I21(N1,N2) TAI21= R21(N1,N2) TGR21=-IG21(N1,N2) TGI21= RG21(N1,N2) TAR22=-R22(N1,N2) TAI22=-I22(N1,N2) TGR22=-RG22(N1,N2) TGI22=-IG22(N1,N2) TQR(K1,K2)=TPIR*TAR21-TPII*TAI21+TPPI*TAR12 TQI(K1,K2)=TPIR*TAI21+TPII*TAR21+TPPI*TAI12 TRGQR(K1,K2)=TPIR*TGR21-TPII*TGI21+TPPI*TGR12 TRGQI(K1,K2)=TPIR*TGI21+TPII*TGR21+TPPI*TGI12 TQR(K1,KK2)=TPIR*TAR11-TPII*TAI11+TPPI*TAR22 TQI(K1,KK2)=TPIR*TAI11+TPII*TAR11+TPPI*TAI22 TRGQR(K1,KK2)=TPIR*TGR11-TPII*TGI11+TPPI*TGR22 TRGQI(K1,KK2)=TPIR*TGI11+TPII*TGR11+TPPI*TGI22 TQR(KK1,K2)=TPIR*TAR22-TPII*TAI22+TPPI*TAR11 TQI(KK1,K2)=TPIR*TAI22+TPII*TAR22+TPPI*TAI11 TRGQR(KK1,K2)=TPIR*TGR22-TPII*TGI22+TPPI*TGR11 TRGQI(KK1,K2)=TPIR*TGI22+TPII*TGR22+TPPI*TGI11 TQR(KK1,KK2)=TPIR*TAR12-TPII*TAI12+TPPI*TAR21 TQI(KK1,KK2)=TPIR*TAI12+TPII*TAR12+TPPI*TAI21 TRGQR(KK1,KK2)=TPIR*TGR12-TPII*TGI12+TPPI*TGR21 TRGQI(KK1,KK2)=TPIR*TGI12+TPII*TGR12+TPPI*TGI21 310 CONTINUE NNMAX=2*NM DO 320 N1=1,NNMAX DO 320 N2=1,NNMAX QR(N1,N2)=TQR(N1,N2) QI(N1,N2)=TQI(N1,N2) RGQR(N1,N2)=TRGQR(N1,N2) RGQI(N1,N2)=TRGQI(N1,N2) 320 CONTINUE CALL TTQ(NM,NCHECK) RETURN END C***************************************************************** c c Calculation of the functiONS c DV1(n)=dvig(0,m,n,arccos x) c and c DV2(n)=[d/d(arccos x)] dvig(0,m,n,arccos x) c 1.LE.N.LE.NMAX c 0.LE.x.LE.1 SUBROUTINE VIGQ (X,NMAX,M,DV1,DV2) INCLUDE 'tmq.par.f' IMPLICIT REAL*16 (A-H,O-Z) REAL*16 DV1(NPN1), DV2(NPN1) A=1Q0 QS=QSQRT(1Q0-X*X) QS1=1Q0/QS DO 1 N=1,NMAX DV1(N)=0Q0 DV2(N)=0Q0 1 CONTINUE IF (M.NE.0) GO TO 20 D1=1Q0 D2=X DO 5 N=1,NMAX QN=QFLOAT(N) QN1=QFLOAT(N+1) QN2=QFLOAT(2*N+1) D3=(QN2*X*D2-QN*D1)/QN1 DER=QS1*(QN1*QN/QN2)*(-D1+D3) DV1(N)=D2 DV2(N)=DER D1=D2 D2=D3 5 CONTINUE RETURN 20 QMM=QFLOAT(M*M) DO 25 I=1,M I2=I*2 A=A*QSQRT(QFLOAT(I2-1)/QFLOAT(I2))*QS 25 CONTINUE D1=0Q0 D2=A DO 30 N=M,NMAX QN=QFLOAT(N) QN2=QFLOAT(2*N+1) QN1=QFLOAT(N+1) QNM=QSQRT(QN*QN-QMM) QNM1=QSQRT(QN1*QN1-QMM) D3=(QN2*X*D2-QNM*D1)/QNM1 DER=QS1*(-QN1*QNM*D1+QN*QNM1*D3)/QN2 DV1(N)=D2 DV2(N)=DER D1=D2 D2=D3 30 CONTINUE RETURN END C********************************************************************** C * C Calculation of the matrix T = - RG(Q) * (Q**(-1)) * C * C Input infortmation is in COMMON /CTT/ * C Output information is in COMMON /CT/ * C * C********************************************************************** SUBROUTINE TTQ(NMAX,NCHECK) INCLUDE 'tmq.par.f' IMPLICIT REAL*8 (A-H,O-Z) REAL*16 F(NPN2,NPN2),B(NPN2),WORK(NPN2), * QR(NPN2,NPN2),QI(NPN2,NPN2), * RGQR(NPN2,NPN2),RGQI(NPN2,NPN2), * A(NPN2,NPN2),C(NPN2,NPN2),D(NPN2,NPN2),E(NPN2,NPN2) REAL*8 TR1(NPN2,NPN2),TI1(NPN2,NPN2) COMPLEX*32 ZQ(NPN2,NPN2),ZW(NPN2) COMPLEX*32 ZQR(NPN2,NPN2),ZAFAC(NPN2,NPN2),ZT(NPN2,NPN2), & ZTHETA(NPN2,NPN2) INTEGER IPIV(NPN2),IPVT(NPN2) COMMON /CHOICE/ ICHOICE COMMON /CT/ TR1,TI1 COMMON /CTT/ QR,QI,RGQR,RGQI NDIM=NPN2 NNMAX=2*NMAX IF (ICHOICE.EQ.2) GO TO 5 C Inversion from NAG-LIB or Waterman's method DO I=1,NNMAX DO J=1,NNMAX ZQ(I,J)=QCMPLX(QR(I,J),QI(I,J)) ZAFAC(I,J)=ZQ(I,J) ENDDO ENDDO INFO=0 CALL ZGETRFq(NNMAX,NNMAX,ZQ,NPN2,IPIV,INFO) IF (INFO.NE.0) WRITE (6,1100) INFO CALL ZGETRIq(NNMAX,ZQ,NPN2,IPIV,ZW,NPN2,INFO) IF (INFO.NE.0) WRITE (6,1100) INFO 1100 FORMAT ('WARNING: info=', I2) DO I=1,NNMAX DO J=1,NNMAX TR=0D0 TI=0D0 DO K=1,NNMAX ARR=RGQR(I,K) ARI=RGQI(I,K) AR=ZQ(K,J) AI=QIMAG(ZQ(K,J)) TR=TR-ARR*AR+ARI*AI TI=TI-ARR*AI-ARI*AR ENDDO TR1(I,J)=TR TI1(I,J)=TI ENDDO ENDDO GOTO 70 C Gaussian elimination 5 DO 10 N1=1,NNMAX DO 10 N2=1,NNMAX F(N1,N2)=QI(N1,N2) 10 CONTINUE IF (NCHECK.EQ.1) THEN CALL INV1Q(NMAX,F,A) ELSE CALL INVERTQ(NDIM,NNMAX,F,A,COND,IPVT,WORK,B) ENDIF CALL PRODQ(QR,A,C,NDIM,NNMAX) CALL PRODQ(C,QR,D,NDIM,NNMAX) DO 20 N1=1,NNMAX DO 20 N2=1,NNMAX C(N1,N2)=D(N1,N2)+QI(N1,N2) 20 CONTINUE IF (NCHECK.EQ.1) THEN CALL INV1Q(NMAX,C,QI) ELSE CALL INVERTQ(NDIM,NNMAX,C,QI,COND,IPVT,WORK,B) ENDIF CALL PRODQ(A,QR,D,NDIM,NNMAX) CALL PRODQ(D,QI,QR,NDIM,NNMAX) CALL PRODQ(RGQR,QR,A,NDIM,NNMAX) CALL PRODQ(RGQI,QI,C,NDIM,NNMAX) CALL PRODQ(RGQR,QI,D,NDIM,NNMAX) CALL PRODQ(RGQI,QR,E,NDIM,NNMAX) DO 30 N1=1,NNMAX DO 30 N2=1,NNMAX TR1(N1,N2)=-A(N1,N2)-C(N1,N2) TI1(N1,N2)= D(N1,N2)-E(N1,N2) 30 CONTINUE 70 RETURN END C********************************************************************** C * C Calculation of the matrix C = A * B . * C All matrices are (N-by-N) * C Declared line dimension of the arrays A,B, and C in the calling * C program is NDIM * C * C********************************************************************** SUBROUTINE PRODQ(A,B,C,NDIM,N) REAL*16 A(NDIM,N),B(NDIM,N),C(NDIM,N),cij DO 10 I=1,N DO 10 J=1,N CIJ=0Q0 DO 5 K=1,N CIJ=CIJ+A(I,K)*B(K,J) 5 CONTINUE C(I,J)=CIJ 10 CONTINUE RETURN END C********************************************************************** SUBROUTINE INV1Q (NMAX,F,A) IMPLICIT REAL*16 (A-H,O-Z) INCLUDE 'tmq.par.f' REAL*16 A(NPN2,NPN2),F(NPN2,NPN2),B(NPN1), * WORK(NPN1),Q1(NPN1,NPN1),Q2(NPN1,NPN1), & P1(NPN1,NPN1),P2(NPN1,NPN1) INTEGER IPVT(NPN1),IND1(NPN1),IND2(NPN1) NDIM=NPN1 NN1=(QFLOAT(NMAX)-0.1Q0)*0.5Q0+1Q0 NN2=NMAX-NN1 DO 5 I=1,NMAX IND1(I)=2*I-1 IF(I.GT.NN1) IND1(I)=NMAX+2*(I-NN1) IND2(I)=2*I IF(I.GT.NN2) IND2(I)=NMAX+2*(I-NN2)-1 5 CONTINUE NNMAX=2*NMAX DO 15 I=1,NMAX I1=IND1(I) I2=IND2(I) DO 15 J=1,NMAX J1=IND1(J) J2=IND2(J) Q1(J,I)=F(J1,I1) Q2(J,I)=F(J2,I2) 15 CONTINUE CALL INVERTQ(NDIM,NMAX,Q1,P1,COND,IPVT,WORK,B) CALL INVERTQ(NDIM,NMAX,Q2,P2,COND,IPVT,WORK,B) DO 30 I=1,NNMAX DO 30 J=1,NNMAX A(J,I)=0Q0 30 CONTINUE DO 40 I=1,NMAX I1=IND1(I) I2=IND2(I) DO 40 J=1,NMAX J1=IND1(J) J2=IND2(J) A(J1,I1)=P1(J,I) A(J2,I2)=P2(J,I) 40 CONTINUE RETURN END C********************************************************************* C * C Inversion of a square matrix * C * C Input parameters: * C * C A - square (N-by-N) matrix * C NDIM - declared line dimension of the matrix A in the calling * C program * C * C Output information: * C * C X - square (N-by-N) matrix - result of inverting matrix A * C COND - estimate of ill-conditioning of the matrix A * C * C Temporary arrays: IPVT,WORK,B * C * C********************************************************************* SUBROUTINE INVERTQ (NDIM,N,A,X,COND,IPVT,WORK,B) IMPLICIT REAL*16 (A-H,O-Z) REAL*16 A(NDIM,N),X(NDIM,N),WORK(N),B(N) INTEGER IPVT(N) CALL DECOMPQ (NDIM,N,A,COND,IPVT,WORK) IF (COND+1Q0.EQ.COND) PRINT 5,COND C IF (COND+1Q0.EQ.COND) STOP 5 FORMAT(' THE MATRIX IS SINGULAR FOR THE GIVEN NUMERICAL ACCURACY ' * ,'COND = ',D12.6) DO 30 I=1,N DO 10 J=1,N B(J)=0Q0 IF (J.EQ.I) B(J)=1Q0 10 CONTINUE CALL SOLVEQ (NDIM,N,A,B,IPVT) DO 30 J=1,N X(J,I)=B(J) 30 CONTINUE RETURN END C******************************************************************** SUBROUTINE DECOMPQ (NDIM,N,A,COND,IPVT,WORK) IMPLICIT REAL*16 (A-H,O-Z) REAL*16 A(NDIM,N),COND,WORK(N) INTEGER IPVT(N) IPVT(N)=1 IF(N.EQ.1) GO TO 80 NM1=N-1 ANORM=0Q0 DO 10 J=1,N T=0Q0 DO 5 I=1,N T=T+QABS(A(I,J)) 5 CONTINUE IF (T.GT.ANORM) ANORM=T 10 CONTINUE DO 35 K=1,NM1 KP1=K+1 M=K DO 15 I=KP1,N IF (QABS(A(I,K)).GT.QABS(A(M,K))) M=I 15 CONTINUE IPVT(K)=M IF (M.NE.K) IPVT(N)=-IPVT(N) T=A(M,K) A(M,K)=A(K,K) A(K,K)=T IF (T.EQ.0Q0) GO TO 35 DO 20 I=KP1,N A(I,K)=-A(I,K)/T 20 CONTINUE DO 30 J=KP1,N T=A(M,J) A(M,J)=A(K,J) A(K,J)=T IF (T.EQ.0Q0) GO TO 30 DO 25 I=KP1,N A(I,J)=A(I,J)+A(I,K)*T 25 CONTINUE 30 CONTINUE 35 CONTINUE DO 50 K=1,N T=0Q0 IF (K.EQ.1) GO TO 45 KM1=K-1 DO 40 I=1,KM1 T=T+A(I,K)*WORK(I) 40 CONTINUE 45 EK=1Q0 IF (T.LT.0Q0) EK=-1Q0 IF (A(K,K).EQ.0Q0) GO TO 90 WORK(K)=-(EK+T)/A(K,K) 50 CONTINUE DO 60 KB=1,NM1 K=N-KB T=0Q0 KP1=K+1 DO 55 I=KP1,N T=T+A(I,K)*WORK(K) 55 CONTINUE WORK(K)=T M=IPVT(K) IF (M.EQ.K) GO TO 60 T=WORK(M) WORK(M)=WORK(K) WORK(K)=T 60 CONTINUE YNORM=0Q0 DO 65 I=1,N YNORM=YNORM+QABS(WORK(I)) 65 CONTINUE CALL SOLVEQ (NDIM,N,A,WORK,IPVT) ZNORM=0Q0 DO 70 I=1,N ZNORM=ZNORM+QABS(WORK(I)) 70 CONTINUE COND=ANORM*ZNORM/YNORM IF (COND.LT.1Q0) COND=1Q0 RETURN 80 COND=1Q0 IF (A(1,1).NE.0Q0) RETURN 90 COND=1Q52 RETURN END C********************************************************************** SUBROUTINE SOLVEQ (NDIM,N,A,B,IPVT) IMPLICIT REAL*16 (A-H,O-Z) REAL*16 A(NDIM,N),B(N) INTEGER IPVT(N) IF (N.EQ.1) GO TO 50 NM1=N-1 DO 20 K=1,NM1 KP1=K+1 M=IPVT(K) T=B(M) B(M)=B(K) B(K)=T DO 10 I=KP1,N B(I)=B(I)+A(I,K)*T 10 CONTINUE 20 CONTINUE DO 40 KB=1,NM1 KM1=N-KB K=KM1+1 B(K)=B(K)/A(K,K) T=-B(K) DO 30 I=1,KM1 B(I)=B(I)+A(I,K)*T 30 CONTINUE 40 CONTINUE 50 B(1)=B(1)/A(1,1) RETURN END C******************************************************************** C * C Calculation of the expansion coefficients for the (I,Q,U,V) * C representation. * C * C Input parameters: * C * C LAM - wavelength of light * C CSCA - scattering cross section * C TR and TI - elements of the t-matrix. Transferred through * C COMMON /CTM/ * C NMAX - dimension of T(M) matrices * C * C Output infortmation: * C * C ALF1,...,ALF4,BET1,BET2 - expansion coefficients * C LMAX - number of coefficients minus 1 * C * C******************************************************************** SUBROUTINE GSPQ(NMAX,CSCA,LAM,ALF1,ALF2,ALF3,ALF4,BET1,BET2,LMAX) INCLUDE 'tmq.par.f' IMPLICIT REAL*8 (A-B,D-H,O-Z),COMPLEX*16 (C) REAL*16 LAM REAL*8 SSIGN(900) REAL*8 CSCA,SSI(NPL),SSJ(NPN1), & ALF1(NPL),ALF2(NPL),ALF3(NPL), & ALF4(NPL),BET1(NPL),BET2(NPL), & TR1(NPL1,NPN4),TR2(NPL1,NPN4), & TI1(NPL1,NPN4),TI2(NPL1,NPN4), & G1(NPL1,NPN6),G2(NPL1,NPN6), & AR1(NPN4),AR2(NPN4),AI1(NPN4),AI2(NPN4), & FR(NPN4,NPN4),FI(NPN4,NPN4),FF(NPN4,NPN4) REAL*4 B1R(NPL1,NPL1,NPN4),B1I(NPL1,NPL1,NPN4), & B2R(NPL1,NPL1,NPN4),B2I(NPL1,NPL1,NPN4), & D1(NPL1,NPN4,NPN4),D2(NPL1,NPN4,NPN4), & D3(NPL1,NPN4,NPN4),D4(NPL1,NPN4,NPN4), & D5R(NPL1,NPN4,NPN4),D5I(NPL1,NPN4,NPN4), & PLUS1(NPN6*NPN4*NPN4*8) REAL*4 & TR11(NPN6,NPN4,NPN4),TR12(NPN6,NPN4,NPN4), & TR21(NPN6,NPN4,NPN4),TR22(NPN6,NPN4,NPN4), & TI11(NPN6,NPN4,NPN4),TI12(NPN6,NPN4,NPN4), & TI21(NPN6,NPN4,NPN4),TI22(NPN6,NPN4,NPN4) COMPLEX*16 CIM(NPN1) COMMON /TMAT/ TR11,TR12,TR21,TR22,TI11,TI12,TI21,TI22 COMMON /CBESS/ B1R,B1I,B2R,B2I COMMON /SS/ SSIGN EQUIVALENCE ( PLUS1(1),TR11(1,1,1) ) EQUIVALENCE (D1(1,1,1),PLUS1(1)), & (D2(1,1,1),PLUS1(NPL1*NPN4*NPN4+1)), & (D3(1,1,1),PLUS1(NPL1*NPN4*NPN4*2+1)), & (D4(1,1,1),PLUS1(NPL1*NPN4*NPN4*3+1)), & (D5R(1,1,1),PLUS1(NPL1*NPN4*NPN4*4+1)) CALL FACT CALL SIGNUM LMAX=2*NMAX L1MAX=LMAX+1 CI=(0D0,1D0) CIM(1)=CI DO 2 I=2,NMAX CIM(I)=CIM(I-1)*CI 2 CONTINUE SSI(1)=1D0 DO 3 I=1,LMAX I1=I+1 SI=DFLOAT(2*I+1) SSI(I1)=SI IF(I.LE.NMAX) SSJ(I)=DSQRT(SI) 3 CONTINUE CI=-CI DO 5 I=1,NMAX SI=SSJ(I) CCI=CIM(I) DO 4 J=1,NMAX SJ=1D0/SSJ(J) CCJ=CIM(J)*SJ/CCI FR(J,I)=CCJ FI(J,I)=CCJ*CI FF(J,I)=SI*SJ 4 CONTINUE 5 CONTINUE NMAX1=NMAX+1 C ***** CALCULATION OF THE ARRAYS B1 AND B2 ***** K1=1 K2=0 K3=0 K4=1 K5=1 K6=2 C PRINT 3300, B1,B2 3300 FORMAT (' b1 and b2') DO 100 N=1,NMAX C ***** CALCULATION OF THE ARRAYS T1 AND T2 ***** DO 10 NN=1,NMAX M1MAX=MIN0(N,NN)+1 DO 6 M1=1,M1MAX M=M1-1 L1=NPN6+M TT1=TR11(M1,N,NN) TT2=TR12(M1,N,NN) TT3=TR21(M1,N,NN) TT4=TR22(M1,N,NN) TT5=TI11(M1,N,NN) TT6=TI12(M1,N,NN) TT7=TI21(M1,N,NN) TT8=TI22(M1,N,NN) T1=TT1+TT2 T2=TT3+TT4 T3=TT5+TT6 T4=TT7+TT8 TR1(L1,NN)=T1+T2 TR2(L1,NN)=T1-T2 TI1(L1,NN)=T3+T4 TI2(L1,NN)=T3-T4 IF(M.EQ.0) GO TO 6 L1=NPN6-M T1=TT1-TT2 T2=TT3-TT4 T3=TT5-TT6 T4=TT7-TT8 TR1(L1,NN)=T1-T2 TR2(L1,NN)=T1+T2 TI1(L1,NN)=T3-T4 TI2(L1,NN)=T3+T4 6 CONTINUE 10 CONTINUE C ***** END OF THE CALCULATION OF THE ARRAYS T1 AND T2 ***** NN1MAX=NMAX1+N DO 40 NN1=1,NN1MAX N1=NN1-1 C ***** CALCULATION OF THE ARRAYS A1 AND A2 ***** CALL CCGQ(N,N1,NMAX,K1,K2,G1) NNMAX=MIN0(NMAX,N1+N) NNMIN=MAX0(1,IABS(N-N1)) KN=N+NN1 DO 15 NN=NNMIN,NNMAX NNN=NN+1 SIG=SSIGN(KN+NN) M1MAX=MIN0(N,NN)+NPN6 AAR1=0D0 AAR2=0D0 AAI1=0D0 AAI2=0D0 DO 13 M1=NPN6,M1MAX M=M1-NPN6 SSS=G1(M1,NNN) RR1=TR1(M1,NN) RI1=TI1(M1,NN) RR2=TR2(M1,NN) RI2=TI2(M1,NN) IF(M.EQ.0) GO TO 12 M2=NPN6-M RR1=RR1+TR1(M2,NN)*SIG RI1=RI1+TI1(M2,NN)*SIG RR2=RR2+TR2(M2,NN)*SIG RI2=RI2+TI2(M2,NN)*SIG 12 AAR1=AAR1+SSS*RR1 AAI1=AAI1+SSS*RI1 AAR2=AAR2+SSS*RR2 AAI2=AAI2+SSS*RI2 13 CONTINUE XR=FR(NN,N) XI=FI(NN,N) AR1(NN)=AAR1*XR-AAI1*XI AI1(NN)=AAR1*XI+AAI1*XR AR2(NN)=AAR2*XR-AAI2*XI AI2(NN)=AAR2*XI+AAI2*XR 15 CONTINUE C ***** END OF THE CALCULATION OF THE ARRAYS A1 AND A2 **** CALL CCGQ(N,N1,NMAX,K3,K4,G2) M1=MAX0(-N1+1,-N) M2=MIN0(N1+1,N) M1MAX=M2+NPN6 M1MIN=M1+NPN6 DO 30 M1=M1MIN,M1MAX BBR1=0D0 BBI1=0D0 BBR2=0D0 BBI2=0D0 DO 25 NN=NNMIN,NNMAX NNN=NN+1 SSS=G2(M1,NNN) BBR1=BBR1+SSS*AR1(NN) BBI1=BBI1+SSS*AI1(NN) BBR2=BBR2+SSS*AR2(NN) BBI2=BBI2+SSS*AI2(NN) 25 CONTINUE B1R(NN1,M1,N)=BBR1 B1I(NN1,M1,N)=BBI1 B2R(NN1,M1,N)=BBR2 B2I(NN1,M1,N)=BBI2 30 CONTINUE 40 CONTINUE 100 CONTINUE C ***** END OF THE CALCULATION OF THE ARRAYS B1 AND B2 **** C ***** CALCULATION OF THE ARRAYS D1,D2,D3,D4, AND D5 ***** c PRINT 3301 3301 FORMAT(' d1, d2, ...') DO 200 N=1,NMAX DO 190 NN=1,NMAX M1=MIN0(N,NN) M1MAX=NPN6+M1 M1MIN=NPN6-M1 NN1MAX=NMAX1+MIN0(N,NN) DO 180 M1=M1MIN,M1MAX M=M1-NPN6 NN1MIN=IABS(M-1)+1 DD1=0D0 DD2=0D0 DO 150 NN1=NN1MIN,NN1MAX XX=SSI(NN1) X1=B1R(NN1,M1,N) X2=B1I(NN1,M1,N) X3=B1R(NN1,M1,NN) X4=B1I(NN1,M1,NN) X5=B2R(NN1,M1,N) X6=B2I(NN1,M1,N) X7=B2R(NN1,M1,NN) X8=B2I(NN1,M1,NN) DD1=DD1+XX*(X1*X3+X2*X4) DD2=DD2+XX*(X5*X7+X6*X8) 150 CONTINUE D1(M1,NN,N)=DD1 D2(M1,NN,N)=DD2 180 CONTINUE MMAX=MIN0(N,NN+2) MMIN=MAX0(-N,-NN+2) M1MAX=NPN6+MMAX M1MIN=NPN6+MMIN DO 186 M1=M1MIN,M1MAX M=M1-NPN6 NN1MIN=IABS(M-1)+1 DD3=0D0 DD4=0D0 DD5R=0D0 DD5I=0D0 M2=-M+2+NPN6 DO 183 NN1=NN1MIN,NN1MAX XX=SSI(NN1) X1=B1R(NN1,M1,N) X2=B1I(NN1,M1,N) X3=B2R(NN1,M1,N) X4=B2I(NN1,M1,N) X5=B1R(NN1,M2,NN) X6=B1I(NN1,M2,NN) X7=B2R(NN1,M2,NN) X8=B2I(NN1,M2,NN) DD3=DD3+XX*(X1*X5+X2*X6) DD4=DD4+XX*(X3*X7+X4*X8) DD5R=DD5R+XX*(X3*X5+X4*X6) DD5I=DD5I+XX*(X4*X5-X3*X6) 183 CONTINUE D3(M1,NN,N)=DD3 D4(M1,NN,N)=DD4 D5R(M1,NN,N)=DD5R D5I(M1,NN,N)=DD5I 186 CONTINUE 190 CONTINUE 200 CONTINUE C ***** END OF THE CALCULATION OF THE D-ARRAYS ***** C ***** CALCULATION OF THE EXPANSION COEFFICIENTS ***** C PRINT 3303 3303 FORMAT (' g1, g2, ...') DK=LAM*LAM/(4D0*CSCA*DACOS(-1D0)) DO 300 L1=1,L1MAX G1L=0D0 G2L=0D0 G3L=0D0 G4L=0D0 G5LR=0D0 G5LI=0D0 L=L1-1 SL=SSI(L1)*DK DO 290 N=1,NMAX NNMIN=MAX0(1,IABS(N-L)) NNMAX=MIN0(NMAX,N+L) IF(NNMAX.LT.NNMIN) GO TO 290 CALL CCGQ(N,L,NMAX,K1,K2,G1) IF(L.GE.2) CALL CCGQ(N,L,NMAX,K5,K6,G2) NL=N+L DO 280 NN=NNMIN,NNMAX NNN=NN+1 MMAX=MIN0(N,NN) M1MIN=NPN6-MMAX M1MAX=NPN6+MMAX SI=SSIGN(NL+NNN) DM1=0D0 DM2=0D0 DO 270 M1=M1MIN,M1MAX M=M1-NPN6 IF(M.GE.0) SSS1=G1(M1,NNN) IF(M.LT.0) SSS1=G1(NPN6-M,NNN)*SI DM1=DM1+SSS1*D1(M1,NN,N) DM2=DM2+SSS1*D2(M1,NN,N) 270 CONTINUE FFN=FF(NN,N) SSS=G1(NPN6+1,NNN)*FFN G1L=G1L+SSS*DM1 G2L=G2L+SSS*DM2*SI IF(L.LT.2) GO TO 280 DM3=0D0 DM4=0D0 DM5R=0D0 DM5I=0D0 MMAX=MIN0(N,NN+2) MMIN=MAX0(-N,-NN+2) M1MAX=NPN6+MMAX M1MIN=NPN6+MMIN DO 275 M1=M1MIN,M1MAX M=M1-NPN6 SSS1=G2(NPN6-M,NNN) DM3=DM3+SSS1*D3(M1,NN,N) DM4=DM4+SSS1*D4(M1,NN,N) DM5R=DM5R+SSS1*D5R(M1,NN,N) DM5I=DM5I+SSS1*D5I(M1,NN,N) 275 CONTINUE G5LR=G5LR-SSS*DM5R G5LI=G5LI-SSS*DM5I SSS=G2(NPN4,NNN)*FFN G3L=G3L+SSS*DM3 G4L=G4L+SSS*DM4*SI 280 CONTINUE 290 CONTINUE G1L=G1L*SL G2L=G2L*SL G3L=G3L*SL G4L=G4L*SL G5LR=G5LR*SL G5LI=G5LI*SL ALF1(L1)=G1L+G2L ALF2(L1)=G3L+G4L ALF3(L1)=G3L-G4L ALF4(L1)=G1L-G2L BET1(L1)=G5LR*2D0 BET2(L1)=G5LI*2D0 LMAX=L IF(DABS(G1L).LT.1D-6) GO TO 500 300 CONTINUE 500 CONTINUE RETURN END C****************************************************************** C C Calculation of Clebsch-Gordan coefficients C (n,m:n1,m1/nn,mm) C for given n and n1. m1=mm-m, index mm is found from m as C mm=m*k1+k2 C C Input parameters : N,N1,NMAX,K1,K2 C N.LE.NMAX C N.GE.1 C N1.GE.0 C N1.LE.N+NMAX C Output parameters : GG(M+NPN6,NN+1) - array of the corresponding C coefficients C /M/.LE.N C /M1/=/M*(K1-1)+K2/.LE.N1 C NN.LE.MIN(N+N1,NMAX) C NN.GE.MAX(/MM/,/N-N1/) C If K1=1 and K2=0, then 0.LE.M.LE.N SUBROUTINE CCGQ(N,N1,NMAX,K1,K2,GG) INCLUDE 'tmq.par.f' IMPLICIT REAL*8 (A-H,O-Z) REAL*8 GG(NPL1,NPN6),CD(0:NPN5),CU(0:NPN5) IF(NMAX.LE.NPN4. & AND.0.LE.N1. & AND.N1.LE.NMAX+N. & AND.N.GE.1. & AND.N.LE.NMAX) GO TO 1 PRINT 5001 STOP 5001 FORMAT(' ERROR IN SUBROUTINE CCGQ') 1 NNF=MIN0(N+N1,NMAX) MIN=NPN6-N MF=NPN6+N IF(K1.EQ.1.AND.K2.EQ.0) MIN=NPN6 DO 100 MIND=MIN,MF M=MIND-NPN6 MM=M*K1+K2 M1=MM-M IF(IABS(M1).GT.N1) GO TO 90 NNL=MAX0(IABS(MM),IABS(N-N1)) IF(NNL.GT.NNF) GO TO 90 NNU=N+N1 NNM=(NNU+NNL)*0.5D0 IF (NNL.EQ.NNU) NNM=NNL CALL CCGIN(N,N1,M,MM,C) CU(NNL)=C IF (NNL.EQ.NNF) GO TO 50 C2=0D0 C1=C DO 7 NN=NNL+1,MIN0(NNM,NNF) A=DFLOAT((NN+MM)*(NN-MM)*(N1-N+NN)) A=A*DFLOAT((N-N1+NN)*(N+N1-NN+1)*(N+N1+NN+1)) A=DFLOAT(4*NN*NN)/A A=A*DFLOAT((2*NN+1)*(2*NN-1)) A=DSQRT(A) B=0.5D0*DFLOAT(M-M1) D=0D0 IF(NN.EQ.1) GO TO 5 B=DFLOAT(2*NN*(NN-1)) B=DFLOAT((2*M-MM)*NN*(NN-1)-MM*N*(N+1)+ & MM*N1*(N1+1))/B D=DFLOAT(4*(NN-1)*(NN-1)) D=D*DFLOAT((2*NN-3)*(2*NN-1)) D=DFLOAT((NN-MM-1)*(NN+MM-1)*(N1-N+NN-1))/D D=D*DFLOAT((N-N1+NN-1)*(N+N1-NN+2)*(N+N1+NN)) D=DSQRT(D) 5 C=A*(B*C1-D*C2) C2=C1 C1=C CU(NN)=C 7 CONTINUE IF (NNF.LE.NNM) GO TO 50 CALL DIRECT(N,M,N1,M1,NNU,MM,C) CD(NNU)=C IF (NNU.EQ.NNM+1) GO TO 50 C2=0D0 C1=C DO 12 NN=NNU-1,NNM+1,-1 A=DFLOAT((NN-MM+1)*(NN+MM+1)*(N1-N+NN+1)) A=A*DFLOAT((N-N1+NN+1)*(N+N1-NN)*(N+N1+NN+2)) A=DFLOAT(4*(NN+1)*(NN+1))/A A=A*DFLOAT((2*NN+1)*(2*NN+3)) A=DSQRT(A) B=DFLOAT(2*(NN+2)*(NN+1)) B=DFLOAT((2*M-MM)*(NN+2)*(NN+1)-MM*N*(N+1) & +MM*N1*(N1+1))/B D=DFLOAT(4*(NN+2)*(NN+2)) D=D*DFLOAT((2*NN+5)*(2*NN+3)) D=DFLOAT((NN+MM+2)*(NN-MM+2)*(N1-N+NN+2))/D D=D*DFLOAT((N-N1+NN+2)*(N+N1-NN-1)*(N+N1+NN+3)) D=DSQRT(D) C=A*(B*C1-D*C2) C2=C1 C1=C CD(NN)=C 12 CONTINUE 50 DO 9 NN=NNL,NNF IF (NN.LE.NNM) GG(MIND,NN+1)=CU(NN) IF (NN.GT.NNM) GG(MIND,NN+1)=CD(NN) c WRITE (6,*) N,M,N1,M1,NN,MM,GG(MIND,NN+1) 9 CONTINUE 90 CONTINUE 100 CONTINUE RETURN END C**************************************************************** C CALCULATION OF THE SCATTERING MATRIX FOR GIVEN EXPANSION C COEFFICIENTS C A1,...,B2 - EXPANSION COEFFICIENTS C LMAX - NUMBER OF COEFFICIENTS MINUS 1 C N - NUMBER OF SCATTERING ANGLES C THE CORRESPONDING SCATTERING ANGLES ARE GIVEN BY C 180*(I-1)/(N-1) (DEGREES), WHERE I NUMBERS THE ANGLES SUBROUTINE MATRQ(A1,A2,A3,A4,B1,B2,LMAX,NPNA,QUIET,F11,F22,F33, & F44,F12,F34) INCLUDE 'tmq.par.f' IMPLICIT REAL*8 (A-H,O-Z) REAL*8 A1(NPL),A2(NPL),A3(NPL),A4(NPL),B1(NPL),B2(NPL),F11(NPNA), & F22(NPNA),F33(NPNA),F44(NPNA),F12(NPNA),F34(NPNA) N=NPNA DN=1D0/DFLOAT(N-1) DA=DACOS(-1D0)*DN DB=180D0*DN L1MAX=LMAX+1 TB=-DB TAA=-DA IF (QUIET.EQ.0) THEN PRINT 1000 1000 FORMAT(' ') PRINT 1001 1001 FORMAT(' ',2X,'S',6X,'ALPHA1',6X,'ALPHA2',6X,'ALPHA3', & 6X,'ALPHA4',7X,'BETA1',7X,'BETA2') DO 10 L1=1,L1MAX L=L1-1 PRINT 1002,L,A1(L1),A2(L1),A3(L1),A4(L1),B1(L1),B2(L1) 10 CONTINUE 1002 FORMAT(' ',I3,6F12.5) PRINT 1000 PRINT 1003 1003 FORMAT(' ',5X,'<',8X,'F11',8X,'F22',8X,'F33', & 8X,'F44',8X,'F12',8X,'F34') ENDIF D6=DSQRT(6D0)*0.25D0 DO 500 I1=1,N TAA=TAA+DA TB=TB+DB U=DCOS(TAA) F11(I1)=0D0 F2=0D0 F3=0D0 F44(I1)=0D0 F12(I1)=0D0 F34(I1)=0D0 P1=0D0 P2=0D0 P3=0D0 P4=0D0 PP1=1D0 PP2=0.25D0*(1D0+U)*(1D0+U) PP3=0.25D0*(1D0-U)*(1D0-U) PP4=D6*(U*U-1D0) DO 400 L1=1,L1MAX L=L1-1 DL=DFLOAT(L) DL1=DFLOAT(L1) F11(I1)=F11(I1)+A1(L1)*PP1 F44(I1)=F44(I1)+A4(L1)*PP1 IF(L.EQ.LMAX) GO TO 350 PL1=DFLOAT(2*L+1) P=(PL1*U*PP1-DL*P1)/DL1 P1=PP1 PP1=P 350 IF(L.LT.2) GO TO 400 F2=F2+(A2(L1)+A3(L1))*PP2 F3=F3+(A2(L1)-A3(L1))*PP3 F12(I1)=F12(I1)+B1(L1)*PP4 F34(I1)=F34(I1)+B2(L1)*PP4 IF(L.EQ.LMAX) GO TO 400 PL2=DFLOAT(L*L1)*U PL3=DFLOAT(L1*(L*L-4)) PL4=1D0/DFLOAT(L*(L1*L1-4)) P=(PL1*(PL2-4D0)*PP2-PL3*P2)*PL4 P2=PP2 PP2=P P=(PL1*(PL2+4D0)*PP3-PL3*P3)*PL4 P3=PP3 PP3=P P=(PL1*U*PP4-DSQRT(DFLOAT(L*L-4))*P4)/DSQRT(DFLOAT(L1*L1-4)) P4=PP4 PP4=P 400 CONTINUE F22(I1)=(F2+F3)*0.5D0 F33(I1)=(F2-F3)*0.5D0 C F22=F22/F11 C F33=F33/F11 C F44=F44/F11 C F12=-F12/F11 C F34=F34/F11 IF (QUIET.EQ.0) PRINT 1004,TB,F11(I1),F22(I1),F33(I1),F44(I1), & F12(I1),F34(I1) 500 CONTINUE IF (QUIET.EQ.0) THEN PRINT 1000 1004 FORMAT(' ',F6.2,6F11.4) ENDIF RETURN END