program lslin

! Program to interpolate data in Solar Longitude linear time coordinate
! (usable with grads) from Netcdf diagfi or concatnc  files
! author Y. Wanherdrick, K. Dassas 2004
! Modified by F.Forget 04/2005
! More modifications by Ehouarn Millour 12/2005
! Modified by Ehouarn Millour 10/2007 (changed evaluation of 'start_var'
! from hard-coded values to a computed value) 
! Read controle field, if available TN, October 2013


implicit none

include "netcdf.inc" ! NetCDF definitions

character (len=50) :: infile
! infile(): input file name
character (len=50), dimension(:), allocatable :: var
! var(): names of the variables
character (len=50) :: title,units
! title(),units(): [netcdf] "title" and "units" attributes
character (len=100) :: outfile
! outfile(): output file name
character (len=100) :: vartmp
! vartmp(): used for temporary storage of various strings
character (len=1) :: answer
! answer: the character 'y' (or 'Y'), if input file is of 'concatnc' type
integer :: nid,varid,ierr
! nid: [netcdf] ID # of input file
! varid: [netcdf] ID # of a variable
! ierr: [netcdf] error code (returned by subroutines)
integer :: nout,varidout
! nout: [netcdf] ID # of output file
! varidout: [netcdf] ID # of a variable (to write in the output file)
integer :: i,j,k,l,x,y
! counters for various loops
integer :: start_var
! starting index/ID # from which physical variables are to be found
integer :: reptime ! Ehouarn: integer or real ? 
! rep_time: starting date/time of the run (given by user)
integer :: day_ini ! Ehouarn: integer or real ?
! day_ini: starting date/time of the run stored in input file
integer, parameter :: length=100
! length: (default) lenght of tab_cntrl()
real, dimension(length) :: tab_cntrl
! tab_cntrl(length): array, stored in the input file,
!                which contains various control parameters.
real, dimension(:), allocatable:: lat,lon,alt,time,lsgcm,timels
! lat(): latitude coordinates (read from input file)
! lon(): longitude coordinates (read from input file)
! alt(): altitude coordinates (read from input file)
! time(): time coordinates (in "sol", read from input file)
! lsgcm(): time coordinate (in unevenly spaced "Ls")
! timels(): new time coordinates (evenly spaced "Ls"; written to output file)
integer :: latlen,lonlen,altlen,timelen,Nls
! latlen: # of elements of lat() array
! lonlen: # of elements of lon() array
! altvar: # of elements of alt() array
! timelen: # of elements of time() and lsgcm() arrays
! Nls: # of elements of timels() array
integer :: nbvarfile,nbvar,ndim !,nbfile
! nbvar: # of time-dependent variables
! nbvarfile: total # of variables (in netcdf file)
! ndim: [netcdf] # of dimensions (3 or 4) of a variable
integer :: latdim,londim,altdim,timedim
! latdim: [netcdf] "latitude" dim ID
! londim: [netcdf] "longitude" dim ID
! altdim: [netcdf] "altdim" dim ID
! timedim: [netcdf] "timedim" dim ID
integer :: latvar,lonvar,altvar,timevar
! latvar: [netcdf] ID of "latitude" variable
! lonvar: [netcdf] ID of "longitude" variable
! altvar: [netcdf] ID of "altitude" variable
! timevar: [netcdf] ID of "Time" variable
integer :: latdimout,londimout,altdimout,timedimout,timevarout
! latdimout: [netcdf] output latitude (dimension) ID
! londimout: [netcdf] output longitude (dimension) ID
! altdimout: [netcdf] output altitude (dimension) ID
! timedimout: [netcdf] output time (dimension) ID
! timevarout: [netcdf] ID of output "Time" variable
integer, dimension(4) :: corner,edges,dim
! corner(4): [netcdf] start indexes (where block of data will be written)
! edges(4): [netcdf] lenght (along dimensions) of block of data to write
! dim(4): [netcdf] lat, long, alt and time dimensions
real, dimension(:,:,:,:), allocatable :: var3d,var3dls
! var3d(,,,): 4D array to store a variable (on initial lat/lon/alt/sol grid)
! var3dls(,,,): 4D array to store a variable (on new lat/lon/alt/Ls grid)
real, dimension(:), allocatable :: var3dxy
! var3dxy(): to store the temporal evolution of a variable (at fixed lat/lon/alt)
real :: deltatsol,deltals,resultat
! deltatsol: time step (in sols) of input file data
! deltals: time step (in Ls) for the data sent to output
! resultat: to temporarily store the result of the interpolation
character (len=3) :: mon
! mon(3): to store (and write to file) the 3 first letters of a month
real :: date
! date: used to compute/build a fake date (for grads output)

!==============================================================================
! 1. Initialisation step
!==============================================================================

!==============================================================================
! 1.1. Get input file name and 'type' (to initialize start_var and reptime)
!==============================================================================

write(*,*) "which file do you want to use?"
read(*,'(a50)') infile 

!write(*,*) "Is it a concatnc file? (y/n)?"
write(*,*) "Do you want to specify the beginning day of the file"
write(*,*) "in case the controle field is not present ? (y/n)?"
read(*,*) answer
if ((answer=="y").or.(answer=="Y")) then
   write(*,*) "Beginning day of the file?"
   read(*,*) reptime 
!   start_var=8 ! 'concatnc' type of file
!else
!   start_var=16 ! 'diagfi' type of file
! N.B.: start_var is now computed; see below
endif


!==============================================================================
! 1.2. Open input file and read/list the variables it contains
!==============================================================================

write(*,*) "opening "//trim(infile)//"..."
ierr = NF_OPEN(infile,NF_NOWRITE,nid)
if (ierr.NE.NF_NOERR) then
   write(*,*) 'Failed to open file '//infile
   write(*,*) NF_STRERROR(ierr)
   stop ""
endif

! Compute 'start_var', the index from which variables are lon-lat-time
! and/or lon-lat-alt-time
! WARNING: We assume here that the ordering of variables in the NetCDF
! file is such that 0D, 1D and 2D variables are placed BEFORE 3D and 4D
! variables

i=1 ! dummy initialization to enter loop below
start_var=0 ! initialization
do while (i.lt.3)
  start_var=start_var+1
  ! request number of dims of variable number 'start_var'
  ierr=NF_INQ_VARNDIMS(nid,start_var,i)
  if (ierr.ne.NF_NOERR) then
    write(*,*) "Failed to get number of dims for variable number:",start_var
    write(*,*) NF_STRERROR(ierr)
    stop ""
  endif
enddo
write(*,*) "start_var=",start_var


ierr=NF_INQ_NVARS(nid,nbvarfile)
! nbvarfile is now equal to the (total) number of variables in input file

allocate(var(nbvarfile-(start_var-1)))

! Yield the list of variables (to the screen)
write(*,*)
do i=start_var,nbvarfile
   ierr=NF_INQ_VARNAME(nid,i,vartmp)
   write(*,*) trim(vartmp)
enddo
!nbvar=0

! Ehouarn: Redundant (and obsolete) lines ?
!  nbvar=nbvarfile-(start_var-1)
!  do j=start_var,nbvarfile
!  ierr=nf_inq_varname(nid,j,var(j-(start_var-1)))
!  enddo
                                       
! Get the variables' names from the input file (and store them in var())
nbvar=nbvarfile-(start_var-1)
do i=1,nbvar
   ierr=NF_INQ_VARNAME(nid,i+(start_var-1),var(i))
   write(*,'(a9,1x,i2,1x,a1,1x,a50)') "variable ",i,":",var(i)
enddo

!==============================================================================
! 1.3. Output file name
!==============================================================================
! outfile="lslin.nc"
outfile=infile(1:len_trim(infile)-3)//"_Ls.nc"
 write(*,*) outfile


!==============================================================================
! 2. Work: read input, build new time coordinate and write it to output
!==============================================================================

!==============================================================================
! 2.1. Read (and check) latitude, longitude and altitude from input file
!==============================================================================

   ierr=NF_INQ_DIMID(nid,"latitude",latdim)
   ierr=NF_INQ_VARID(nid,"latitude",latvar)
   if (ierr.NE.NF_NOERR) then
      write(*,*) 'ERROR: Field <latitude> is missing'
      write(*,*) NF_STRERROR(ierr)
      stop ""  
   endif
   ierr=NF_INQ_DIMLEN(nid,latdim,latlen)
!  write(*,*) "latlen: ",latlen

   ierr=NF_INQ_DIMID(nid,"longitude",londim)
   ierr=NF_INQ_VARID(nid,"longitude",lonvar)
   if (ierr.NE.NF_NOERR) then
      write(*,*) 'ERROR: Field <longitude> is missing'
      write(*,*) NF_STRERROR(ierr)
      stop "" 
   endif
   ierr=NF_INQ_DIMLEN(nid,londim,lonlen)
!  write(*,*) "lonlen: ",lonlen

   ierr=NF_INQ_DIMID(nid,"altitude",altdim)
   ierr=NF_INQ_VARID(nid,"altitude",altvar)
   if (ierr.NE.NF_NOERR) then
      write(*,*) 'ERROR: Field <altitude> is missing'
      write(*,*) NF_STRERROR(ierr)
!     stop ""
       altlen = 1 
   else
      ierr=NF_INQ_DIMLEN(nid,altdim,altlen)
   endif
   write(*,*) "altlen: ",altlen

! Allocate lat(), lon() and alt()
      allocate(lat(latlen))
      allocate(lon(lonlen))
      allocate(alt(altlen))

! Read lat(),lon() and alt() from input file





      ierr = NF_GET_VAR_REAL(nid,latvar,lat)
      ierr = NF_GET_VAR_REAL(nid,lonvar,lon)
      ierr = NF_GET_VAR_REAL(nid,altvar,alt)
      if (ierr.NE.NF_NOERR) then
          if (altlen.eq.1) alt(1)=0.
      end if


!==============================================================================
! 2.2. Create (and initialize latitude, longitude and altitude in) output file
!==============================================================================

call initiate(outfile,lat,lon,alt,nout,&
           latdimout,londimout,altdimout,timedimout,timevarout)

!==============================================================================
! 2.3. Read time from input file
!==============================================================================

ierr=NF_INQ_DIMID(nid,"Time",timedim)
if (ierr.NE.NF_NOERR) then
   write(*,*) 'ERROR: Dimension <Time> is missing'
   write(*,*) NF_STRERROR(ierr)
   stop ""
endif
ierr=NF_INQ_VARID(nid,"Time",timevar)
if (ierr.NE.NF_NOERR) then
   write(*,*) 'ERROR: Field <Time> is missing'
   write(*,*) NF_STRERROR(ierr)
   stop ""
endif

ierr=NF_INQ_DIMLEN(nid,timedim,timelen)
write(*,*) "timelen: ",timelen

allocate(time(timelen))
allocate(lsgcm(timelen))




ierr = NF_GET_VAR_REAL(nid,timevar,time)


!==============================================================================
! 2.4. Initialize day_ini (starting day of the run)
!==============================================================================


write(*,*) 'answer',answer
if ((answer/="y").and.(answer/="Y")) then
   ! input file is of 'concatnc' type; the starting date of the run
   ! is stored in the "controle" array
   ierr = NF_INQ_VARID (nid, "controle", varid)
   if (ierr .NE. NF_NOERR) then
      write(*,*) 'ERROR: <controle> variable is missing'
      write(*,*) NF_STRERROR(ierr)
      stop ""
   endif




   ierr = NF_GET_VAR_REAL(nid, varid, tab_cntrl)


   if (ierr .NE. NF_NOERR) then
      write(*,*) 'ERROR: Failed to read <controle>'
      write(*,*) NF_STRERROR(ierr)
     stop ""
   endif

   day_ini = tab_cntrl(4)                                               
   day_ini = modulo(day_ini,669)                                                    
   write(*,*) 'day_ini', day_ini
else
   day_ini= reptime
   write(*,*) 'day_ini', day_ini
endif

!==============================================================================
! 2.5. Build timels() (i.e.: time, but in evenly spaced "Ls" time steps)
!==============================================================================

! compute time step, in sols, of input dataset
deltatsol=time(2)-time(1)
write(*,*) 'deltatsol',deltatsol

! compute time/dates in "Ls"; result stored in lsgcm()
do i=1,timelen
   call sol2ls(day_ini+time(i),lsgcm(i)) 
enddo

write(*,*) 'Input data LS range :', lsgcm(1),lsgcm(timelen)

!******************************************
write(*,*) "Automatic Ls timetsep (y/n)?"
read(*,*) answer
if ((answer=="y").or.(answer=="Y")) then
!   *********************************************
!   Trick of the trade:
!   Use the value of deltatsol to determine
!   a suitable value for deltals
!   *********************************************
    deltals=1./12.
    if (0.6*deltatsol.ge.1/6.) deltals=1./6.
    if (0.6*deltatsol.ge.0.25) deltals=0.25
    if (0.6*deltatsol.ge.0.5) deltals=0.5
    if (0.6*deltatsol.ge.0.75) deltals=0.75
    if (0.6*deltatsol.ge.1) deltals=1.
    if (0.6*deltatsol.ge.2) deltals=2.
    if (0.6*deltatsol.ge.3) deltals=3.
    if (0.6*deltatsol.ge.5) deltals=5.
else
    write(*,*) "New timestep in Ls (deg)"
    read(*,*) deltals
endif
  NLs=int(Int((lsgcm(timelen)-lsgcm(1))/deltals) +1)
!********************************************
allocate(timels(Nls))

! Build timels()
timels(1) = 0.01*nint(100.*lsgcm(1)) ! Ehouarn: what the !!!???!!!
do k=2,Nls
   timels(k) = timels(k-1) + deltals
end do

write(*,*) 'timestep in Ls (deg) ', deltals
write(*,*) 'output data LS range : ', timels(1),timels(Nls)

!==============================================================================
! 2.6. Write timels() to output file
!==============================================================================

do k=1,Nls



ierr= NF_PUT_VARA_REAL(nout,timevarout,k,1,timels(k))

enddo


!==============================================================================
! 3. Read variables, interpolate them along the new time coordinate
!    and send the result to output
!==============================================================================

do j=1,nbvar ! loop on the variables to read/interpolate/write

!==============================================================================
! 3.1 Check that variable exists, and get some of its attributes
!==============================================================================
   write(*,*) "variable ",var(j)
   ! Get the variable's ID
   ierr=NF_INQ_VARID(nid,var(j),varid)
   if (ierr.NE.NF_NOERR) then
      write(*,*) 'ERROR: Field <',var(j),'> not found'
      write(*,*) NF_STRERROR(ierr)
      stop ""
   endif
   ! Get the value of 'ndim' for this varriable
   ierr=NF_INQ_VARNDIMS(nid,varid,ndim)
   write(*,*) 'ndim', ndim

!==============================================================================
! 3.2 Prepare a few things in order to interpolate/write
!==============================================================================

   if (ndim==3) then
      allocate(var3d(lonlen,latlen,timelen,1))
      allocate(var3dls(lonlen,latlen,Nls,1))
      allocate(var3dxy(timelen))

      dim(1)=londimout
      dim(2)=latdimout
      dim(3)=timedimout

      corner(1)=1
      corner(2)=1
      corner(3)=1
      corner(4)=1

      edges(1)=lonlen 
      edges(2)=latlen 
      edges(3)=Nls
      edges(4)=1

   else if (ndim==4) then
      allocate(var3d(lonlen,latlen,altlen,timelen))
      allocate(var3dls(lonlen,latlen,altlen,Nls))
      allocate(var3dxy(timelen))

      dim(1)=londimout
      dim(2)=latdimout
      dim(3)=altdimout
      dim(4)=timedimout

      corner(1)=1
      corner(2)=1
      corner(3)=1
      corner(4)=1

      edges(1)=lonlen
      edges(2)=latlen
      edges(3)=altlen
      edges(4)=Nls
   endif

!==============================================================================
! 3.3 Write this variable's definition and attributes to the output file
!==============================================================================
   units="                                                    "
   title="                                                    "
   ierr=NF_GET_ATT_TEXT(nid,varid,"title",title)
   ierr=NF_GET_ATT_TEXT(nid,varid,"units",units)

   call def_var(nout,var(j),title,units,ndim,dim,varidout,ierr)

!==============================================================================
! 3.4 Read variable
!==============================================================================




   ierr = NF_GET_VAR_REAL(nid,varid,var3d)


!==============================================================================
! 3.5 Interpolate
!==============================================================================

! 2D variable  (lon, lat, time)    
! interpolation of var at timels
   if (ndim==3) then
      do x=1,lonlen
       do y=1,latlen
!        write(*,*) 'd: x, y', x, y
        do l=1,timelen
        var3dxy(l)=var3d(x,y,l,1)
        enddo
        do l=1,Nls
        call interpolf(timels(l),resultat,lsgcm,var3dxy,timelen)
        var3dls(x,y,l,1)=resultat
        enddo
       enddo
      enddo
! 3D variable (lon, lat, alt, time)      
! interpolation of var at timels
   else if (ndim==4) then
      do x=1,lonlen
       do y=1,latlen
        do k=1,altlen
        do l=1,timelen
        var3dxy(l)=var3d(x,y,k,l)
        enddo
         do l=1,Nls
        call interpolf(timels(l),resultat,lsgcm,var3dxy,timelen)
        var3dls(x,y,k,l)=resultat
         enddo
        enddo
       enddo
      enddo
   endif

!==============================================================================
! 3.4 Write variable to output file
!==============================================================================




   ierr= NF_PUT_VARA_REAL(nout,varidout,corner,edges,var3dls)


   if (ierr.ne.NF_NOERR) then
      write(*,*) 'PUT_VAR ERROR: ',NF_STRERROR(ierr)
      stop ""
   endif

   deallocate(var3d)
   deallocate(var3dls)
   deallocate(var3dxy)

enddo ! of do j=1,nbvar loop

deallocate(time)
deallocate(lsgcm)

! close input and output files
ierr=nf_close(nid)
ierr=NF_CLOSE(nout)


!==============================================================================
! 4. Build a companion file 'lslin.ctl', so that output file can be 
!    processed by Grads
!==============================================================================

!  ----------------------------------------------------
!  Writing ctl file to directly read Ls coordinate in grads
!  (because of bug in grads that refuse to read date like 0089 in .nc files)
!open(33,file='lslin.ctl')
 open(33,file=infile(1:len_trim(infile)-3)//"_Ls.ctl")
 date= (timels(1)-int(timels(1)))*365.
 mon='jan'
 if(date.ge.32) mon='feb'
 if(date.ge.60) mon='mar'
 if(date.ge.91) mon='apr'
 if(date.ge.121) mon='may'
 if(date.ge.152) mon='jun'
 if(date.ge.182) mon='jul'
 if(date.ge.213) mon='aug'
 if(date.ge.244) mon='sep'
 if(date.ge.274) mon='oct'
 if(date.ge.305) mon='nov'
 if(date.ge.335) mon='dec'
write(33,98) outfile
98 format("DSET ",a)
  write(33,99) Nls, 15,mon, int(timels(1)),nint(deltals*12),'mo'
99 format("TDEF Time ",i5," LINEAR ", i2,a3,i4.4,1x,i2,a2)
    
   deallocate(timels)
contains

!************************************
subroutine initiate (filename,lat,lon,alt,&
                     nout,latdimout,londimout,altdimout,timedimout,timevarout)
!==============================================================================
! Purpose:
! Create and initialize a data file (NetCDF format)
!==============================================================================
! Remarks:
! The NetCDF file (created in this subroutine) remains open
!==============================================================================

implicit none

include "netcdf.inc" ! NetCDF definitions

!==============================================================================
! Arguments:
!==============================================================================
character (len=*), intent(in):: filename
! filename(): the file's name
real, dimension(:), intent(in):: lat
! lat(): latitude
real, dimension(:), intent(in):: lon
! lon(): longitude
real, dimension(:), intent(in):: alt
! alt(): altitude
integer, intent(out):: nout
! nout: [netcdf] file ID
integer, intent(out):: latdimout
! latdimout: [netcdf] lat() (i.e.: latitude)  ID
integer, intent(out):: londimout
! londimout: [netcdf] lon()  ID
integer, intent(out):: altdimout
! altdimout: [netcdf] alt()  ID
integer, intent(out):: timedimout
! timedimout: [netcdf] "Time"  ID
integer, intent(out):: timevarout
! timevarout: [netcdf] "Time" (considered as a variable) ID

!==============================================================================
! Local variables:
!==============================================================================
!integer :: latdim,londim,altdim,timedim
integer :: nvarid,ierr
! nvarid: [netcdf] ID of a variable
! ierr: [netcdf]  return error code (from called subroutines)

!==============================================================================
! 1. Create (and open) output file
!==============================================================================
write(*,*) "creating "//trim(adjustl(filename))//'...'
ierr = NF_CREATE(filename,IOR(NF_CLOBBER,NF_64BIT_OFFSET),nout)
! NB: setting NF_CLOBBER mode means that it's OK to overwrite an existing file
if (ierr.NE.NF_NOERR) then
   WRITE(*,*)'ERROR: Impossible to create the file.'
   stop ""
endif

!==============================================================================
! 2. Define/write "dimensions" and get their IDs
!==============================================================================

ierr = NF_DEF_DIM(nout, "latitude", size(lat), latdimout)
ierr = NF_DEF_DIM(nout, "longitude", size(lon), londimout)
ierr = NF_DEF_DIM(nout, "altitude", size(alt), altdimout)
ierr = NF_DEF_DIM(nout, "Time", NF_UNLIMITED, timedimout)

! End netcdf define mode
ierr = NF_ENDDEF(nout)

!==============================================================================
! 3. Write "Time" and its attributes
!==============================================================================

call def_var(nout,"Time","Time","years since 0000-00-0 00:00:00",1,&
             (/timedimout/),timevarout,ierr)

!==============================================================================
! 4. Write "latitude" (data and attributes)
!==============================================================================

call def_var(nout,"latitude","latitude","degrees_north",1,&
             (/latdimout/),nvarid,ierr)

ierr = NF_PUT_VAR_REAL (nout,nvarid,lat)

!==============================================================================
! 4. Write "longitude" (data and attributes)
!==============================================================================

call def_var(nout,"longitude","East longitude","degrees_east",1,&
             (/londimout/),nvarid,ierr)

ierr = NF_PUT_VAR_REAL (nout,nvarid,lon)

!==============================================================================
! 4. Write "altitude" (data and attributes)
!==============================================================================

! Switch to netcdf define mode
ierr = NF_REDEF (nout)

ierr = NF_DEF_VAR (nout,"altitude",NF_FLOAT,1,altdimout,nvarid)

ierr = NF_PUT_ATT_TEXT (nout,nvarid,"long_name",8,"altitude")
ierr = NF_PUT_ATT_TEXT (nout,nvarid,'units',2,"km")
ierr = NF_PUT_ATT_TEXT (nout,nvarid,'positive',2,"up")

! End netcdf define mode
ierr = NF_ENDDEF(nout)

ierr = NF_PUT_VAR_REAL (nout,nvarid,alt)

end Subroutine initiate
!************************************
subroutine def_var(nid,name,title,units,nbdim,dim,nvarid,ierr)
!==============================================================================
! Purpose: Write a variable (i.e: add a variable to a dataset)
! called "name"; along with its attributes "title", "units"...
! to a file (following the NetCDF format)
!==============================================================================
! Remarks:
! The NetCDF file must be open
!==============================================================================

implicit none

include "netcdf.inc" ! NetCDF definitions

!==============================================================================
! Arguments:
!==============================================================================
integer, intent(in) :: nid
! nid: [netcdf] file ID #
character (len=*), intent(in) :: name
! name(): [netcdf] variable's name
character (len=*), intent(in) :: title
! title(): [netcdf] variable's "title" attribute
character (len=*), intent(in) :: units
! unit(): [netcdf] variable's "units" attribute
integer, intent(in) :: nbdim
! nbdim: number of dimensions of the variable
integer, dimension(nbdim), intent(in) :: dim
! dim(nbdim): [netcdf] dimension(s) ID(s)
integer, intent(out) :: nvarid
! nvarid: [netcdf] ID # of the variable
integer, intent(out) :: ierr
! ierr: [netcdf] subroutines returned error code

! Switch to netcdf define mode
ierr=NF_REDEF(nid)

! Insert the definition of the variable
ierr=NF_DEF_VAR(nid,adjustl(name),NF_FLOAT,nbdim,dim,nvarid)

! Write the attributes
ierr=NF_PUT_ATT_TEXT(nid,nvarid,"title",len_trim(adjustl(title)),adjustl(title))
ierr=NF_PUT_ATT_TEXT(nid,nvarid,"units",len_trim(adjustl(units)),adjustl(units))

! End netcdf define mode
ierr=NF_ENDDEF(nid)

end subroutine def_var
!************************************
subroutine sol2ls(sol,Ls)
!==============================================================================
! Purpose: 
! Convert a date/time, given in sol (martian day),
! into solar longitude date/time, in Ls (in degrees),
! where sol=0 is (by definition) the northern hemisphere
!  spring equinox (where Ls=0).
!==============================================================================
! Notes:
! Even though "Ls" is cyclic, if "sol" is greater than N (martian) year,
! "Ls" will be increased by N*360
! Won't work as expected if sol is negative (then again,
! why would that ever happen?)
!==============================================================================

implicit none

!==============================================================================
! Arguments:
!==============================================================================
real,intent(in) :: sol
real,intent(out) :: Ls

!==============================================================================
! Local variables:
!==============================================================================
real year_day,peri_day,timeperi,e_elips,twopi,degrad
data year_day /669./            ! # of sols in a martian year
data peri_day /485.0/           
data timeperi /1.9082314/
data e_elips  /0.093358/
data twopi       /6.2831853/    ! 2.*pi
data degrad   /57.2957795/      ! pi/180

real zanom,xref,zx0,zdx,zteta,zz

integer count_years
integer iter

!==============================================================================
! 1. Compute Ls
!==============================================================================

zz=(sol-peri_day)/year_day
zanom=twopi*(zz-nint(zz))
xref=abs(zanom)

!  The equation zx0 - e * sin (zx0) = xref, solved by Newton
zx0=xref+e_elips*sin(xref)
do iter=1,20 ! typically, 2 or 3 iterations are enough
   zdx=-(zx0-e_elips*sin(zx0)-xref)/(1.-e_elips*cos(zx0))
   zx0=zx0+zdx
   if(abs(zdx).le.(1.e-7)) then
!      write(*,*)'iter:',iter,'     |zdx|:',abs(zdx)
      exit
   endif
enddo

if(zanom.lt.0.) zx0=-zx0

zteta=2.*atan(sqrt((1.+e_elips)/(1.-e_elips))*tan(zx0/2.))
Ls=zteta-timeperi

if(Ls.lt.0.) then
   Ls=Ls+twopi
else
   if(Ls.gt.twopi) then
      Ls=Ls-twopi
   endif
endif

Ls=degrad*Ls
! Ls is now in degrees

!==============================================================================
! 1. Account for (eventual) years included in input date/time sol
!==============================================================================

count_years=0 ! initialize
zz=sol  ! use "zz" to store (and work on) the value of sol
do while (zz.ge.year_day)
   count_years=count_years+1
   zz=zz-year_day
enddo

! Add 360 degrees to Ls for every year
if (count_years.ne.0) then
   Ls=Ls+360.*count_years
endif


end subroutine sol2ls
!************************************

Subroutine interpolf(x,y,xd,yd,nd)
!interpolation, give y = f(x) with array xd,yd known, size nd
! Version with CONSTANT values oustide limits
! Variable declaration
! --------------------
!  Arguments :
real x,y
real xd(*),yd(*)
integer nd
!  internal
integer i,j
real y_undefined
                                                                                
! run
! ---
      y_undefined=1.e20
                                                                                
      y=0.
   if ((x.le.xd(1)).and.(x.le.xd(nd))) then
    if (xd(1).lt.xd(nd)) y = yd(1) !y_undefined
    if (xd(1).ge.xd(nd)) y = y_undefined ! yd(nd)
   else if ((x.ge.xd(1)).and.(x.ge.xd(nd))) then
    if (xd(1).lt.xd(nd)) y =  y_undefined ! yd(nd)
    if (xd(1).ge.xd(nd)) y = y_undefined ! yd(1)
    y = yd(nd)
   else
    do i=1,nd-1
     if ( ( (x.ge.xd(i)).and.(x.lt.xd(i+1)) ).or.((x.le.xd(i)).and.(x.gt.xd(i+1))) ) then
     y=yd(i)+(x-xd(i))*(yd(i+1)-yd(i))/(xd(i+1)-xd(i))
     goto 99
     end if
    end do
   end if

!     write (*,*)' x , y' , x,y
!     do i=1,nd
!       write (*,*)' i, xd , yd' ,i, xd(i),yd(i)
!     end do
!     stop
                                                                                
99   continue
                                                                                
end subroutine interpolf
     
end