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alphadiag.f90
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alphadiag.f90
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SUBROUTINE ALPHADIAG(AK_TF,BETADF,PHIDF,THETADF,CALPHA,CXALPH,CXALOF, &
CXE0_TF,CXEPS,CXSC,CXSCR1,CXZC,CXZW,DX,IBETH, &
IBETH1,ICOMP,IOCC,IPBC,IPHI,IPHI1,IXYZ0,JORTH,MYID, &
MXCOMP,MXNAT,MXN3,NAT,NAT0,NAT3,NCOMP,NX,NY,NZ, &
CXRLOC,CSHAPE,SHPAR)
USE DDPRECISION,ONLY : WP
USE DDCOMMON_8,ONLY : CMDFFT
IMPLICIT NONE
!--------------------------- alphadiag v3 -------------------------------------
!*** Arguments:
CHARACTER(6) :: CALPHA
CHARACTER(9) :: CSHAPE
INTEGER :: IBETH,IBETH1,IPBC,IPHI,IPHI1,JORTH,MXCOMP,MXNAT,MXN3, &
MYID,NAT,NAT0,NAT3,NCOMP,NX,NY,NZ
COMPLEX(WP) :: &
CXALOF(NAT,3), &
CXALPH(NAT,3), &
CXE0_TF(3), &
CXEPS(MXCOMP), &
CXSC(NAT,3,3), &
CXSCR1(NAT,3), &
CXZC(NX+1+IPBC*(NX-1),NY+1+IPBC*(NY-1),NZ+1+IPBC*(NZ-1),6), &
CXZW(2*NX,2*NY,2*NZ,3), &
CXRLOC(MXCOMP+1,3,3)
INTEGER*2 :: &
ICOMP(NAT,3), &
IOCC(NAT)
INTEGER :: &
IXYZ0(NAT0,3)
REAL(WP) :: &
AK_TF(3), &
BETADF(MXNAT), &
DX(3), &
PHIDF(MXNAT), &
SHPAR(12), &
THETADF(MXNAT)
!*** Local Variables:
LOGICAL :: INIT
CHARACTER :: CMSGNM*70
INTEGER :: IA,IC,IC2,IC3,L
REAL(WP) :: AK1,AK2,AK3,B1,B2,B3,B3L,COSBE,COSPH,COSTH,EMKD,PI, &
SINBE,SINPH,SINTH,SUM
REAL(WP) :: &
R(3,3), &
RI(3,3)
COMPLEX(WP) :: CXI,CXRR,CXSUM1,CXSUM2,CXSUM3,CXSUM4,CXSUM5, &
CXSUM6,CXTERM
!*** Common:
! CHARACTER(6) :: CMETHD
!-----------------------------------------------------------------------
! COMMON /M8/CMETHD
!-----------------------------------------------------------------------
SAVE INIT,CXI,PI
DATA CXI/(0._WP,1._WP)/
DATA INIT/.TRUE./
!***********************************************************************
! Given:
! AK_TF(1-3)=(kx,ky,kz)*d, where d=effective lattice spacing
! BETADF(1-NAT)
! PHIDF(1-NAT)
! THETADF(1-NAT): orientation angles beta,phi,theta (radians)
! specifying orientation of "Dielectric Frame" (DF
! relative to the "Target Frame" (TF)
! CALPHA = polarizability prescription
! = 'LATTDR' for LDR of Draine & Goodman (1993)
! = 'GKDLDR' for LDR of Gutkowicz-Krusin & Draine (2004)
! = 'FLTRCD' for filtered coupled dipole approach
! of Gay-Balmaz & Martin (2002) and
! Yurkin, Min & Hoekstra (2010)
! [= 'SCLDR' not supported in present version]
! CMETHD = determines 3-d FFT routine used by ESELF
! CSHAPE = descriptor of target shape
! CXE0_TF(1-3) = polarization vector in lattice coordinates
! (assumed to be normalized)
! CXEPS(1-NCOMP)=distinct values of dielectric constant
! CXSC(1-NAT,1-3,1-3) = complex scratch space for SCLDR calculation
! CXSCR1(1-NAT,1-3) = complex scratch space for SCLDR calculation
! CXZC = complex scratch space needed by ESELF
! CXZW = complex scratch space needed by ESELF
! DX(1-3)=(dx/d,dy/d,dz/d), where dx,dy,dz=lattice spacings in
! x,y,z directions, and d=(dx*dy*dz)**(1/3)
! IBETH= MYID+IBETH1 if first time through combined BETA/THETA
! orientation loop
! IBETH1=starting value of IBETH (see above)
! ICOMP(1-NAT3)=composition identifier for each lattice site and
! direction (ICOMP=0 if lattice site is unoccupied)
! storage scheme:
! 1x,2x,...,NATx,1y,2y,...,NATy,1z,2z,...,NATz
! IOCC(1-NAT) == 0 if site unoccupied
! == 1 if site occupied
! IPHI = IPHI1 if first time through PHI orientation loop
! IPHI1= starting value of IPHI (see above)
! JORTH= 1 if first incident polarization state
! MXCOMP = dimensioning information
! MXN3 = dimensioning information
! MYID = parallel process identifier (=0 if only 1 process)
! NAT = number of sites in extended target (incl. vacuum sites)
! NAT3 = 3*number of sites in extended target (incl. vacuum sites)
! NCOMP= number of different dielectric tensor elements in target
! NX = x-dimension of extended target
! NY = y-dimension of extended target
! NZ = z-dimension of extended target
! SHPAR(1-10)=target shape parameters
! Returns:
! CXALPH(J,1-3)=(alpha_11,alpha_22,alpha_33)/d^3 for dipole J=1-NAT
! where alpha_ij=complex polarizability tensor.
!***
! If CALPHA = LATTDR:
! Compute dipole polarizability using "Lattice Dispersion Relation"
! of Draine & Goodman (1993,ApJ,March 10). It is required that
! polarizability be such that an infinite lattice of such dipoles
! reproduce the continuum dispersion relation for radiation
! propagating with direction and polarization of radiation incident
! on the DDA target.
! If CALPHA = GKDLDR:
! Compute dipole polarizability using "Lattice Dispersion Relation"
! of Gutkowicz-Krusin and Draine (2004).. It is required that
! polarizability be such that an infinite lattice of such dipoles
! reproduce the continuum dispersion relation for radiation
! propagating with direction and polarization of radiation incident
! on the DDA target. This is the recommended option. It is nearly
! but not exactly identical to LATTDR.
! If CALPHA = FLTRCD = "Filtered Discrete Dipole"
! Compute dipole polarizability for "Filtered Coupled Dipole" approach
! of Piller & Martin (1998) and Gay-Balmaz & Martin (2002)
! and recently discussed by Yurkin, Min, & Hoekstra (2010)
!***
! Note: CXALPH = polarizability/d^3
! In the event that ICOMP=0, then we set CXALPH=1.
!***********************************************************************
! B.T.Draine, Princeton Univ. Obs.
! History:
! 90.09.13 (BTD): Corrected error in DO loop limit.
! 90.11.01 (BTD): Special treatment for "vacuum" sites in order
! to allow FFT treatment.
! 90.11.02 (BTD): Set CXALPH=(1.,0.) at vacuum sites.
! 91.04.30 (BTD): Modified to include both O[(kd)^2] correction term
! from Goedecke & Obrien (1988) in addition to
! radiative reaction correction.
! 91.05.07 (BTD): Modified to allow easy choice among three methods
! for computing polarizability.
! 91.05.07 (BTD): Added call to WRIMSG to record which method in use
! 91.05.08 (BTD): Added CALPHA to argument list.
! 91.05.09 (BTD): Added printing of kd and magnitude of correction
! terms.
! 91.05.13 (BTD): Experiment with use of approximate directional
! average for coefficient of CXEPS in Lattice
! Disperision Relation theory
! 91.05.13 (BTD): Corrected error in radiative reaction correction
! (error presumably introduced during last week)
! 91.05.14 (BTD): Added separate options LDRXYZ and LDRAVG
! 91.05.15 (BTD): Added option LDR000 to omit CXEPS-dependent
! correction term
! 91.05.30 (BTD): Changed LDRXYZ -> LDR100
! Added option LDR111
! 91.09.12 (BTD): Corrected error in numerical coefficient for
! LDRAVG case
! 91.09.17 (BTD): Eliminate options LDR000,LDRXYZ,LDRAVG
! Introduce option LATTDR (LATTice Dispersion Relation)
! which includes explicit dependence
! on direction and polarization state
! remove AK1 from argument list
! add AKR, CXE0R to argument list
! 92.05.14 (BTD): Introduce option LDRISO to experiment with
! using average directional correction term
! rather than using correction for incident direction
! and polarization
! 92.05.16 (BTD): Correct error in LDRISO option: average SUM should be
! 3/15 rather than 4/15
! 97.11.02 (BTD): Add DX to argument list to allow use with noncubic
! lattices (additional modifications still required!!)
! 97.12.26 (BTD): Add CXALOF to argument list to allow use with noncubic
! lattices (additional modifications still required).
! 97.12.30 (BTD): Add code to evaluate alpha for noncubic case,
! using subroutine NONCUBIC to evaluate the lattice
! sums R0,R1,R2,R3
! 98.01.14 (BTD): Change sign of radiative reaction correction term.
! 98.01.19 (BTD): Change treatment of R_1,C3, and C4
! and output value of C4
! temporary modification to allow value of C4 to be
! read in from file 'alpha.par'
! 98.01.22 (BTD): Minor change in computation of radiative reaction
! correction.
! 98.03.10 (BTD): set C4=-C3, disable reading C4 from 'alpha.par'
! 98.04.27 (BTD): declared IC1,IC2,IC3 as integers.
! 99.02.09 (BTD): experiment with change in expression used to calculate
! off-diagonal elements of polarizability tensor
! experiment with C4=-C3-R1 to "cancel" the contribution
! of R1 to the off-diagonal terms
! 03.01.29 (BTD): remove code to calculate alpha for noncubic lattice
! (hold for release in future version)
! 04.02.26 (BTD): add new option 'GKDLDR' to use Gutkowicz-Krusin
! and Draine (2004) lattice dispersion relation
! 04.03.31 (BTD): replace WRITE(0,... with CALL WRIMSG(...
! 04.04.01 (BTD): added DUM13,DUM14 to COMMON/M6/ to accomodate use of
! COMMON/M6/ in communicating NPY,NPZ to subroutineS
! MATVEC and CMATVEC
! 04.05.21 (BTD): cleanup -- eliminated a number of unused local
! variables
! 04.09.14 (BTD): modify to allow target to be made of anisotropic
! material with arbitrary orientation, with microcrystal
! orientation at each lattice site specified by angles
! BETADF,PHIDF,THETADF giving orientation of Dielectric
! Frame relative to Target Frame
! 05.06.16 (BTD): Changed DUM13,DUM14 in COMMON/M6/ from integer to real
! 06.09.28 (BTD): *** Version 6.2.3 ***
! Note: CXZC is not used at all by alpha and could be
! deleted from the argument list!
! 06.09.29 (BTD): Added IPBC to argument list
! Modified dimensioning of CXZC when IPBC=1
! Note: CXZC and CXSC do not appear to be used at
! present. Nevertheless, keep CXZC and CXSC in argument
! list in case complex scratch space is needed in some
! future version of ALPHA
! 07.06.30 (BTD): moved CMDFFT from COMMON/M6/... CMDFFT
! to COMMON/M8/CMDFFT
! COMMON/M6/ deleted -- no longer needed by alpha
! 07.08.04 (BTD): Version 7.0.3
! * replaced COMMON/M8/ with USE MODULE DDCOMMON_8
! 07.09.11 (BTD): Changed IXYZ0 from INTEGER*2 to INTEGER
! 07.10.27 (BTD): Changed SHPAR(6) -> SHPAR(10)
! 08.02.17 (BTD): Changed SHPAR(10) -> SHPAR(12)
! 08.03.11 (BTD): v7.0.5
! renamed SUBROUTINE ALPHA -> SUBROUTINE ALPHADIAG
! 08.03.14 (BTD): corrected dimensioning
! IXYZ0(MXNAT,3) -> IXYZ0(NAT0,3)
! BETADF(MXNAT) -> BETADF(NAT0)
! PHIDF(MXNAT) -> PHIDF(NAT0)
! THETADF(MXNAT) -> THETADF(NAT0)
! 08.07.27 (BTD): corrected dimensioning
! BETADF(NAT0) -> BETADF(MXNAT)
! PHIDF(NAT0) -> PHIDF(MXNAT)
! THETADF(NAT0) -> THETADF(MXNAT)
! 11.08.03 (BTD): eliminated variable CXALDS from argument list -- not used
! 11.12.20 (BTD): v7.1.1
! Dominika Dabrowska (Instituto Astrofisico de Andalucia)
! reported problem with rotations of dielectric frame when
! using option LATTDR
! problem has now been corrected:
! previous version of code only allowed for possible
! rotation of dielectric frames for option GKDLDR
! code has now been modified to also consider possible
! rotation of dielectric frames for option LATTDR
! 12.06.02 (BTD): v7.2.1
! replaced CXE0R -> CXE0_TF
! replaced AKR -> AK_TF
! 12.12.28 (BTD): v7.3.0 alphadiag_v3
! * modified to handle case FLTRCD: calculate alpha
! following prescription of
! end history
! Copyright (C) 1993,1996,1997,1998,1999,2003,2004,2006,2007,2008,2011,2012
! B.T. Draine and P.J. Flatau
! This code is covered by the GNU General Public License.
!***********************************************************************
!*** diagnostic
! write(0,*)'alphadiag_v3 ckpt 1, myid=',myid,' jorth=',jorth
! write(0,fmt='(a,3f10.5)')' AK_TF =',AK_TF
! write(0,*)'icomp(1,1-3)=',icomp(1,1),icomp(1,2),icomp(1,3)
!***
PI=4._WP*ATAN(1._WP)
AK2=AK_TF(1)*AK_TF(1)+AK_TF(2)*AK_TF(2)+AK_TF(3)*AK_TF(3)
AK1=SQRT(AK2)
AK3=AK1*AK2
CXRR=-(AK3/1.5_WP)*CXI
!*** EMKD = |m|*k_0*d , where |m|=refractive index
! k_0 = wave vector in vacuo
! d = lattice spacing
EMKD=SQRT(ABS(CXEPS(1)))*AK1
!***********************************************************************
!*** Lattice dispersion relation (Draine & Goodman 1993)
IF(CALPHA=='LATTDR')THEN
!*** diagnostic
! write(0,*)'alphadiag_v3 ckpt 2'
!***
WRITE(CMSGNM,FMT='(A,F6.4)') &
'Lattice dispersion relation for |m|k_0d=',EMKD
CALL WRIMSG('ALPHA ',CMSGNM)
!*** Compute sum (a_j*e_j)^2 , where a_j=unit propagation vector
! e_j=unit polarization vector
SUM=0.0_WP
DO L=1,3
SUM=SUM+(AK_TF(L)*ABS(CXE0_TF(L)))**2
ENDDO
SUM=SUM/AK2
B1=-1.8915316_WP*AK2
B2=(0.1648469_WP-1.7700004_WP*SUM)*AK2
DO L=1,3
DO IA=1,NAT
IC=ICOMP(IA,L)
IF(IC>0)THEN
!*** First compute Clausius-Mossotti polarizability:
CXTERM=(.75_WP/PI)*(CXEPS(IC)-1._WP)/(CXEPS(IC)+2._WP)
!*** Determine polarizability by requiring that infinite lattice of
! dipoles have dipersion relation of continuum.
CXTERM=CXTERM/(1._WP+CXTERM*(B1+CXEPS(IC)*B2))
!*** Radiative-reaction correction:
CXALPH(IA,L)=CXTERM/(1._WP+CXTERM*CXRR)
!*** diagnostic
! write(0,fmt='(a,3i3,1pe11.3,1pe10.3)') &
! 'alphadiag_v3 ckpt 3: IA,L,IC=',IA,L,IC,cxalph(ia,l)
!*** end diagnostic
! set off-diagonal terms to zero
CXALOF(IA,L)=0._WP
ELSEIF(IC==0)THEN
! To avoid divisions by zero, etc., set CXALPH=1 for vacuum sites.
CXALPH(IA,L)=1._WP
CXALOF(IA,L)=0._WP
ENDIF
ENDDO
ENDDO
!*** Lattice dispersion relation: modified
! (Gutkowicz-Krusin & Draine 2004)
ELSEIF(CALPHA=='GKDLDR')THEN
!*** diagnostic
! write(0,*)'alphadiag_v3 ckpt 4, myid=',myid
!***
IF(MYID==0)THEN
!*** diagnostic
! write(0,*)'alphadiag_v3 ckpt 5'
!***
WRITE(CMSGNM,FMT='(A,F6.4)') &
'GKDLDR Lattice dispersion relation for |m|k_0d=',EMKD
CALL WRIMSG('ALPHA ',CMSGNM)
ENDIF
! B1 = (c_1/pi)*ak2 = (-5.9424219/pi)*ak2 = -1.8915316*ak2
! B2 = (c_2/pi)*ak2 = (0.5178819/pi)*ak2 = 0.1648469*ak2
! B3 = -[(3c_2+c_3)/pi]*ak2 = -[(3*0.5178819+4.0069747)/pi]*ak2
! = -1.7700004*ak2
! B3L = B3*A(I)**2 where a_i = unit vector in direction of propagation
!*** diagnostic
! write(0,*)'alphadiag_v3 ckpt 6'
!***
B1=-1.8915316_WP*AK2
B2=0.1648469_WP*AK2
B3=-1.7700004_WP*AK2
DO L=1,3
B3L=B3*AK_TF(L)*AK_TF(L)/AK2
DO IA=1,NAT
IC=ICOMP(IA,L)
!*** diagnostic
! write(0,fmt='(i7,i3,i3,a)')ia,l,ic, &
! ' =ia,l,ic: alphadiag_v3 ckpt 7'
!***
IF(IC>0)THEN
!*** First compute Clausius-Mossotti polarizability:
CXTERM=(.75_WP/PI)*(CXEPS(IC)-1._WP)/(CXEPS(IC)+2._WP)
!*** Determine polarizability by requiring that infinite lattice of
! dipoles have dipersion relation of continuum.
CXTERM=CXTERM/(1._WP+CXTERM*(B1+CXEPS(IC)*(B2+B3L)))
!*** Radiative-reaction correction:
CXALPH(IA,L)=CXTERM/(1._WP+CXTERM*CXRR)
! set off-diagonal terms to zero
CXALOF(IA,L)=0._WP
ELSEIF(IC==0)THEN
! To avoid divisions by zero, etc., set CXALPH=1 for vacuum sites.
CXALPH(IA,L)=1._WP
CXALOF(IA,L)=0._WP
ENDIF
ENDDO
ENDDO
ELSEIF(CALPHA=='FLTRCD')THEN
!*** diagnostic
! write(0,*)'alphadiag_v3 ckpt 8, myid=',myid
!***
IF(MYID==0)THEN
!*** diagnostic
! write(0,*)'alphadiag_v3 ckpt 9'
!***
WRITE(CMSGNM,FMT='(A,F6.4)') &
'FLTRCD for |m|k_0d=',EMKD
CALL WRIMSG('ALPHA ',CMSGNM)
ENDIF
! x = (kd)
! B1 = (4/3)*x^2
! B2 = (2/3*pi)*ln[(pi-x)/(pi+x)]*x^3
!*** diagnostic
! write(0,*)'alphadiag_v3 ckpt 10'
!***
! prescription for alpha from Yurkin, Min & Hoekstra (2010):
B1=(4._WP*AK2+(2._WP/PI)*LOG((PI-AK1)/(PI+AK1))*AK3)/3._WP
DO L=1,3
DO IA=1,NAT
IC=ICOMP(IA,L)
!*** diagnostic
! write(0,fmt='(i7,i3,i3,a)')ia,l,ic, &
! ' =ia,l,ic: alphadiag_v3 ckpt 11'
!***
IF(IC>0)THEN
!*** First compute Clausius-Mossotti polarizability:
CXTERM=(.75_WP/PI)*(CXEPS(IC)-1._WP)/(CXEPS(IC)+2._WP)
! now apply corretion term
CXTERM=CXTERM/(1._WP+CXTERM*B1)
!*** Radiative-reaction correction
! Note that we are applying it differently from other authors
! (e.g., Piller & Martin 1998, Gay-Balmaz & Martin 2002,
! Yurkin, Min & Hoekstra 2010) who would have
! CXTERM=CXTERM/(1._WP+B1*CXTERM+CXTERM*CXRR)
! whereas we write
! CXTERM=[CXTERM/(1._WP+B1*CXTERM)]/
! [1._WP+CXTERM*CXRR/(1._WP+B1*CXTERM)]
! although to leading order (x^3) they are the same
CXALPH(IA,L)=CXTERM/(1._WP+CXTERM*CXRR)
! set off-diagonal terms to zero
CXALOF(IA,L)=0._WP
ELSEIF(IC==0)THEN
! To avoid divisions by zero, etc., set CXALPH=1 for vacuum sites.
CXALPH(IA,L)=1._WP
CXALOF(IA,L)=0._WP
ENDIF
ENDDO
ENDDO
ELSE
WRITE(CMSGNM,FMT='(A)') 'Error: invalid option for subroutine ALPHA'
CALL WRIMSG('ALPHA ',CMSGNM)
STOP
ENDIF
!*** diagnostic
! write(0,*)'alphadiag_v3 ckpt 12'
!***
! Now enter module to handle possible microcrystal rotation at each
! lattice site. BETADF,PHIDF,THETADF = 3 rotation angles specifying
! orientation of "Dielectric Frame" (in which dielectric tensor is
! diagonal) relative to Target Frame.
DO IA=1,NAT
IC=ICOMP(IA,1)
!*** diagnostic
! write(0,*)'alphadiag_v3 ckpt 13, ia=',ia,' ic=',ic
!***
IF(IC>0)THEN
IC2=ICOMP(IA,2)
IC3=ICOMP(IA,3)
IF(IC/=IC2.OR.IC/=IC3)THEN
!*** diagnostic
! write(0,*)'alphadiag_v3 ckpt 14, ic,ic2,ic3=',ic,ic2,ic3
!***
COSTH=COS(THETADF(IA))
COSPH=COS(PHIDF(IA))
COSBE=COS(BETADF(IA))
!*** diagnostic
! write(0,fmt='(a,3f10.6)')'costh,cosph,cosbe=', &
! costh,cosph,cosbe
!***
IF(COSTH*COSBE*COSPH<1._WP)THEN
! if nonzero rotation, recalculate CXALPH and CXALOF
SINTH=SIN(THETADF(IA))
SINPH=SIN(PHIDF(IA))
SINBE=SIN(BETADF(IA))
! Define R = rotation matrix
R(1,1)=COSTH
R(1,2)=SINTH*COSPH
R(1,3)=SINTH*SINPH
R(2,1)=-SINTH*COSBE
R(2,2)=COSTH*COSBE*COSPH-SINBE*SINPH
R(2,3)=COSTH*COSBE*SINPH+SINBE*COSPH
R(3,1)=SINTH*SINBE
R(3,2)=-COSTH*SINBE*COSPH-COSBE*SINPH
R(3,3)=-COSTH*SINBE*SINPH+COSBE*COSPH
! Define RI = inverse of R
RI(1,1)=COSTH
RI(1,2)=-SINTH*COSBE
RI(1,3)=SINTH*SINBE
RI(2,1)=SINTH*COSPH
RI(2,2)=COSTH*COSBE*COSPH-SINBE*SINPH
RI(2,3)=-COSTH*SINBE*COSPH-COSBE*SINPH
RI(3,1)=SINTH*SINPH
RI(3,2)=COSTH*COSBE*SINPH+SINBE*COSPH
RI(3,3)=-COSTH*SINBE*SINPH+COSBE*COSPH
! calculate diagonal elements:
CXSUM1=0._WP
CXSUM2=0._WP
CXSUM3=0._WP
CXSUM4=0._WP
CXSUM5=0._WP
CXSUM6=0._WP
DO L=1,3
CXSUM1=CXSUM1+R(1,L)*CXALPH(IA,L)*RI(L,1)
CXSUM2=CXSUM2+R(2,L)*CXALPH(IA,L)*RI(L,2)
CXSUM3=CXSUM3+R(3,L)*CXALPH(IA,L)*RI(L,3)
CXSUM4=CXSUM4+R(2,L)*CXALPH(IA,L)*RI(L,3)
CXSUM5=CXSUM5+R(3,L)*CXALPH(IA,L)*RI(L,1)
CXSUM6=CXSUM6+R(1,L)*CXALPH(IA,L)*RI(L,2)
ENDDO
CXALPH(IA,1)=CXSUM1
CXALPH(IA,2)=CXSUM2
CXALPH(IA,3)=CXSUM3
CXALOF(IA,1)=CXSUM4
CXALOF(IA,2)=CXSUM5
CXALOF(IA,3)=CXSUM6
ENDIF
ENDIF
ENDIF
ENDDO
!*** diagnostic
! write(0,*)'alphadiag_v3 ckpt 15'
!***
RETURN
END SUBROUTINE ALPHADIAG