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miev0.f
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SUBROUTINE MIEV0 ( XX, CREFIN, PERFCT, MIMCUT, ANYANG,
$ NUMANG, XMU, NMOM, IPOLZN, MOMDIM, PRNT,
$ QEXT, QSCA, GQSC, PMOM, SFORW, SBACK, S1,
$ S2, TFORW, TBACK, SPIKE )
c Author: Dr. Warren J. Wiscombe (wiscombe@climate.gsfc.nasa.gov)
c NASA Goddard Space Flight Center
c Code 913
c Greenbelt, MD 20771
c
c REFERENCES:
c ----------
c (1) Wiscombe, W., 1979: Mie Scattering Calculations--Advances
c in Technique And Fast, Vector-Speed Computer Codes,
c Ncar Tech Note Tn-140+Str, National Center For
c Atmospheric Research, Boulder, Colorado (NCAR no
c longer distributes this, so contact the author or
c NTIS for a copy)
c (2) Wiscombe, W., 1980: Improved Mie Scattering Algorithms,
c Appl. Opt. 19, 1505-1509
c (3) Dave, J.V., 1970a: Coefficients of the Legendre and
c Fourier Series for the Scattering Functions of
c Spherical Particles, Appl. Opt. 9, 1888-1896
c (4) Dave, J.V., 1970b: Intensity and Polarization of the
c Radiation Emerging from a Plane-Parallel Atmosphere
c Containing Monodisperse Aerosols, Appl. Opt. 9, 2673-84
c (5) Van De Hulst, 1957, 1982: Light Scattering by Small
c Particles, Dover Press, New York.
c (6) Bohren, C. and D. Huffman, Absorption and Scattering of
c Light by Small Particles, Wiley, New York. (has a
c Mie program in the back of the book)
c
c For more info, see MIEV-documentation.txt.
c
c **********************************************************************************
c Modified for use in sizmie.f by Alf Kirkevåg.
c **********************************************************************************
cak NB! jeg har endret MAXTRM for aa kunne bruke fordelinger med
cak store radier (opp til 100 mikrometer).
cak Paa grunn at de samme subrutinene blir brukt i straalingstransportmodellen,
cak har jeg her skiftet navn paa disse:
cak errmsg til errmsga (nytt navn)
cak wrtbad wrtbada
cak wrtdim wrtdima
cak tstbad tstbada
C COMPUTES MIE SCATTERING AND EXTINCTION EFFICIENCIES; ASYMMETRY
C FACTOR; FORWARD- AND BACKSCATTER AMPLITUDE; SCATTERING
C AMPLITUDES VS. SCATTERING ANGLE FOR INCIDENT POLARIZATION PARALLEL
C AND PERPENDICULAR TO THE PLANE OF SCATTERING;
C COEFFICIENTS IN THE LEGENDRE POLYNOMIAL EXPANSIONS OF EITHER THE
C UNPOLARIZED PHASE FUNCTION OR THE POLARIZED PHASE MATRIX;
C SOME QUANTITIES NEEDED IN POLARIZED RADIATIVE TRANSFER; AND
C INFORMATION ABOUT WHETHER OR NOT A RESONANCE HAS BEEN HIT.
C
C INPUT AND OUTPUT VARIABLES ARE DESCRIBED IN FILE MIEV.DOC
C
C ROUTINES CALLED : BIGA, CKINMI, SMALL1, SMALL2, TESTMI,
C MIPRNT, LPCOEF, ERRMSG
C
C I N T E R N A L V A R I A B L E S
C -----------------------------------
C
C AN,BN MIE COEFFICIENTS LITTLE-A-SUB-N, LITTLE-B-SUB-N
C ( REF. 1, EQ. 16 )
C ANM1,BNM1 MIE COEFFICIENTS LITTLE-A-SUB-(N-1),
C LITTLE-B-SUB-(N-1); USED IN -GQSC- SUM
C ANP COEFFS. IN S+ EXPANSION ( REF. 2, P. 1507 )
C BNP COEFFS. IN S- EXPANSION ( REF. 2, P. 1507 )
C ANPM COEFFS. IN S+ EXPANSION ( REF. 2, P. 1507 )
C WHEN MU IS REPLACED BY - MU
C BNPM COEFFS. IN S- EXPANSION ( REF. 2, P. 1507 )
C ( REF. 1, P. 11 FF. )
C RBIGA(N) BESSEL FUNCTION RATIO CAPITAL-A-SUB-N (REF. 2, EQ. 2)
C ( REAL VERSION, FOR WHEN IMAG REFRAC INDEX = 0 )
C RIORIV 1 / MRE
C RN 1 / N
C RTMP (REAL) TEMPORARY VARIABLE
C SP(J) S+ FOR J-TH ANGLE ( REF. 2, P. 1507 )
C SM(J) S- FOR J-TH ANGLE ( REF. 2, P. 1507 )
C SPS(J) S+ FOR (NUMANG+1-J)-TH ANGLE ( ANYANG=FALSE )
C SMS(J) S- FOR (NUMANG+1-J)-TH ANGLE ( ANYANG=FALSE )
C TAUN ANGULAR FUNCTION LITTLE-TAU-SUB-N ( REF. 2, EQ. 4 )
C AT J-TH ANGLE
C TCOEF N ( N+1 ) ( 2N+1 ) (FOR SUMMING TFORW,TBACK SERIES)
C TWONP1 2N + 1
C YESANG TRUE IF SCATTERING AMPLITUDES ARE TO BE CALCULATED
C ZETNM1 RICATTI-BESSEL FUNCTION ZETA-SUB-(N-1) OF ARGUMENT
C -XX- ( REF. 2, EQ. 17 )
C ZETN RICATTI-BESSEL FUNCTION ZETA-SUB-N OF ARGUMENT -XX-
C
C ----------------------------------------------------------------------
C -------- I / O SPECIFICATIONS FOR SUBROUTINE MIEV0 -----------------
C ----------------------------------------------------------------------
LOGICAL ANYANG, PERFCT, PRNT(*)
INTEGER IPOLZN, MOMDIM, NUMANG, NMOM, i
REAL GQSC, MIMCUT, PMOM( 0:MOMDIM, * ), QEXT, QSCA, SPIKE,
$ XMU(*), XX, radius, pi, lambda
COMPLEX CREFIN, SFORW, SBACK, S1(*), S2(*), TFORW(*), TBACK(*)
C ----------------------------------------------------------------------
C
PARAMETER ( MAXANG = 501, MXANG2 = MAXANG/2 + 1 )
C
C ** NOTE -- MAXTRM = 10100 IS NECES-
C ** SARY TO DO SOME OF THE TEST PROBS,
C ** BUT 1100 IS SUFFICIENT FOR MOST
C ** CONCEIVABLE APPLICATIONS
PARAMETER ( MAXTRM = 10100 ) ! A.K.
c PARAMETER ( MAXTRM = 1100 )
PARAMETER ( ONETHR = 1./3. )
C
LOGICAL CALCMO(4), NOABS, OK, PASS1, YESANG
INTEGER NPQUAN
REAL MIM, MRE, MM, NP1DN
REAL RBIGA( MAXTRM ), PIN( MAXANG ), PINM1( MAXANG )
COMPLEX AN, BN, ANM1, BNM1, ANP, BNP, ANPM, BNPM,
$ CDENAN, CDENBN, CIOR, CIORIV, CTMP, ZET, ZETNM1, ZETN
COMPLEX CBIGA( MAXTRM ), LITA( MAXTRM ), LITB( MAXTRM ),
$ SP( MAXANG ), SM( MAXANG ), SPS( MXANG2 ), SMS( MXANG2 )
SAVE PASS1
SQ( CTMP ) = REAL( CTMP )**2 + AIMAG( CTMP )**2
DATA PASS1 / .TRUE. /
C
C
C ** SAVE SOME INPUT VARIABLES AND REPLACE THEM
C ** WITH VALUES NEEDED TO DO THE SELF-TEST
IF ( PASS1 )
$ CALL TESTMI( .FALSE., XX, CREFIN, MIMCUT, PERFCT, ANYANG,
$ NMOM, IPOLZN, NUMANG, XMU, QEXT, QSCA, GQSC,
$ SFORW, SBACK, S1, S2, TFORW, TBACK, PMOM,
$ MOMDIM )
C ** CHECK INPUT AND CALCULATE
C ** CERTAIN VARIABLES FROM INPUT
C
10 CALL CKINMI( NUMANG, MAXANG, XX, PERFCT, CREFIN, MOMDIM,
$ NMOM, IPOLZN, ANYANG, XMU, CALCMO, NPQUAN )
C
IF ( PERFCT .AND. XX .LE. 0.1 ) THEN
C ** USE TOTALLY-REFLECTING
C ** SMALL-PARTICLE LIMIT
C
CALL SMALL1 ( XX, NUMANG, XMU, QEXT, QSCA, GQSC, SFORW,
$ SBACK, S1, S2, TFORW, TBACK, LITA, LITB )
NTRM = 2
GO TO 200
END IF
C
IF ( .NOT.PERFCT ) THEN
C
CIOR = CREFIN
IF ( AIMAG( CIOR ) .GT. 0.0 ) CIOR = CONJG( CIOR )
MRE = REAL( CIOR )
MIM = - AIMAG( CIOR )
NOABS = MIM .LE. MIMCUT
CIORIV = 1.0 / CIOR
RIORIV = 1.0 / MRE
C
IF ( XX * AMAX1( 1.0, CABS(CIOR) ) .LE. 0.1 ) THEN
C
C ** USE GENERAL-REFRACTIVE-INDEX
C ** SMALL-PARTICLE LIMIT
C ** ( REF. 2, P. 1508 )
C
CALL SMALL2 ( XX, CIOR, .NOT.NOABS, NUMANG, XMU, QEXT,
$ QSCA, GQSC, SFORW, SBACK, S1, S2, TFORW,
$ TBACK, LITA, LITB )
NTRM = 2
GO TO 200
END IF
C
END IF
C
NANGD2 = ( NUMANG + 1 ) / 2
YESANG = NUMANG .GT. 0
C ** ESTIMATE NUMBER OF TERMS IN MIE SERIES
C ** ( REF. 2, P. 1508 )
IF ( XX.LE.8.0 ) THEN
NTRM = XX + 4. * XX**ONETHR + 1.
ELSE IF ( XX.LT.4200. ) THEN
NTRM = XX + 4.05 * XX**ONETHR + 2.
ELSE
NTRM = XX + 4. * XX**ONETHR + 2.
END IF
IF ( NTRM+1 .GT. MAXTRM )
$ CALL ERRMSGA( 'MIEV0--PARAMETER MAXTRM TOO SMALL', .TRUE. )
C
C ** CALCULATE LOGARITHMIC DERIVATIVES OF
C ** J-BESSEL-FCN., BIG-A-SUB-(1 TO NTRM)
IF ( .NOT.PERFCT )
$ CALL BIGA( CIOR, XX, NTRM, NOABS, YESANG, RBIGA, CBIGA )
C
C ** INITIALIZE RICATTI-BESSEL FUNCTIONS
C ** (PSI,CHI,ZETA)-SUB-(0,1) FOR UPWARD
C ** RECURRENCE ( REF. 1, EQ. 19 )
XINV = 1.0 / XX
PSINM1 = SIN( XX )
CHINM1 = COS( XX )
PSIN = PSINM1 * XINV - CHINM1
CHIN = CHINM1 * XINV + PSINM1
ZETNM1 = CMPLX( PSINM1, CHINM1 )
ZETN = CMPLX( PSIN, CHIN )
C ** INITIALIZE PREVIOUS COEFFI-
C ** CIENTS FOR -GQSC- SERIES
ANM1 = ( 0.0, 0.0 )
BNM1 = ( 0.0, 0.0 )
C ** INITIALIZE ANGULAR FUNCTION LITTLE-PI
C ** AND SUMS FOR S+, S- ( REF. 2, P. 1507 )
IF ( ANYANG ) THEN
DO 60 J = 1, NUMANG
PINM1( J ) = 0.0
PIN( J ) = 1.0
SP ( J ) = ( 0.0, 0.0 )
SM ( J ) = ( 0.0, 0.0 )
60 CONTINUE
ELSE
DO 70 J = 1, NANGD2
PINM1( J ) = 0.0
PIN( J ) = 1.0
SP ( J ) = ( 0.0, 0.0 )
SM ( J ) = ( 0.0, 0.0 )
SPS( J ) = ( 0.0, 0.0 )
SMS( J ) = ( 0.0, 0.0 )
70 CONTINUE
END IF
C ** INITIALIZE MIE SUMS FOR EFFICIENCIES, ETC.
QSCA = 0.0
GQSC = 0.0
SFORW = ( 0., 0. )
SBACK = ( 0., 0. )
TFORW( 1 ) = ( 0., 0. )
TBACK( 1 ) = ( 0., 0. )
C
C
C --------- LOOP TO SUM MIE SERIES -----------------------------------
C
MM = + 1.0
SPIKE = 1.0
DO 100 N = 1, NTRM
C ** COMPUTE VARIOUS NUMERICAL COEFFICIENTS
FN = N
RN = 1.0 / FN
NP1DN = 1.0 + RN
TWONP1 = 2 * N + 1
COEFF = TWONP1 / ( FN * ( N + 1 ) )
TCOEF = TWONP1 * ( FN * ( N + 1 ) )
C
C ** CALCULATE MIE SERIES COEFFICIENTS
IF ( PERFCT ) THEN
C ** TOTALLY-REFLECTING CASE
C
AN = ( ( FN*XINV ) * PSIN - PSINM1 ) /
$ ( ( FN*XINV ) * ZETN - ZETNM1 )
BN = PSIN / ZETN
C
ELSE IF ( NOABS ) THEN
C ** NO-ABSORPTION CASE
C
CDENAN = ( RIORIV*RBIGA(N) + ( FN*XINV ) ) * ZETN - ZETNM1
AN = ( ( RIORIV*RBIGA(N) + ( FN*XINV ) ) * PSIN - PSINM1 )
$ / CDENAN
CDENBN = ( MRE * RBIGA(N) + ( FN*XINV ) ) * ZETN - ZETNM1
BN = ( ( MRE * RBIGA(N) + ( FN*XINV ) ) * PSIN - PSINM1 )
$ / CDENBN
ELSE
C ** ABSORPTIVE CASE
C
CDENAN = ( CIORIV * CBIGA(N) + ( FN*XINV ) ) * ZETN - ZETNM1
CDENBN = ( CIOR * CBIGA(N) + ( FN*XINV ) ) * ZETN - ZETNM1
AN = ( ( CIORIV * CBIGA(N) + ( FN*XINV ) ) * PSIN - PSINM1 )
$ / CDENAN
BN = ( ( CIOR * CBIGA(N) + ( FN*XINV ) ) * PSIN - PSINM1 )
$ / CDENBN
QSCA = QSCA + TWONP1 * ( SQ( AN ) + SQ( BN ) )
C
END IF
C ** SAVE MIE COEFFICIENTS FOR *PMOM* CALCULATION
LITA( N ) = AN
LITB( N ) = BN
C
IF ( .NOT.PERFCT .AND. N.GT.XX ) THEN
C ** FLAG RESONANCE SPIKES
DENAN = CABS( CDENAN )
DENBN = CABS( CDENBN )
RATIO = DENAN / DENBN
IF( RATIO.LE.0.2 .OR. RATIO.GE.5.0 )
$ SPIKE = AMIN1( SPIKE, DENAN, DENBN )
END IF
C ** INCREMENT MIE SUMS FOR NON-ANGLE-
C ** DEPENDENT QUANTITIES
C
SFORW = SFORW + TWONP1 * ( AN + BN )
TFORW( 1 ) = TFORW( 1 ) + TCOEF * ( AN - BN )
SBACK = SBACK + ( MM * TWONP1 ) * ( AN - BN )
TBACK( 1 ) = TBACK( 1 ) + ( MM * TCOEF ) * ( AN + BN )
GQSC = GQSC + ( FN - RN ) * REAL( ANM1 * CONJG( AN )
$ + BNM1 * CONJG( BN ) )
$ + COEFF * REAL( AN * CONJG( BN ) )
C
IF ( YESANG ) THEN
C ** PUT MIE COEFFICIENTS IN FORM
C ** NEEDED FOR COMPUTING S+, S-
C ** ( REF. 2, P. 1507 )
ANP = COEFF * ( AN + BN )
BNP = COEFF * ( AN - BN )
C ** INCREMENT MIE SUMS FOR S+, S-
C ** WHILE UPWARD RECURSING
C ** ANGULAR FUNCTIONS LITTLE PI
C ** AND LITTLE TAU
IF ( ANYANG ) THEN
C ** ARBITRARY ANGLES
C
C ** VECTORIZABLE LOOP
DO 80 J = 1, NUMANG
RTMP = ( XMU( J ) * PIN( J ) ) - PINM1( J )
TAUN = FN * RTMP - PINM1( J )
SP( J ) = SP( J ) + ANP * ( PIN( J ) + TAUN )
SM( J ) = SM( J ) + BNP * ( PIN( J ) - TAUN )
PINM1( J ) = PIN( J )
PIN( J ) = ( XMU( J ) * PIN( J ) ) + NP1DN * RTMP
80 CONTINUE
C
ELSE
C ** ANGLES SYMMETRIC ABOUT 90 DEGREES
ANPM = MM * ANP
BNPM = MM * BNP
C ** VECTORIZABLE LOOP
DO 90 J = 1, NANGD2
RTMP = ( XMU( J ) * PIN( J ) ) - PINM1( J )
TAUN = FN * RTMP - PINM1( J )
SP ( J ) = SP ( J ) + ANP * ( PIN( J ) + TAUN )
SMS( J ) = SMS( J ) + BNPM * ( PIN( J ) + TAUN )
SM ( J ) = SM ( J ) + BNP * ( PIN( J ) - TAUN )
SPS( J ) = SPS( J ) + ANPM * ( PIN( J ) - TAUN )
PINM1( J ) = PIN( J )
PIN( J ) = ( XMU( J ) * PIN( J ) ) + NP1DN * RTMP
90 CONTINUE
C
END IF
END IF
C ** UPDATE RELEVANT QUANTITIES FOR NEXT
C ** PASS THROUGH LOOP
MM = - MM
ANM1 = AN
BNM1 = BN
C ** UPWARD RECURRENCE FOR RICATTI-BESSEL
C ** FUNCTIONS ( REF. 1, EQ. 17 )
C
ZET = ( TWONP1 * XINV ) * ZETN - ZETNM1
ZETNM1 = ZETN
ZETN = ZET
PSINM1 = PSIN
PSIN = REAL( ZETN )
100 CONTINUE
C
C ---------- END LOOP TO SUM MIE SERIES --------------------------------
C
C
QEXT = 2. / XX**2 * REAL( SFORW )
IF ( PERFCT .OR. NOABS ) THEN
QSCA = QEXT
ELSE
QSCA = 2. / XX**2 * QSCA
END IF
C
GQSC = 4. / XX**2 * GQSC
SFORW = 0.5 * SFORW
SBACK = 0.5 * SBACK
TFORW( 2 ) = 0.5 * ( SFORW + 0.25 * TFORW( 1 ) )
TFORW( 1 ) = 0.5 * ( SFORW - 0.25 * TFORW( 1 ) )
TBACK( 2 ) = 0.5 * ( SBACK + 0.25 * TBACK( 1 ) )
TBACK( 1 ) = 0.5 * ( - SBACK + 0.25 * TBACK( 1 ) )
C
IF ( YESANG ) THEN
C ** RECOVER SCATTERING AMPLITUDES
C ** FROM S+, S- ( REF. 1, EQ. 11 )
IF ( ANYANG ) THEN
C ** VECTORIZABLE LOOP
DO 110 J = 1, NUMANG
S1( J ) = 0.5 * ( SP( J ) + SM( J ) )
S2( J ) = 0.5 * ( SP( J ) - SM( J ) )
110 CONTINUE
C
ELSE
C ** VECTORIZABLE LOOP
DO 120 J = 1, NANGD2
S1( J ) = 0.5 * ( SP( J ) + SM( J ) )
S2( J ) = 0.5 * ( SP( J ) - SM( J ) )
120 CONTINUE
C ** VECTORIZABLE LOOP
DO 130 J = 1, NANGD2
S1( NUMANG+1 - J ) = 0.5 * ( SPS( J ) + SMS( J ) )
S2( NUMANG+1 - J ) = 0.5 * ( SPS( J ) - SMS( J ) )
130 CONTINUE
END IF
C
END IF
C ** CALCULATE LEGENDRE MOMENTS
200 IF ( NMOM.GT.0 )
$ CALL LPCOEF ( NTRM, NMOM, IPOLZN, MOMDIM, CALCMO, NPQUAN,
$ LITA, LITB, PMOM )
C
IF ( AIMAG(CREFIN) .GT. 0.0 ) THEN
C ** TAKE COMPLEX CONJUGATES
C ** OF SCATTERING AMPLITUDES
SFORW = CONJG( SFORW )
SBACK = CONJG( SBACK )
DO 210 I = 1, 2
TFORW( I ) = CONJG( TFORW(I) )
TBACK( I ) = CONJG( TBACK(I) )
210 CONTINUE
C
DO 220 J = 1, NUMANG
S1( J ) = CONJG( S1(J) )
S2( J ) = CONJG( S2(J) )
220 CONTINUE
C
END IF
C
IF ( PASS1 ) THEN
C ** COMPARE TEST CASE RESULTS WITH
C ** CORRECT ANSWERS AND ABORT IF BAD;
C ** OTHERWISE RESTORE USER INPUT AND PROCEED
C
CALL TESTMI ( .TRUE., XX, CREFIN, MIMCUT, PERFCT, ANYANG,
$ NMOM, IPOLZN, NUMANG, XMU, QEXT, QSCA, GQSC,
$ SFORW, SBACK, S1, S2, TFORW, TBACK, PMOM,
$ MOMDIM )
PASS1 = .FALSE.
GO TO 10
C
END IF
C
IF ( PRNT(1) .OR. PRNT(2) )
$ CALL MIPRNT( PRNT, XX, PERFCT, CREFIN, NUMANG, XMU, QEXT,
$ QSCA, GQSC, NMOM, IPOLZN, MOMDIM, CALCMO,
$ PMOM, SFORW, SBACK, TFORW, TBACK, S1, S2 )
C
RETURN
C
END
SUBROUTINE CKINMI( NUMANG, MAXANG, XX, PERFCT, CREFIN, MOMDIM,
$ NMOM, IPOLZN, ANYANG, XMU, CALCMO, NPQUAN )
C
C CHECK FOR BAD INPUT TO 'MIEV0' AND CALCULATE -CALCMO,NPQUAN-
C
C ROUTINES CALLED : ERRMSGA, WRTBADA
C
LOGICAL WRTBADA, WRTDIMA
LOGICAL PERFCT, ANYANG, CALCMO(*)
INTEGER NUMANG, MAXANG, MOMDIM, NMOM, IPOLZN, NPQUAN
REAL XX, XMU(*)
COMPLEX CREFIN
C
CHARACTER*4 STRING
LOGICAL INPERR
C
C
INPERR = .FALSE.
IF ( NUMANG.GT.MAXANG ) INPERR = WRTDIMA( 'MAXANG', NUMANG )
IF ( NUMANG.LT.0 ) INPERR = WRTBADA( 'NUMANG' )
IF ( XX.LT.0. ) INPERR = WRTBADA( 'XX' )
IF ( .NOT.PERFCT .AND. REAL(CREFIN).LE.0. )
$ INPERR = WRTBADA( 'CREFIN' )
IF ( MOMDIM.LT.1 ) INPERR = WRTBADA( 'MOMDIM' )
C
IF ( NMOM.NE.0 ) THEN
IF ( NMOM.LT.0 .OR. NMOM.GT.MOMDIM ) INPERR = WRTBADA('NMOM')
IF ( IABS(IPOLZN).GT.4444 ) INPERR = WRTBADA( 'IPOLZN' )
NPQUAN = 0
DO 5 L = 1, 4
CALCMO( L ) = .FALSE.
5 CONTINUE
IF ( IPOLZN.NE.0 ) THEN
C ** PARSE OUT -IPOLZN- INTO ITS DIGITS
C ** TO FIND WHICH PHASE QUANTITIES ARE
C ** TO HAVE THEIR MOMENTS CALCULATED
C
WRITE( STRING, '(I4)' ) IABS(IPOLZN)
DO 10 J = 1, 4
IP = ICHAR( STRING(J:J) ) - ICHAR( '0' )
IF ( IP.GE.1 .AND. IP.LE.4 ) CALCMO( IP ) = .TRUE.
IF ( IP.EQ.0 .OR. (IP.GE.5 .AND. IP.LE.9) )
$ INPERR = WRTBADA( 'IPOLZN' )
NPQUAN = MAX0( NPQUAN, IP )
10 CONTINUE
END IF
END IF
C
IF ( ANYANG ) THEN
C ** ALLOW FOR SLIGHT IMPERFECTIONS IN
C ** COMPUTATION OF COSINE
DO 20 I = 1, NUMANG
IF ( XMU(I).LT.-1.00001 .OR. XMU(I).GT.1.00001 )
$ INPERR = WRTBADA( 'XMU' )
20 CONTINUE
ELSE
DO 22 I = 1, ( NUMANG + 1 ) / 2
IF ( XMU(I).LT.-0.00001 .OR. XMU(I).GT.1.00001 )
$ INPERR = WRTBADA( 'XMU' )
22 CONTINUE
END IF
C
IF ( INPERR )
$ CALL ERRMSGA( 'MIEV0--INPUT ERROR(S). ABORTING...', .TRUE. )
C
IF ( XX.GT.20000.0 .OR. REAL(CREFIN).GT.10.0 .OR.
$ ABS( AIMAG(CREFIN) ).GT.10.0 ) CALL ERRMSGA(
$ 'MIEV0--XX OR CREFIN OUTSIDE TESTED RANGE', .FALSE. )
C
RETURN
END
SUBROUTINE LPCOEF ( NTRM, NMOM, IPOLZN, MOMDIM, CALCMO, NPQUAN,
$ A, B, PMOM )
C
C CALCULATE LEGENDRE POLYNOMIAL EXPANSION COEFFICIENTS (ALSO
C CALLED MOMENTS) FOR PHASE QUANTITIES ( REF. 5 FORMULATION )
C
C INPUT: NTRM NUMBER TERMS IN MIE SERIES
C NMOM, IPOLZN, MOMDIM 'MIEV0' ARGUMENTS
C CALCMO FLAGS CALCULATED FROM -IPOLZN-
C NPQUAN DEFINED IN 'MIEV0'
C A, B MIE SERIES COEFFICIENTS
C
C OUTPUT: PMOM LEGENDRE MOMENTS ('MIEV0' ARGUMENT)
C
C ROUTINES CALLED : ERRMSGA, LPCO1T, LPCO2T
C
C *** NOTES ***
C
C (1) EQS. 2-5 ARE IN ERROR IN DAVE, APPL. OPT. 9,
C 1888 (1970). EQ. 2 REFERS TO M1, NOT M2; EQ. 3 REFERS TO
C M2, NOT M1. IN EQS. 4 AND 5, THE SUBSCRIPTS ON THE SECOND
C TERM IN SQUARE BRACKETS SHOULD BE INTERCHANGED.
C
C (2) THE GENERAL-CASE LOGIC IN THIS SUBROUTINE WORKS CORRECTLY
C IN THE TWO-TERM MIE SERIES CASE, BUT SUBROUTINE 'LPCO2T'
C IS CALLED INSTEAD, FOR SPEED.
C
C (3) SUBROUTINE 'LPCO1T', TO DO THE ONE-TERM CASE, IS NEVER
C CALLED WITHIN THE CONTEXT OF 'MIEV0', BUT IS INCLUDED FOR
C COMPLETE GENERALITY.
C
C (4) SOME IMPROVEMENT IN SPEED IS OBTAINABLE BY COMBINING THE
C 310- AND 410-LOOPS, IF MOMENTS FOR BOTH THE THIRD AND FOURTH
C PHASE QUANTITIES ARE DESIRED, BECAUSE THE THIRD PHASE QUANTITY
C IS THE REAL PART OF A COMPLEX SERIES, WHILE THE FOURTH PHASE
C QUANTITY IS THE IMAGINARY PART OF THAT VERY SAME SERIES. BUT
C MOST USERS ARE NOT INTERESTED IN THE FOURTH PHASE QUANTITY,
C WHICH IS RELATED TO CIRCULAR POLARIZATION, SO THE PRESENT
C SCHEME IS USUALLY MORE EFFICIENT.
C
LOGICAL CALCMO(*)
INTEGER IPOLZN, MOMDIM, NMOM, NTRM, NPQUAN
REAL PMOM( 0:MOMDIM, * )
COMPLEX A(*), B(*)
C
C ** SPECIFICATION OF LOCAL VARIABLES
C
C AM(M) NUMERICAL COEFFICIENTS A-SUB-M-SUPER-L
C IN DAVE, EQS. 1-15, AS SIMPLIFIED IN REF. 5.
C
C BI(I) NUMERICAL COEFFICIENTS B-SUB-I-SUPER-L
C IN DAVE, EQS. 1-15, AS SIMPLIFIED IN REF. 5.
C
C BIDEL(I) 1/2 BI(I) TIMES FACTOR CAPITAL-DEL IN DAVE
C
C CM,DM() ARRAYS C AND D IN DAVE, EQS. 16-17 (MUELLER FORM),
C CALCULATED USING RECURRENCE DERIVED IN REF. 5
C
C CS,DS() ARRAYS C AND D IN REF. 4, EQS. A5-A6 (SEKERA FORM),
C CALCULATED USING RECURRENCE DERIVED IN REF. 5
C
C C,D() EITHER -CM,DM- OR -CS,DS-, DEPENDING ON -IPOLZN-
C
C EVENL TRUE FOR EVEN-NUMBERED MOMENTS; FALSE OTHERWISE
C
C IDEL 1 + LITTLE-DEL IN DAVE
C
C MAXTRM MAX. NO. OF TERMS IN MIE SERIES
C
C MAXMOM MAX. NO. OF NON-ZERO MOMENTS
C
C NUMMOM NUMBER OF NON-ZERO MOMENTS
C
C RECIP(K) 1 / K
C
PARAMETER ( MAXTRM = 1102, MAXMOM = 2*MAXTRM, MXMOM2 = MAXMOM/2,
$ MAXRCP = 4*MAXTRM + 2 )
REAL AM( 0:MAXTRM ), BI( 0:MXMOM2 ), BIDEL( 0:MXMOM2 ),
$ RECIP( MAXRCP )
COMPLEX CM( MAXTRM ), DM( MAXTRM ), CS( MAXTRM ), DS( MAXTRM ),
$ C( MAXTRM ), D( MAXTRM )
EQUIVALENCE ( C, CM ), ( D, DM )
LOGICAL PASS1, EVENL
SAVE PASS1, RECIP
DATA PASS1 / .TRUE. /
C
C
IF ( PASS1 ) THEN
C
DO 1 K = 1, MAXRCP
RECIP( K ) = 1.0 / K
1 CONTINUE
PASS1 = .FALSE.
C
END IF
C
DO 5 J = 1, MAX0( 1, NPQUAN )
DO 5 L = 0, NMOM
PMOM( L, J ) = 0.0
5 CONTINUE
C
IF ( NTRM.EQ.1 ) THEN
CALL LPCO1T ( NMOM, IPOLZN, MOMDIM, CALCMO, A, B, PMOM )
RETURN
ELSE IF ( NTRM.EQ.2 ) THEN
CALL LPCO2T ( NMOM, IPOLZN, MOMDIM, CALCMO, A, B, PMOM )
RETURN
END IF
C
IF ( NTRM+2 .GT. MAXTRM )
$ CALL ERRMSGA( 'LPCOEF--PARAMETER MAXTRM TOO SMALL', .TRUE. )
C
C ** CALCULATE MUELLER C, D ARRAYS
CM( NTRM+2 ) = ( 0., 0. )
DM( NTRM+2 ) = ( 0., 0. )
CM( NTRM+1 ) = ( 1. - RECIP( NTRM+1 ) ) * B( NTRM )
DM( NTRM+1 ) = ( 1. - RECIP( NTRM+1 ) ) * A( NTRM )
CM( NTRM ) = ( RECIP(NTRM) + RECIP(NTRM+1) ) * A( NTRM )
$ + ( 1. - RECIP(NTRM) ) * B( NTRM-1 )
DM( NTRM ) = ( RECIP(NTRM) + RECIP(NTRM+1) ) * B( NTRM )
$ + ( 1. - RECIP(NTRM) ) * A( NTRM-1 )
C
DO 10 K = NTRM-1, 2, -1
CM( K ) = CM( K+2 ) - ( 1. + RECIP(K+1) ) * B( K+1 )
$ + ( RECIP(K) + RECIP(K+1) ) * A( K )
$ + ( 1. - RECIP(K) ) * B( K-1 )
DM( K ) = DM( K+2 ) - ( 1. + RECIP(K+1) ) * A( K+1 )
$ + ( RECIP(K) + RECIP(K+1) ) * B( K )
$ + ( 1. - RECIP(K) ) * A( K-1 )
10 CONTINUE
CM( 1 ) = CM( 3 ) + 1.5 * ( A( 1 ) - B( 2 ) )
DM( 1 ) = DM( 3 ) + 1.5 * ( B( 1 ) - A( 2 ) )
C
IF ( IPOLZN.GE.0 ) THEN
C
DO 20 K = 1, NTRM + 2
C( K ) = ( 2*K - 1 ) * CM( K )
D( K ) = ( 2*K - 1 ) * DM( K )
20 CONTINUE
C
ELSE
C ** COMPUTE SEKERA C AND D ARRAYS
CS( NTRM+2 ) = ( 0., 0. )
DS( NTRM+2 ) = ( 0., 0. )
CS( NTRM+1 ) = ( 0., 0. )
DS( NTRM+1 ) = ( 0., 0. )
C
DO 30 K = NTRM, 1, -1
CS( K ) = CS( K+2 ) + ( 2*K + 1 ) * ( CM( K+1 ) - B( K ) )
DS( K ) = DS( K+2 ) + ( 2*K + 1 ) * ( DM( K+1 ) - A( K ) )
30 CONTINUE
C
DO 40 K = 1, NTRM + 2
C( K ) = ( 2*K - 1 ) * CS( K )
D( K ) = ( 2*K - 1 ) * DS( K )
40 CONTINUE
C
END IF
C
C
IF( IPOLZN.LT.0 ) NUMMOM = MIN0( NMOM, 2*NTRM - 2 )
IF( IPOLZN.GE.0 ) NUMMOM = MIN0( NMOM, 2*NTRM )
IF ( NUMMOM .GT. MAXMOM )
$ CALL ERRMSGA( 'LPCOEF--PARAMETER MAXTRM TOO SMALL', .TRUE. )
C
C ** LOOP OVER MOMENTS
DO 500 L = 0, NUMMOM
LD2 = L / 2
EVENL = MOD( L,2 ) .EQ. 0
C ** CALCULATE NUMERICAL COEFFICIENTS
C ** A-SUB-M AND B-SUB-I IN DAVE
C ** DOUBLE-SUMS FOR MOMENTS
IF( L.EQ.0 ) THEN
C
IDEL = 1
DO 60 M = 0, NTRM
AM( M ) = 2.0 * RECIP( 2*M + 1 )
60 CONTINUE
BI( 0 ) = 1.0
C
ELSE IF( EVENL ) THEN
C
IDEL = 1
DO 70 M = LD2, NTRM
AM( M ) = ( 1. + RECIP( 2*M-L+1 ) ) * AM( M )
70 CONTINUE
DO 75 I = 0, LD2-1
BI( I ) = ( 1. - RECIP( L-2*I ) ) * BI( I )
75 CONTINUE
BI( LD2 ) = ( 2. - RECIP( L ) ) * BI( LD2-1 )
C
ELSE
C
IDEL = 2
DO 80 M = LD2, NTRM
AM( M ) = ( 1. - RECIP( 2*M+L+2 ) ) * AM( M )
80 CONTINUE
DO 85 I = 0, LD2
BI( I ) = ( 1. - RECIP( L+2*I+1 ) ) * BI( I )
85 CONTINUE
C
END IF
C ** ESTABLISH UPPER LIMITS FOR SUMS
C ** AND INCORPORATE FACTOR CAPITAL-
C ** DEL INTO B-SUB-I
MMAX = NTRM - IDEL
IF( IPOLZN.GE.0 ) MMAX = MMAX + 1
IMAX = MIN0( LD2, MMAX - LD2 )
IF( IMAX.LT.0 ) GO TO 600
DO 90 I = 0, IMAX
BIDEL( I ) = BI( I )
90 CONTINUE
IF( EVENL ) BIDEL( 0 ) = 0.5 * BIDEL( 0 )
C
C ** PERFORM DOUBLE SUMS JUST FOR
C ** PHASE QUANTITIES DESIRED BY USER
IF( IPOLZN.EQ.0 ) THEN
C
DO 110 I = 0, IMAX
C ** VECTORIZABLE LOOP (CRAY)
SUM = 0.0
DO 100 M = LD2, MMAX - I
SUM = SUM + AM( M ) *
$ ( REAL( C(M-I+1) * CONJG( C(M+I+IDEL) ) )
$ + REAL( D(M-I+1) * CONJG( D(M+I+IDEL) ) ) )
100 CONTINUE
PMOM( L,1 ) = PMOM( L,1 ) + BIDEL( I ) * SUM
110 CONTINUE
PMOM( L,1 ) = 0.5 * PMOM( L,1 )
GO TO 500
C
END IF
C
IF ( CALCMO(1) ) THEN
DO 160 I = 0, IMAX
C ** VECTORIZABLE LOOP (CRAY)
SUM = 0.0
DO 150 M = LD2, MMAX - I
SUM = SUM + AM( M ) *
$ REAL( C(M-I+1) * CONJG( C(M+I+IDEL) ) )
150 CONTINUE
PMOM( L,1 ) = PMOM( L,1 ) + BIDEL( I ) * SUM
160 CONTINUE
END IF
C
C
IF ( CALCMO(2) ) THEN
DO 210 I = 0, IMAX
C ** VECTORIZABLE LOOP (CRAY)
SUM = 0.0
DO 200 M = LD2, MMAX - I
SUM = SUM + AM( M ) *
$ REAL( D(M-I+1) * CONJG( D(M+I+IDEL) ) )
200 CONTINUE
PMOM( L,2 ) = PMOM( L,2 ) + BIDEL( I ) * SUM
210 CONTINUE
END IF
C
C
IF ( CALCMO(3) ) THEN
DO 310 I = 0, IMAX
C ** VECTORIZABLE LOOP (CRAY)
SUM = 0.0
DO 300 M = LD2, MMAX - I
SUM = SUM + AM( M ) *
$ ( REAL( C(M-I+1) * CONJG( D(M+I+IDEL) ) )
$ + REAL( C(M+I+IDEL) * CONJG( D(M-I+1) ) ) )
300 CONTINUE
PMOM( L,3 ) = PMOM( L,3 ) + BIDEL( I ) * SUM
310 CONTINUE
PMOM( L,3 ) = 0.5 * PMOM( L,3 )
END IF
C
C
IF ( CALCMO(4) ) THEN
DO 410 I = 0, IMAX
C ** VECTORIZABLE LOOP (CRAY)
SUM = 0.0
DO 400 M = LD2, MMAX - I
SUM = SUM + AM( M ) *
$ ( AIMAG( C(M-I+1) * CONJG( D(M+I+IDEL) ) )
$ + AIMAG( C(M+I+IDEL) * CONJG( D(M-I+1) ) ) )
400 CONTINUE
PMOM( L,4 ) = PMOM( L,4 ) + BIDEL( I ) * SUM
410 CONTINUE
PMOM( L,4 ) = - 0.5 * PMOM( L,4 )
END IF
C
500 CONTINUE
C
C
600 RETURN
END
SUBROUTINE LPCO1T ( NMOM, IPOLZN, MOMDIM, CALCMO, A, B, PMOM )
C
C CALCULATE LEGENDRE POLYNOMIAL EXPANSION COEFFICIENTS (ALSO
C CALLED MOMENTS) FOR PHASE QUANTITIES IN SPECIAL CASE WHERE
C NO. TERMS IN MIE SERIES = 1
C
C INPUT: NMOM, IPOLZN, MOMDIM 'MIEV0' ARGUMENTS
C CALCMO FLAGS CALCULATED FROM -IPOLZN-
C A(1), B(1) MIE SERIES COEFFICIENTS
C
C OUTPUT: PMOM LEGENDRE MOMENTS
C
LOGICAL CALCMO(*)
INTEGER IPOLZN, MOMDIM, NMOM
REAL PMOM( 0:MOMDIM, * )
COMPLEX A(*), B(*), CTMP, A1B1C
SQ( CTMP ) = REAL( CTMP )**2 + AIMAG( CTMP )**2
C
C
A1SQ = SQ( A(1) )
B1SQ = SQ( B(1) )
A1B1C = A(1) * CONJG( B(1) )
C
IF( IPOLZN.LT.0 ) THEN
C
IF( CALCMO(1) ) PMOM( 0,1 ) = 2.25 * B1SQ
IF( CALCMO(2) ) PMOM( 0,2 ) = 2.25 * A1SQ
IF( CALCMO(3) ) PMOM( 0,3 ) = 2.25 * REAL( A1B1C )
IF( CALCMO(4) ) PMOM( 0,4 ) = 2.25 *AIMAG( A1B1C )
C
ELSE
C
NUMMOM = MIN0( NMOM, 2 )
C ** LOOP OVER MOMENTS
DO 100 L = 0, NUMMOM
C
IF( IPOLZN.EQ.0 ) THEN
IF( L.EQ.0 ) PMOM( L,1 ) = 1.5 * ( A1SQ + B1SQ )
IF( L.EQ.1 ) PMOM( L,1 ) = 1.5 * REAL( A1B1C )
IF( L.EQ.2 ) PMOM( L,1 ) = 0.15 * ( A1SQ + B1SQ )
GO TO 100
END IF
C
IF( CALCMO(1) ) THEN
IF( L.EQ.0 ) PMOM( L,1 ) = 2.25 * ( A1SQ + B1SQ / 3. )
IF( L.EQ.1 ) PMOM( L,1 ) = 1.5 * REAL( A1B1C )
IF( L.EQ.2 ) PMOM( L,1 ) = 0.3 * B1SQ
END IF
C
IF( CALCMO(2) ) THEN
IF( L.EQ.0 ) PMOM( L,2 ) = 2.25 * ( B1SQ + A1SQ / 3. )
IF( L.EQ.1 ) PMOM( L,2 ) = 1.5 * REAL( A1B1C )
IF( L.EQ.2 ) PMOM( L,2 ) = 0.3 * A1SQ
END IF
C
IF( CALCMO(3) ) THEN
IF( L.EQ.0 ) PMOM( L,3 ) = 3.0 * REAL( A1B1C )
IF( L.EQ.1 ) PMOM( L,3 ) = 0.75 * ( A1SQ + B1SQ )
IF( L.EQ.2 ) PMOM( L,3 ) = 0.3 * REAL( A1B1C )
END IF
C
IF( CALCMO(4) ) THEN
IF( L.EQ.0 ) PMOM( L,4 ) = - 1.5 * AIMAG( A1B1C )
IF( L.EQ.1 ) PMOM( L,4 ) = 0.0
IF( L.EQ.2 ) PMOM( L,4 ) = 0.3 * AIMAG( A1B1C )
END IF
C
100 CONTINUE
C
END IF
C
RETURN
END
SUBROUTINE LPCO2T ( NMOM, IPOLZN, MOMDIM, CALCMO, A, B, PMOM )
C
C CALCULATE LEGENDRE POLYNOMIAL EXPANSION COEFFICIENTS (ALSO
C CALLED MOMENTS) FOR PHASE QUANTITIES IN SPECIAL CASE WHERE
C NO. TERMS IN MIE SERIES = 2
C
C INPUT: NMOM, IPOLZN, MOMDIM 'MIEV0' ARGUMENTS
C CALCMO FLAGS CALCULATED FROM -IPOLZN-
C A(1-2), B(1-2) MIE SERIES COEFFICIENTS
C
C OUTPUT: PMOM LEGENDRE MOMENTS
C
LOGICAL CALCMO(*)
INTEGER IPOLZN, MOMDIM, NMOM
REAL PMOM( 0:MOMDIM, * )
COMPLEX A(*), B(*)
COMPLEX A2C, B2C, CTMP, CA, CAC, CAT, CB, CBC, CBT, CG, CH
SQ( CTMP ) = REAL( CTMP )**2 + AIMAG( CTMP )**2
C
C
CA = 3. * A(1) - 5. * B(2)
CAT= 3. * B(1) - 5. * A(2)
CAC = CONJG( CA )
A2SQ = SQ( A(2) )
B2SQ = SQ( B(2) )
A2C = CONJG( A(2) )
B2C = CONJG( B(2) )
C
IF( IPOLZN.LT.0 ) THEN
C ** LOOP OVER SEKERA MOMENTS
NUMMOM = MIN0( NMOM, 2 )
DO 50 L = 0, NUMMOM
C
IF( CALCMO(1) ) THEN
IF( L.EQ.0 ) PMOM( L,1 ) = 0.25 * ( SQ(CAT) +
$ (100./3.) * B2SQ )
IF( L.EQ.1 ) PMOM( L,1 ) = (5./3.) * REAL( CAT * B2C )
IF( L.EQ.2 ) PMOM( L,1 ) = (10./3.) * B2SQ
END IF
C
IF( CALCMO(2) ) THEN
IF( L.EQ.0 ) PMOM( L,2 ) = 0.25 * ( SQ(CA) +
$ (100./3.) * A2SQ )
IF( L.EQ.1 ) PMOM( L,2 ) = (5./3.) * REAL( CA * A2C )
IF( L.EQ.2 ) PMOM( L,2 ) = (10./3.) * A2SQ
END IF
C
IF( CALCMO(3) ) THEN
IF( L.EQ.0 ) PMOM( L,3 ) = 0.25 * REAL( CAT*CAC +
$ (100./3.)*B(2)*A2C )
IF( L.EQ.1 ) PMOM( L,3 ) = 5./6. * REAL( B(2)*CAC +
$ CAT*A2C )
IF( L.EQ.2 ) PMOM( L,3 ) = 10./3. * REAL( B(2) * A2C )
END IF
C
IF( CALCMO(4) ) THEN
IF( L.EQ.0 ) PMOM( L,4 ) = -0.25 * AIMAG( CAT*CAC +
$ (100./3.)*B(2)*A2C )
IF( L.EQ.1 ) PMOM( L,4 ) = -5./6. * AIMAG( B(2)*CAC +
$ CAT*A2C )
IF( L.EQ.2 ) PMOM( L,4 ) = -10./3. * AIMAG( B(2) * A2C )
END IF
C
50 CONTINUE
C
ELSE
C
CB = 3. * B(1) + 5. * A(2)
CBT= 3. * A(1) + 5. * B(2)
CBC = CONJG( CB )
CG = ( CBC*CBT + 10.*( CAC*A(2) + B2C*CAT) ) / 3.
CH = 2.*( CBC*A(2) + B2C*CBT )
C
C ** LOOP OVER MUELLER MOMENTS
NUMMOM = MIN0( NMOM, 4 )
DO 100 L = 0, NUMMOM
C
IF( IPOLZN.EQ.0 .OR. CALCMO(1) ) THEN
IF( L.EQ.0 ) PM1 = 0.25 * SQ(CA) + SQ(CB) / 12.
$ + (5./3.) * REAL(CA*B2C) + 5.*B2SQ
IF( L.EQ.1 ) PM1 = REAL( CB * ( CAC/6. + B2C ) )
IF( L.EQ.2 ) PM1 = SQ(CB)/30. + (20./7.) * B2SQ
$ + (2./3.) * REAL( CA * B2C )
IF( L.EQ.3 ) PM1 = (2./7.) * REAL( CB * B2C )
IF( L.EQ.4 ) PM1 = (40./63.) * B2SQ
IF ( CALCMO(1) ) PMOM( L,1 ) = PM1
END IF
C
IF( IPOLZN.EQ.0 .OR. CALCMO(2) ) THEN
IF( L.EQ.0 ) PM2 = 0.25*SQ(CAT) + SQ(CBT) / 12.
$ + (5./3.) * REAL(CAT*A2C) + 5.*A2SQ
IF( L.EQ.1 ) PM2 = REAL( CBT * ( CONJG(CAT)/6. + A2C) )
IF( L.EQ.2 ) PM2 = SQ(CBT)/30. + (20./7.) * A2SQ
$ + (2./3.) * REAL( CAT * A2C )
IF( L.EQ.3 ) PM2 = (2./7.) * REAL( CBT * A2C )
IF( L.EQ.4 ) PM2 = (40./63.) * A2SQ
IF ( CALCMO(2) ) PMOM( L,2 ) = PM2
END IF
C
IF( IPOLZN.EQ.0 ) THEN
PMOM( L,1 ) = 0.5 * ( PM1 + PM2 )
GO TO 100
END IF
C
IF( CALCMO(3) ) THEN
IF( L.EQ.0 ) PMOM( L,3 ) = 0.25 * REAL( CAC*CAT + CG +
$ 20.*B2C*A(2) )
IF( L.EQ.1 ) PMOM( L,3 ) = REAL( CAC*CBT + CBC*CAT +
$ 3.*CH ) / 12.
IF( L.EQ.2 ) PMOM( L,3 ) = 0.1 * REAL( CG + (200./7.) *
$ B2C * A(2) )
IF( L.EQ.3 ) PMOM( L,3 ) = REAL( CH ) / 14.
IF( L.EQ.4 ) PMOM( L,3 ) = 40./63. * REAL( B2C * A(2) )
END IF
C
IF( CALCMO(4) ) THEN
IF( L.EQ.0 ) PMOM( L,4 ) = 0.25 * AIMAG( CAC*CAT + CG +
$ 20.*B2C*A(2) )
IF( L.EQ.1 ) PMOM( L,4 ) = AIMAG( CAC*CBT + CBC*CAT +
$ 3.*CH ) / 12.
IF( L.EQ.2 ) PMOM( L,4 ) = 0.1 * AIMAG( CG + (200./7.) *