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! For input atomic data file formats see Readme file attached at the end
! **********************************************************************
! Program EQUIB (FORTRAN 77)
!
! Programming history:
!
! 1981 May 3 IDH Version 1
! 1981 May 5 IDH Minibug fixed!
! 1981 May 7 IDH Now takes collision rates or strengths
! 1981 Aug 3 SA Interpolates collision strengths
! 1981 Aug 7 SA Input method changed
! 1984 Nov 19 RESC SA files entombed in scratch disk. Logical
! filenames given to SA's data files.
! 1995 Aug DPR Changed input file format. Increased matrices.
! 1996 Feb XWL Tidy up. SUBROUTINES SPLMAT, HGEN, CFY and CFD
! modified such that matrix sizes (i.e. maximum
! of Te and maximum no of levels) can now be cha
! by modifying the parameters NDIM1, NDIM2 and N
! in the Main program. EASY!
! Now takes collision rates as well.
! All variables are declared explicitly
! Generate two extra files (ionpop.lis and ionra
! of plain stream format for plotting
! 1996 June CJP Changed input data format for cases IBIG=1,2.
! Fixed readin bug for IBIG=2 case.
! Now reads reformatted upsilons (easier to see
! and the 0 0 0 data end is excluded for these c
! The A values have a different format for IBIG=
! 2009 April RW Converted to F90, inputs from cmd line, version
! written purely to do diagnostics.
! 2012 February RW Tidying up, combining into simpler routines for NEAT
! ***** N.B!! NO TRAPS FOR BAD DATA!! TAKE CARE!! ****C
!
module mod_equib
use mod_globals
contains
subroutine get_diagnostic(ion,levu,levl,inratio,diagtype,fixedq,result,ndim2,ndim1,atomicdata,iion,tlower,tupper)
use mod_atomicdata
use mod_helium
implicit none
integer :: NDIM1, NDIM2, NDIM1T3, MAXND
!Maximum no of Te & levels
!NDIM1T3 should be at least 3*NDIM1
!Maximum no. of Ne increments
parameter (MAXND=100)
integer :: G(NDIM2), &
& ITRANA(2,NDIM2),ITRANB(2,NDIM2),ITRANC(2,NDIM2),LOOP
type(atomic_data),dimension(:),intent(in) :: atomicdata
integer :: iion,nion
real(kind=dp) :: N(NDIM2)
real(kind=dp) :: & !TDRAT(2,MAXND)
& TNIJ(NDIM2,NDIM2), FINTIJ(NDIM2,NDIM2), &
& WAVA(NDIM2), WAVB(NDIM2), WAVC(NDIM2), CS(NDIM2,NDIM2), &
& QEFF(NDIM2,NDIM2), QQ(NDIM1), &
& QOM(NDIM1,NDIM2,NDIM2), A(NDIM2,NDIM2), E(NDIM2), T(NDIM1), &
& ROOTT(NDIM1), X(NDIM2,NDIM2), Y(NDIM2), &
& X2(NDIM2,NDIM2), XKEEP(NDIM2,NDIM2), Y2(NDIM2), YKEEP(NDIM2), &
& HMH(NDIM1,NDIM1), D(NDIM1)
character(len=20) :: LABEL(NDIM2)
character(len=10) :: ION
integer :: I, I1, I2, J, KK, LL, JT, JJD, &
& NLEV, NTEMP, IBIG, IRATS, &
& NLEV1, INT, IND, IOPT, IT, IM1, JM1, IP1, &
& IAPR, IBPR, ICPR, IKT, IA, IB, IC, IA1, IA2, IB1, IB2, IC1, IC2
real(kind=dp) :: TEMPI, TINC, DENSI, DINC, DENS, DLOGD, TEMP, TLOGT, &
& TEMP2, DD, DELTEK, EXPE, VALUE, SUMN, TTT, TTP, AHB, EJI, WAV, &
& RLINT, FINT, SUMA, SUMB, FRAT, DEE
real(kind=dp) :: fixedq
real(kind=dp) :: inratio,result
character(len=20) :: levu,levl
character(len=1) :: diagtype
real(kind=dp), DIMENSION(:,:), ALLOCATABLE :: RESULTS
real(kind=dp) :: valtest(3)
integer :: test
real(kind=dp) :: tlower,tupper ! lower and upper limits for temperature calculations
!debugging
#ifdef CO
print *,"subroutine: get_diagnostic. ion=",ion,levu,levl,inratio,diagtype,fixedq
#endif
! check if ratio is meaningful
if (inratio .le. 0.d0 .or. inratio .gt. 1.e10) then
result=0.d0
return
endif
ndim1t3=3*ndim1
g=0
itrana=0
itranb=0
itranc=0
valtest=0.d0
test=0
d=0.d0
read(levu,*) ((ITRANA(LL,KK),LL=1,2),KK=1,ndim2)!150)
read(levl,*) ((ITRANB(LL,KK),LL=1,2),KK=1,ndim2)!150)
!Transfer atomic data to local variables
nion = 0
do i = 1,iion
if(atomicdata(i)%ion .eq. ion) nion=i
enddo
if (nion .eq. 0) then
print *,"I'm afraid. I'm afraid, Dave."
nion = 1
endif
! print*,nion,atomicdata(nion)%ion,ion
nlev=atomicdata(nion)%nlevs
ntemp=atomicdata(nion)%ntemps
T(1:ntemp)= log10(atomicdata(nion)%Temps(1:ntemp))
ROOTT(1:ntemp)=atomicdata(nion)%rootT(1:ntemp)
Label(1:nlev)=atomicdata(nion)%labels(1:nlev)
QOM(1:ntemp,1:nlev,1:nlev)=atomicdata(nion)%col_str(1:ntemp,1:nlev,1:nlev)
A(1:nlev,1:nlev)=atomicdata(nion)%A_coeffs(1:nlev,1:nlev)
E(1:nlev)=atomicdata(nion)%Waveno(1:nlev)
G(1:nlev)=atomicdata(nion)%G(1:nlev)
irats=0
ibig=0
NLEV1 = NLEV - 1
ITRANC = 0
!*****LOOP STARTS HERE*************************
do LOOP = 1, 9
if (diagtype .eq. "t" .or. diagtype .eq. "T") then
if (LOOP .eq. 1) then
TEMPI=tlower
else
TEMPI= valtest(1)
endif
INT=4
TINC=(tupper-tlower)/((INT-1)**(LOOP))
densi=fixedq
dinc=0
ind=1
allocate(RESULTS(3,INT))
else
if (LOOP .eq. 1) then
densi=0
else
densi=valtest(2)
endif
IND=4
DINC=(100000.)/((IND-1)**(LOOP))
TempI=fixedq
TINC=0
INT=1
allocate(results(3,IND))
endif
if (densi .le. 0) densi=1
if (tempi .lt. tlower) tempi=tlower
!Start of Te loop
do JT = 1, INT
TEMP=TEMPI+(JT-1)*TINC
!Start of Ne loop
do JJD = 1, IND
DENS=DENSI+(JJD-1)*DINC
if (TEMP.LE.0.D0.OR.DENS.LE.0.D0) then
write (6,6100)
print *,"Temp = ", TEMP, ", Dens = ", DENS, ", Ion = ",ion,diagtype
call exit(200)
endif
DLOGD = log10(DENS)
TLOGT = log10(TEMP)
TEMP2= sqrt(TEMP)
!Form matrices
X=0.0
CS=0.0
QEFF=0.0
TNIJ=0.0
Y=0.0
IOPT=0
if (NTEMP.EQ.1) then
write (6,*)
write (6,*) &
& 'Coll. strengths available for 1 Te only - assuming const'
elseif (NTEMP.EQ.2) then
write (6,*)
write (6,*) &
& 'Coll. strengths available for 2 Te only - linear interp'
else
call SPLMAT(T, NTEMP, IOPT, NDIM1, NDIM1T3, HMH)
call CFD(TLOGT,T,NTEMP,NDIM1,HMH,D)
endif
do I = 2, NLEV
do J = I, NLEV
!Negative!
DELTEK = (E(I-1)-E(J))*1.4388463D0
EXPE = EXP(DELTEK/TEMP)
do IT = 1, NTEMP
if (IRATS.EQ.0.D+00) then
QQ(IT) = QOM(IT,I-1,J)
else
!Take out the exp. depend.
QQ(IT) = QOM(IT,I-1,J) / EXPE
!before interpolation
endif
enddo
if (NTEMP.EQ.1) then
DD = QQ(1)
elseif (NTEMP.EQ.2) then
DD = QQ(1) + &
& (QQ(2) - QQ(1))/(T(2) - T(1)) * (TLOGT - T(1))
else
call CFY(TLOGT, DD, T, QQ, NTEMP, NDIM1, D)
endif
if (IRATS.EQ.0.D+00) then
CS(I-1,J) = DD
else
CS(I-1,J) = DD * EXPE
endif
if (IRATS .EQ. 0.D+00) then
QEFF(I-1,J) = 8.63D-06*CS(I-1,J) * EXPE / (G(I-1)*TEMP2)
QEFF(J,I-1) = 8.63D-06 * CS(I-1,J) / (G(J)*TEMP2)
else
QEFF(I-1,J) = CS(I-1,J) * 10. ** IRATS
!Be careful
QEFF(J,I-1) = G(I-1) * QEFF(I-1,J) / (EXPE * G(J))
!G integer!
endif
enddo
enddo
do I = 2, NLEV
do J = 1, NLEV
if (J.NE.I) then
X(I,J) = X(I,J) + DENS * QEFF(J,I)
X(I,I) = X(I,I) - DENS * QEFF(I,J)
if (J.GT.I) then
X(I,J) = X(I,J) + A(J,I)
else
X(I,I) = X(I,I) - A(I,J)
endif
endif
enddo
enddo
do I = 2, NLEV
IM1 = I - 1
VALUE = 0.D0 - X(I,1)
Y(IM1) = VALUE
Y2(IM1) = VALUE
YKEEP(IM1) = VALUE
do J = 2, NLEV
JM1 = J - 1
VALUE = X(I,J)
X(IM1,JM1) = VALUE
X2(IM1,JM1) = VALUE
XKEEP(IM1,JM1) = VALUE
enddo
enddo
!Solve matrices for populations
call LUSLV(X,Y,NLEV1,NDIM2)
do I = NLEV, 2, -1
N(I) = Y(I-1)
enddo
SUMN = 1.D0
do I = 2, NLEV
SUMN = SUMN + N(I)
enddo
do I = 2, NLEV
N(I) = N(I) / SUMN
enddo
N(1) = 1.D0 / SUMN
!Output data
TTT=TEMP*1.0D-4
TTP=TTT**(-0.87D0)
!Eff. recombination coef. of Hb
! AHB=3.036D-14*TTP
ahb=10**(gamm4861(temp,dens)+11.38871) ! as used in RL routines. differs by <<1% from previous simpler approximation unless ne>>1e4
do I = 1, NLEV1
IP1 = I + 1
do J = IP1, NLEV
if (A(J,I).NE.0.D0) then
EJI = E(J) - E(I)
WAV = 1.D8 / EJI
RLINT = A(J,I) * EJI
RLINT = RLINT *N(J)
TNIJ(I,J)=RLINT
FINT=N(J)*A(J,I)*4861.D0/(DENS*AHB*WAV)
FINTIJ(I,J)=FINT
endif
enddo
enddo
!Search ITRANA, ITRANB & ITRANC for transitions & sum up
SUMA=0.D0
SUMB=0.D0
IAPR=0
IBPR=0
ICPR=0
do IKT = 1, NDIM2
IA1=ITRANA(1,IKT)
IA2=ITRANA(2,IKT)
if (IA1.NE.0.AND.IA2.NE.0) then
SUMA=SUMA+TNIJ(IA1,IA2)
IAPR=IAPR+1
endif
IB1=ITRANB(1,IKT)
IB2=ITRANB(2,IKT)
if (IB1.NE.0.AND.IB2.NE.0) then
IBPR=IBPR+1
SUMB=SUMB+TNIJ(IB1,IB2)
endif
IC1=ITRANC(1,IKT)
IC2=ITRANC(2,IKT)
if (IC1.NE.0.AND.IC2.NE.0) then
ICPR=ICPR+1
endif
enddo
if (SUMB.eq.0.d0) then
FRAT= 0.d0
else
FRAT=SUMA/SUMB
endif
if (diagtype .eq. "t" .or. diagtype .eq. "T") then
RESULTS(1, JT) = TEMP
RESULTS(2, JT) = DENS
RESULTS(3, JT) = FRAT-inratio
else
RESULTS(1, JJD) = TEMP
RESULTS(2, JJD) = DENS
RESULTS(3, JJD) = FRAT-inratio
endif !End of the Ne loop
enddo
do IA = 1, IAPR
I1=ITRANA(1,IA)
I2=ITRANA(2,IA)
DEE=E(I2)-E(I1)
WAVA(IA)=1.D8/DEE
enddo
do IB = 1, IBPR
I1=ITRANB(1,IB)
I2=ITRANB(2,IB)
DEE=E(I2)-E(I1)
WAVB(IB)=1.D8/DEE
enddo
do IC = 1, ICPR
I1=ITRANC(1,IC)
I2=ITRANC(2,IC)
DEE=E(I2)-E(I1)
WAVC(IC)=1.D8/DEE
enddo
enddo !End of the Te loop
! here, find the value in RESULTS which is closest to zero
! sort values in results to find two lowest values
!print*,results
!print*," "
if (diagtype .eq. "D" .or. diagtype .eq. "d") then
INT = ind
endif
! loop through array and find out where the sign changes.
do I=2,INT
test=0
if (sign(results(3,I),results(3,1)) .ne. results(3,I)) then !when this condition is fulfilled, the values in the array are now a different sign to the first value in the array
valtest(:) = (results(:,I-1)) ! return the value before the sign change so that the next loop starts at a sensible value
test=1
exit
endif
enddo
if(test .eq. 0 .and. loop .lt. 9) then !test fails if no change of sign
!this kicks in then, and checks if it should be upper or lower limit
if(abs(results(3,1)) .lt. abs(results(3,INT))) then
valtest(:)=results(:,1)
elseif(abs(results(3,INT)) .lt. abs(results(3,1))) then
valtest(:)=results(:,INT-1)
else !A simplistic work-around for this problem:
result = -1d0 !it flags the value as ill-defined so that it
deallocate(results)!can be dealt with without breaking the code.
return !It's set to zero later and excluded from
!the averaging. Turns out long train rides
!are good for sorting such problems.
!print*,"Valtest failed"
!print*,ion,levu,levl,loop,inratio,diagtype
!print*,results
!call exit(1)
endif
elseif(test .eq. 0 .and. loop .eq. 9) then !test fails if no change of sign
!this kicks in then, and checks if it should be upper or lower limit
if(abs(results(3,1)) .lt. abs(results(3,INT))) then
valtest(:)=results(:,1)
elseif(abs(results(3,INT)) .lt. abs(results(3,1))) then
valtest(:)=results(:,INT)
else
result = -1d0
deallocate(results)
return
!print*,"Valtest failed"
!print*,ion,levu,levl,loop,inratio,diagtype
!print*,results
!call exit(1)
endif
endif
!LOOP = LOOP + 1
DEALLOCATE(RESULTS) !thanks Bruce!
enddo
!********LOOP WOULD END HERE**********************
if (diagtype .eq. "D" .or. diagtype .eq. "d") then
result = valtest(2)
else
result = valtest(1)
endif
return
6100 FORMAT (' PROCESSING COMPLETED'/ &
& ' GOODBYE!!'///)
end subroutine get_diagnostic
subroutine get_abundance(ion,levels,tempi,densi,iobs,abund,ndim2,ndim1,atomicdata,iion)
use mod_atomicdata
implicit none
!INTEGER maxlevs,maxtemps
integer :: NDIM1, NDIM2, NDIM1T3, MAXND
!Maximum no of Te & levels
!PARAMETER (NDIM1=maxtemps, NDIM2=maxlevs)!35, NDIM2=150)
!NDIM1T3 should be at least 3*NDIM1
!PARAMETER (NDIM1T3 = 3*NDIM1)!105)
!Maximum no. of Ne increments
PARAMETER (MAXND=100)
integer :: G(NDIM2), &
& ITRANA(2,NDIM2),ITRANB(2,NDIM2),ITRANC(2,NDIM2)
type(atomic_data),dimension(:),intent(in) :: atomicdata
integer :: nion,iion
real(kind=dp) :: N(NDIM2)
real(kind=dp) :: TDRAT(2,MAXND), TNIJ(NDIM2,NDIM2), FINTIJ(NDIM2,NDIM2), &
& WAVA(NDIM2), WAVB(NDIM2), WAVC(NDIM2), CS(NDIM2,NDIM2), &
& QEFF(NDIM2,NDIM2), QQ(NDIM1), &
& QOM(NDIM1,NDIM2,NDIM2), A(NDIM2,NDIM2), E(NDIM2), T(NDIM1), &
& ROOTT(NDIM1), X(NDIM2,NDIM2), Y(NDIM2), &
& X2(NDIM2,NDIM2), XKEEP(NDIM2,NDIM2), Y2(NDIM2), YKEEP(NDIM2), &
& HMH(NDIM1,NDIM1), D(NDIM1)
character(len=20) :: LABEL(NDIM2)
character(len=10) :: ION
integer :: I, I1, I2, J, KK, LL, JT, JJD, &
& NLEV, NTEMP, IBIG, IRATS, &
& NLEV1, INT, IND, IOPT, IT, IM1, JM1, IP1, &
& IAPR, IBPR, ICPR, IKT, IA, IB, IC, IA1, IA2, IB1, IB2, IC1, IC2
real(kind=dp) :: TEMPI, TINC, DENSI, DINC, DENS, DLOGD, TEMP, TLOGT, &
& TEMP2, DD, DELTEK, EXPE, VALUE, SUMN, TTT, TTP, AHB, EJI, WAV, &
& RLINT, FINT, SUMA, SUMB, SUMC, FRAT, DEE
character(len=20) :: levels
real(kind=dp) :: iobs, abund
!debugging
#ifdef CO
print *,"subroutine: get_abundance. ion=",ion
#endif
ndim1t3=3*ndim1
g=0
itrana=0
itranb=0
itranc=0
d=0.d0
read(levels,*) ((ITRANC(LL,KK),LL=1,2),KK=1,ndim2)!150)
tinc=0
dinc=0
int=1
ind=1
nion = 0
do i = 1,iion
if(atomicdata(i)%ion .eq. ion(1:10)) nion=i
enddo
if (nion .eq. 0) then
print *, "Dave, my mind is going. I can feel it."
nion = 1
endif
! print*,nion,atomicdata(nion)%ion,ion
nlev=atomicdata(nion)%nlevs
ntemp=atomicdata(nion)%ntemps
T(1:ntemp)=log10(atomicdata(nion)%Temps(1:ntemp))
ROOTT(1:ntemp)=atomicdata(nion)%rootT(1:ntemp)
Label(1:nlev)=atomicdata(nion)%labels(1:nlev)
QOM(1:ntemp,1:nlev,1:nlev)=atomicdata(nion)%col_str(1:ntemp,1:nlev,1:nlev)
A(1:nlev,1:nlev)=atomicdata(nion)%A_coeffs(1:nlev,1:nlev)
E(1:nlev)=atomicdata(nion)%Waveno(1:nlev)
G(1:nlev)=atomicdata(nion)%G(1:nlev)
irats=0
ibig=0
NLEV1 = NLEV - 1
!Start of Te loop
do JT = 1, INT
TEMP=TEMPI+(JT-1)*TINC
!Start of Ne loop
do JJD = 1, IND
DENS=DENSI+(JJD-1)*DINC
if (TEMP.LE.0.D0.OR.DENS.LE.0.D0) then
write (6,6100)
print *,"Temp = ", TEMP, ", Dens = ", DENS, ", Ion = ",ion
call exit(200)
endif
DLOGD = log10(DENS)
TLOGT = log10(TEMP)
TEMP2= sqrt(TEMP)
!Form matrices
X = 0.D0
CS=0.D0
QEFF=0.D0
TNIJ = 0.D0
Y=0.D0
IOPT=0
if (NTEMP.EQ.1) then
write (6,*)
write (6,*) &
& 'Coll. strengths available for 1 Te only - assuming const'
elseif (NTEMP.EQ.2) then
write (6,*)
write (6,*) &
& 'Coll. strengths available for 2 Te only - linear interp'
else
call SPLMAT(T, NTEMP, IOPT, NDIM1, NDIM1T3, HMH)
call CFD(TLOGT,T,NTEMP,NDIM1,HMH,D)
endif
do I = 2, NLEV
do J = I, NLEV
!Negative!
DELTEK = (E(I-1)-E(J))*1.4388463D0
EXPE = EXP(DELTEK/TEMP)
do IT = 1, NTEMP
if (IRATS.EQ.0.D+00) then
QQ(IT) = QOM(IT,I-1,J)
else
!Take out the exp. depend.
QQ(IT) = QOM(IT,I-1,J) / EXPE
!before interpolation
endif
enddo
if (NTEMP.EQ.1) then
DD = QQ(1)
elseif (NTEMP.EQ.2) then
DD = QQ(1) + &
& (QQ(2) - QQ(1))/(T(2) - T(1)) * (TLOGT - T(1))
else
call CFY(TLOGT, DD, T, QQ, NTEMP, NDIM1, D)
endif
if (IRATS.EQ.0.D+00) then
CS(I-1,J) = DD
else
CS(I-1,J) = DD * EXPE
endif
if (IRATS .EQ. 0.D+00) then
QEFF(I-1,J) = 8.63D-06*CS(I-1,J) * EXPE / (G(I-1)*TEMP2)
QEFF(J,I-1) = 8.63D-06 * CS(I-1,J) / (G(J)*TEMP2)
else
QEFF(I-1,J) = CS(I-1,J) * 10. ** IRATS
!Be careful
QEFF(J,I-1) = G(I-1) * QEFF(I-1,J) / (EXPE * G(J))
!G integer!
endif
enddo
enddo
do I = 2, NLEV
do J = 1, NLEV
if (J.NE.I) then
X(I,J) = X(I,J) + DENS * QEFF(J,I)
X(I,I) = X(I,I) - DENS * QEFF(I,J)
if (J.GT.I) then
X(I,J) = X(I,J) + A(J,I)
else
X(I,I) = X(I,I) - A(I,J)
endif
endif
enddo
enddo
do I = 2, NLEV
IM1 = I - 1
VALUE = 0.D0 - X(I,1)
Y(IM1) = VALUE
Y2(IM1) = VALUE
YKEEP(IM1) = VALUE
do J = 2, NLEV
JM1 = J - 1
VALUE = X(I,J)
X(IM1,JM1) = VALUE
X2(IM1,JM1) = VALUE
XKEEP(IM1,JM1) = VALUE
enddo
enddo
!Solve matrices for populations
call LUSLV(X,Y,NLEV1,NDIM2)
do I = NLEV, 2, -1
N(I) = Y(I-1)
enddo
SUMN = 1.D0
do I = 2, NLEV
SUMN = SUMN + N(I)
enddo
do I = 2, NLEV
N(I) = N(I) / SUMN
enddo
N(1) = 1.D0 / SUMN
!Output data
TTT=TEMP*1.0D-4
TTP=TTT**(-0.87D0)
!Eff. recombination coef. of Hb
AHB=3.036D-14*TTP
do I = 1, NLEV1
IP1 = I + 1
do J = IP1, NLEV
if (A(J,I).NE.0.D0) then
EJI = E(J) - E(I)
WAV = 1.D8 / EJI
RLINT = A(J,I) * EJI
RLINT = RLINT *N(J)
TNIJ(I,J)=RLINT
FINT=N(J)*A(J,I)*4861.D0/(DENS*AHB*WAV)
FINTIJ(I,J)=FINT
endif
enddo
enddo
!Search ITRANA, ITRANB & ITRANC for transitions & sum up
SUMA=0.D0
SUMB=0.D0
SUMC=0.D0
IAPR=0
IBPR=0
ICPR=0
do IKT = 1, NDIM2
IA1=ITRANA(1,IKT)
IA2=ITRANA(2,IKT)
if (IA1.NE.0.AND.IA2.NE.0) then
SUMA=SUMA+TNIJ(IA1,IA2)
IAPR=IAPR+1
endif
IB1=ITRANB(1,IKT)
IB2=ITRANB(2,IKT)
if (IB1.NE.0.AND.IB2.NE.0) then
IBPR=IBPR+1
SUMB=SUMB+TNIJ(IB1,IB2)
endif
IC1=ITRANC(1,IKT)
IC2=ITRANC(2,IKT)
if (IC1.NE.0.AND.IC2.NE.0) then
ICPR=ICPR+1
SUMC=SUMC+FINTIJ(IC1,IC2)
endif
enddo
if (sumb .gt. 0) then
FRAT=SUMA/SUMB
else
FRAT=0.d0
endif
if (SUMC.ne.0.d0) SUMC = 1./SUMC
TDRAT(1,JJD)=DENS
TDRAT(2,JJD)=FRAT
abund = sumc*iobs/100
!End of the Ne loop
enddo
do IA = 1, IAPR
I1=ITRANA(1,IA)
I2=ITRANA(2,IA)
DEE=E(I2)-E(I1)
WAVA(IA)=1.D8/DEE
enddo
do IB = 1, IBPR
I1=ITRANB(1,IB)
I2=ITRANB(2,IB)
DEE=E(I2)-E(I1)
WAVB(IB)=1.D8/DEE
enddo
do IC = 1, ICPR
I1=ITRANC(1,IC)
I2=ITRANC(2,IC)
DEE=E(I2)-E(I1)
WAVC(IC)=1.D8/DEE
enddo
!End of the Te loop
enddo
return
6100 FORMAT (' PROCESSING COMPLETED'/ &
& ' GOODBYE!!'///)
end subroutine get_abundance
!---- PROC LUSLV
!Solving linear equations
subroutine LUSLV(A,B,N,M)
implicit none
integer :: M, N
real(kind=dp) :: A(M,M),B(M)
#ifdef DEBUG
print *,"subroutine: luslv"
#endif
call LURED(A,N,M)
call RESLV(A,B,N,M)
return
end subroutine luslv
!
!---- PROC LURED
subroutine LURED(A,N,NR)
implicit none
integer :: N, NR, NM1, I, J, K, IP1
real(kind=dp) :: A(NR,NR), FACT
#ifdef DEBUG
print *,"subroutine: lured"
#endif
if (N.EQ.1) return
NM1=N-1
do I=1,NM1
IP1=I+1
do K=IP1,N
FACT=A(K,I)/A(I,I)
do J=IP1,N
A(K,J)=A(K,J)-A(I,J)*FACT
enddo
enddo
enddo
return
end subroutine lured
!
!---- PROC RESLV
!Resolve A with B
subroutine RESLV(A,B,N,NR)
implicit none
integer :: N, NR, NM1, I, J, K, L, IP1
real(kind=dp) :: A(NR,NR),B(NR)
#ifdef DEBUG
print *,"subroutine: reslv"
#endif
if (N.EQ.1) GOTO 1
NM1=N-1
do I=1,NM1
IP1=I+1
do J=IP1,N
B(J)=B(J)-B(I)*A(J,I)/A(I,I)
enddo
enddo
B(N)=B(N)/A(N,N)
do I=1,NM1
K=N-I
L=K+1
do J=L,N
B(K)=B(K)-B(J)*A(K,J)
enddo
B(K)=B(K)/A(K,K)
enddo
return
1 B(N)=B(N)/A(N,N)
return
end subroutine reslv
!
!---- PROC SPLMAT
subroutine SPLMAT(XX,NPT,IOPT,NDIM, NDIMT3, HMH)
implicit none
integer :: NDIM, NDIMT3, NPT, IOPT, NPM, NELEM
real(kind=dp) :: XX(NDIM),GH(NDIMT3),Y(NDIM), HMH(NDIM,NDIM)
#ifdef DEBUG
print *,"subroutine: splmat"
#endif
NPM=NPT-2
call GHGEN(GH,XX,NPT,IOPT,NDIM,NDIMT3)
NELEM=3*NPM-2
call ELU(GH,NPM,NDIMT3)
call HGEN(XX,GH,Y,NPT,IOPT,NDIM,NDIMT3,HMH)
return
end subroutine splmat
!
!---- PROC DERIV
! Calculate the first derivative of the lagrangian interpolator
! of a function F, tabulated at the N points XY(I), I=1 to N.
! The derivative is given as the coefficients of F(I), I=1 to N,
! in the array D(I), I=1 to N.
subroutine DERIV(XY,D,X,N,NDIM)
implicit none
integer :: N ,NDIM, I, J, K
real(kind=dp) :: XY(NDIM),D(NDIM), X, P1, P2, S
#ifdef DEBUG
print *,"subroutine: deriv"
#endif
do I=1,N
P1=1.
S=0.
do J=1,N
if (J.NE.I) then
P1=P1*(XY(I)-XY(J))
P2=1.
do K=1,N
if (K.NE.I.AND.K.NE.J) P2=P2*(X-XY(K))
enddo
S=S+P2
endif
enddo
D(I)=S/P1
enddo
return
end subroutine deriv
!
!---- PROC HGEN
! Cubic spline interpolation
! The equation for the second derivatives at internal points
! is of the form G*YPP=B, where G has been evaluated and LU
! decomposed.
! this routine writes B=HMH*Y and then solves YPP=G**(-1)*HMH*Y,
! =HMH*Y.
! Three options are provided for boundary conditions-
! IOPT = 0 YPP=0 at end points
! IOPT = 1 YP=0 at end points
! IOPT = 2 YP at end points from lagarnge interpolant of a set of
! internal points.
subroutine HGEN(XX,GH,Y,NPT,IOPT,NDIM,NDIMT3,HMH)
implicit none
integer :: NPT, IOPT, NDIM, NDIMT3, NDIM3, NIP, I, J, K, NPM, &
& INDX
real(kind=dp) :: XX(NDIM), GH(NDIMT3), Y(NDIM), HMH(NDIM,NDIM), &
& XY(5),D(5),C(2,5), A0, AN1, H1, H2
#ifdef DEBUG
print *,"subroutine: hgen"
#endif
if (IOPT.EQ.2) then !Case of derivative boundary condition, with
NDIM3=5 !derivatives from NIP-point Lagrange at
NIP=3 !internal points
do J=1,2
do I=1,NIP
K=(NPT-NIP)*(J-1)
XY(I)=XX(K+I)
enddo
K=1+(NPT-1)*(J-1)
call DERIV(XY,D,XX(K),NIP,NDIM3)
do I=1,NIP
C(J,I)=D(I)
enddo
enddo
endif
!Set up matrix equation G*YPP=HMH*Y
A0=XX(2)-XX(1)
AN1=XX(NPT)-XX(NPT-1)
NPM=NPT-2
hmh=0d0
do I=1,NPM
H1=6./(XX(I+1)-XX(I))
H2=6./(XX(I+2)-XX(I+1))
HMH(I,I)=H1
HMH(I,I+1)=-H1-H2
HMH(I,I+2)=H2
! do J=1,NPT
! HMH(I,J)=0.
! if (J.EQ.I) HMH(I,J)=H1
! if (J.EQ.I+2) HMH(I,J)=H2
! if (J.EQ.I+1) HMH(I,J)=-H1-H2
! enddo
enddo
!Correct matrix for case of
if (IOPT.EQ.1.OR.IOPT.EQ.2) then
!derivative boundary conditions
HMH(1,1)=HMH(1,1)+3/A0
HMH(1,2)=HMH(1,2)-3/A0
HMH(NPM,NPT-1)=HMH(NPM,NPT-1)-3/AN1
HMH(NPM,NPT)=HMH(NPM,NPT)+3/AN1
endif
if (IOPT.EQ.2) then
do J=1,NIP
HMH(1,J)=HMH(1,J)+3*C(1,J)
K=NPT+J-NIP
HMH(NPM,K)=HMH(NPM,K)-3*C(2,J)
enddo
endif
!Solve matrix equation with results in the form
do I=1,NPT
!YPP=HMH*Y. matrix g has been LU decomposed
Y(1)=HMH(1,I)
INDX=0
do J=2,NPM
INDX=INDX+3
Y(J)=HMH(J,I)-GH(INDX)*Y(J-1)
enddo
INDX=INDX+1
Y(NPM)=Y(NPM)/GH(INDX)
do J=2,NPM
K=NPM-J+1
INDX=INDX-3
Y(K)=(Y(K)-GH(INDX+1)*Y(K+1))/GH(INDX)
enddo
HMH(2:npm+1,I)=Y(1:npm)
!Insert values for second derivative at end
HMH(1,I)=0.
!points: first and last rows of the matrix
HMH(NPT,I)=0.
enddo
!Case of derivative boundary conditions
if (IOPT.GT.0) then
do J=1,NPT
HMH(1,J)=-0.5*HMH(2,J)
HMH(NPT,J)=-0.5*HMH(NPT-1,J)
enddo
HMH(1,1)=HMH(1,1)-3/(A0*A0)
HMH(1,2)=HMH(1,2)+3/(A0*A0)
HMH(NPT,NPT-1)=HMH(NPT,NPT-1)+3/(AN1*AN1)
HMH(NPT,NPT)=HMH(NPT,NPT)-3/(AN1*AN1)
endif
if (IOPT.EQ.2) then
do J=1,NIP
HMH(1,J)=HMH(1,J)-3*C(1,J)/A0
K=NPT+J-NIP
HMH(NPT,K)=HMH(NPT,K)+3*C(2,J)/AN1
enddo
endif
return
end subroutine hgen
!
!---- PROC GHGEN
subroutine GHGEN(GH,XX,NPT,IOPT,NDIM,NDIMT3)
implicit none
integer :: NPT, IOPT, NDIM, NDIMT3, INDX, NPTM, I, J, IP, JP, IK
real(kind=dp) :: XX(NDIM),GH(NDIMT3)
#ifdef DEBUG
print *,"subroutine: ghgen"
#endif
INDX=0
NPTM=NPT-1
do I=2,NPTM
IP=I-1
do J=1,3
JP=IP+J-2
if (JP.GE.1.AND.JP.LE.NPTM-1) then
INDX=INDX+1
if (J.EQ.2) then
GH(INDX)=2*(XX(I+1)-XX(I-1))
else
IK=I+(J-1)/2
GH(INDX)=XX(IK)-XX(IK-1)
endif
endif
enddo
enddo
if (IOPT.GE.1) then
GH(1)=GH(1)-(XX(2)-XX(1))/2.
GH(INDX)=GH(INDX)-(XX(NPT)-XX(NPT-1))/2.
endif
return
end subroutine ghgen
!
!---- PROC ELU
subroutine ELU(GH,N,NDIM)
implicit none
integer :: N, NDIM, INDX, I, J, JP
real(kind=dp) :: GH(NDIM)
#ifdef DEBUG
print *,"subroutine: elu"
#endif
INDX=0
do I=1,N
do J=1,3
JP=I+J-2
if (JP.GE.1.AND.JP.LE.N) then
INDX=INDX+1
if (I.GT.1) then
if (J.EQ.1) then
GH(INDX)=GH(INDX)/GH(INDX-2)
endif
if (J.EQ.2) then
GH(INDX)=GH(INDX)-GH(INDX-1)*GH(INDX-2)
endif
endif
endif
enddo
enddo
return
end subroutine elu
!
!---- PROC CFY
subroutine CFY(X,Y,XX,YY,NPT,NDIM,D)
implicit none
integer :: NPT, NDIM, J
real(kind=dp) :: XX(NDIM),YY(NDIM), D(NDIM), X, Y, TT
#ifdef DEBUG
print *,"subroutine: cfy"
#endif
if (X.LT.XX(1)) then
Y=YY(1)
endif
if (X.GT.XX(NPT)) then
Y=YY(NPT)
endif
TT=0.
do J=1,NPT
TT=TT+D(J)*YY(J)
enddo
Y=TT
return
end subroutine cfy
!
!---- PROC CFD
subroutine CFD(X,XX,NPT,NDIM, HMH, D)
implicit none
integer :: NPT, NDIM, NPTM, I, J
real(kind=dp) :: X, XX(NDIM), HMH(NDIM,NDIM), D(NDIM), X1, X2, A1, A2, HI
#ifdef DEBUG
print *,"subroutine: cfd"
#endif
if (X.LT.XX(1)) then
!write(6,400) XX(1)
return
endif
if (X.GT.XX(NPT)) then
!write(6,401) XX(NPT)
return
endif
NPTM=NPT-1
do I=1,NPTM
if (X.LT.XX(I+1)) then
X1=XX(I+1)-X
X2=X-XX(I)
HI=XX(I+1)-XX(I)
A1=X1*(X1*X1/(6*HI)-HI/6)
A2=X2*(X2*X2/(6*HI)-HI/6)
do J=1,NPT
D(J)=(A1*HMH(I,J)+A2*HMH(I+1,J))
enddo
D(I)=D(I)+X1/HI
D(I+1)=D(I+1)+X2/HI
return
endif
enddo
end subroutine cfd
end module mod_equib
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