Index: trunk/LMDZ.MARS/util/README.exec
===================================================================
--- trunk/LMDZ.MARS/util/README.exec	(revision 280)
+++ trunk/LMDZ.MARS/util/README.exec	(revision 281)
@@ -52,7 +52,9 @@
 integrating the hydrostatic equation, recasts data along the vertical
 direction.
-The vertical coordinate can be either "above areoid altitudes" or
-"pressure". Some interpolation along the vertical direction is also
-done, following instructions given by user.
+The vertical coordinate can be either 1) pressure, 2) above areoid
+altitudes, 3) above local surface altitudes or 4) distance to center of
+the planet. Some interpolation along the vertical direction is also
+done, following instructions given by user (levels may be specified
+or given as minimu,maximum and number of levels).
 For "above areoid altitudes" output, Atmospheric pressure is added to
 output dataset; for "pressure coordinate" outputs, the above areoid
@@ -77,8 +79,11 @@
 output file is : 
 name_of_input_file_P.nc with pressure coordinate 
-name_of_input_file_Z.nc with altitude above areoid coordinate 
+name_of_input_file_A.nc with altitude above areoid coordinate 
+name_of_input_file_S.nc with altitude above local surface coordinate 
+name_of_input_file_R.nc with altitude as distance to center of planet 
 
 MODIFICATION :
 01/2010 : correction to interpolate above surface if density is not available.
+03/2011 : added possibility to have output as distance to center of planet
 
 --------------------------------------------------------------------
@@ -98,5 +103,4 @@
 10/2007 Utility lslin.F90 (not used by the gcm)
 changed evaluation of 'start_var' from hard-coded values to a computed value
-
 
 
Index: trunk/LMDZ.MARS/util/zrecast.F90
===================================================================
--- trunk/LMDZ.MARS/util/zrecast.F90	(revision 280)
+++ trunk/LMDZ.MARS/util/zrecast.F90	(revision 281)
@@ -7,7 +7,9 @@
 ! integrating the hydrostatic equation, recasts data along the vertical
 ! direction.
-! The vertical coordinate can be either "above areoid altitudes" or
-! "pressure". Some interpolation along the vertical direction is also
-! done, following instructions given by user.
+! The vertical coordinate can be either 1) pressure, 2) above areoid
+! altitudes, 3) above local surface altitudes  or 4) distance to center of
+! the planet. Some interpolation along the vertical direction is also
+! done, following instructions given by user (levels may be specified
+! or given as minimu,maximum and number of levels).
 ! For "above areoid altitudes" output, Atmospheric pressure is added to
 ! output dataset; for "pressure coordinate" outputs, the above areoid
@@ -47,5 +49,6 @@
 !              when interpolating log-wise and the density field is not
 !              available.
-
+! EM 03/2011 : Add possibility to have outputs as distance to center
+!              of planet
 implicit none
 
@@ -101,4 +104,6 @@
 real,dimension(:,:,:,:),allocatable :: za_gcm ! GCM above areoid levels (m)
 real,dimension(:,:,:,:),allocatable :: zs_gcm ! GCM above surface heights (m)
+real,dimension(:,:,:,:),allocatable :: ra_gcm ! radial distance (m) to
+                                          ! center of Mars, (of GCM grid points)
 real,dimension(:,:,:,:),allocatable :: indata ! to store a GCM 4D dataset
 real,dimension(:,:,:,:),allocatable :: outdata ! to store a 4D dataset
@@ -108,4 +113,5 @@
 integer ztype ! Flag for vertical coordinate of output
 ! ztype=1: pressure  ztype=2: above areoid  ztype=3: above local surface
+! ztype=4: distance to center of planet
 integer nblev ! # of levels (along vertical coordinate) for output data
 real pmin,pmax ! min and max values for output pressure coordinate
@@ -114,4 +120,5 @@
 real,dimension(:),allocatable :: zareoid ! Above areoid heights for output data
 real,dimension(:),allocatable :: zsurface ! Above surface heights for output
+real,dimension(:),allocatable :: zradius ! distance to center of planet
 logical :: have_rho ! Flag: true if density 'rho' is available
 logical :: have_sigma ! Flag: true if sigma levels are known (false if hybrid
@@ -140,4 +147,5 @@
 if (ierr.ne.NF_NOERR) then
    write(*,*) 'ERROR: Pb opening file ',trim(infile)
+   write(*,*) NF_STRERROR(ierr)
    stop ""
 endif
@@ -150,4 +158,5 @@
 if (ierr.ne.NF_NOERR) then
   write(*,*) 'ERROR: Failed geting number of variables from file'
+  write(*,*) NF_STRERROR(ierr)
   stop
 endif
@@ -166,5 +175,9 @@
 enddo
 
-allocate(var(nbvar4dinfile))
+allocate(var(nbvar4dinfile),stat=ierr)
+if (ierr.ne.0) then
+  write(*,*) "Error! failed memory allocation of var(nbvar4dinfile)"
+  stop
+endif
 
 write(*,*) ""
@@ -247,5 +260,10 @@
         stop "Error: Failed to get lat length"
       else
-        allocate(lat(latlength))
+        allocate(lat(latlength),stat=ierr)
+        if (ierr.ne.0) then
+          write(*,*) "Error: Failed to allocate lat(latlength)"
+          write(*,*) "     latlength=",latlength
+          stop
+        endif
         ierr=NF_GET_VAR_REAL(infid,tmpvarid,lat)
         if (ierr.ne.NF_NOERR) then
@@ -264,5 +282,10 @@
       stop "Error: Failed to get latitude length"
     else
-      allocate(lat(latlength))
+      allocate(lat(latlength),stat=ierr)
+      if (ierr.ne.0) then
+        write(*,*) "Error: Failed to allocate lat(latlength)"
+        write(*,*) "     latlength=",latlength
+        stop
+      endif
       ierr=NF_GET_VAR_REAL(infid,tmpvarid,lat)
       if (ierr.ne.NF_NOERR) then
@@ -290,5 +313,10 @@
         stop "Error: Failed to get lon length"
       else
-        allocate(lon(lonlength))
+        allocate(lon(lonlength),stat=ierr)
+        if (ierr.ne.0) then
+          write(*,*) "Error: Failed to allocate lon(lonlength)"
+          write(*,*) "     lonlength=",lonlength
+          stop
+        endif
         ierr=NF_GET_VAR_REAL(infid,tmpvarid,lon)
         if (ierr.ne.NF_NOERR) then
@@ -307,5 +335,10 @@
       stop "Error: Failed to get longitude length"
     else
-      allocate(lon(lonlength))
+      allocate(lon(lonlength),stat=ierr)
+      if (ierr.ne.0) then
+        write(*,*) "Error: Failed to allocate lon(lonlength)"
+        write(*,*) "     lonlength=",lonlength
+        stop
+      endif
       ierr=NF_GET_VAR_REAL(infid,tmpvarid,lon)
       if (ierr.ne.NF_NOERR) then
@@ -333,5 +366,10 @@
         stop "Error: Failed to get time length"
       else
-        allocate(time(timelength))
+        allocate(time(timelength),stat=ierr)
+        if (ierr.ne.0) then
+          write(*,*) "Error: Failed to allocate time(timelength)"
+          write(*,*) "     timelength=",timelength
+          stop
+        endif
         ierr=NF_GET_VAR_REAL(infid,tmpvarid,time)
         if (ierr.ne.NF_NOERR) then
@@ -350,5 +388,10 @@
       stop "Error: Failed to get Time length"
     else
-      allocate(time(timelength))
+      allocate(time(timelength),stat=ierr)
+      if (ierr.ne.0) then
+        write(*,*) "Error: Failed to allocate time(timelength)"
+        write(*,*) "     timelength=",timelength
+        stop
+      endif
       ierr=NF_GET_VAR_REAL(infid,tmpvarid,time)
       if (ierr.ne.NF_NOERR) then
@@ -389,5 +432,10 @@
 else
   have_sigma=.true.
-  allocate(sigma(altlength))
+  allocate(sigma(altlength),stat=ierr)
+  if (ierr.ne.0) then
+    write(*,*) "Error: Failed to allocate sigma(altlength)"
+    write(*,*) "     altlength=",altlength
+    stop
+  endif
   ierr=NF_GET_VAR_REAL(infid,tmpvarid,sigma)
   if (ierr.ne.NF_NOERR) then
@@ -403,5 +451,10 @@
     stop "Error: Failed to get aps ID"
   else
-    allocate(aps(altlength))
+    allocate(aps(altlength),stat=ierr)
+    if (ierr.ne.0) then
+      write(*,*) "Error: Failed to allocate aps(altlength)"
+      write(*,*) "     altlength=",altlength
+      stop
+    endif
     ierr=NF_GET_VAR_REAL(infid,tmpvarid,aps)
     if (ierr.ne.NF_NOERR) then
@@ -415,5 +468,10 @@
     stop "Error: Failed to get bps ID"
   else
-    allocate(bps(altlength))
+    allocate(bps(altlength),stat=ierr)
+    if (ierr.ne.0) then
+      write(*,*) "Error: Failed to allocate bps(altlength)"
+      write(*,*) "     altlength=",altlength
+      stop
+    endif
     ierr=NF_GET_VAR_REAL(infid,tmpvarid,bps)
     if (ierr.ne.NF_NOERR) then
@@ -429,4 +487,5 @@
   write(*,*) "Failed allocation of phisinit(lonlength,latlength) !!!"
   write(*,*) "lonlength=",lonlength," latlength=",latlength
+  stop
 endif
 ! look for 'phisinit' in current file
@@ -475,6 +534,7 @@
 write(*,*) "Which vertical coordinate should the output be in?"
 ztype=0
-do while ((ztype.lt.1).or.(ztype.gt.3))
-  write(*,*) "(1: pressure, 2: above areoid altitude 3: above local surface)"
+do while ((ztype.lt.1).or.(ztype.gt.4))
+  write(*,*) "(1: pressure, 2: altitude above areoid, "
+  write(*,*) " 3: above local surface, 4: distance to center of Mars)"
   read(*,*)ztype
 enddo
@@ -498,13 +558,13 @@
   ! ask for # of points and end values for pressure or above areoid cases
   write(*,*) ""
-  if (ztype.le.2) then
+  if ((ztype.le.2).or.(ztype.le.4)) then
     write(*,*) "Enter min and max of vertical coordinate (Pa or m)"
     write(*,*) " (in that order and on the same line)"
     if (ztype.eq.1) then ! pressure coordinate
       read(*,*) pmin,pmax
-    else ! above areoid coordinate
+    else ! altitude coordinate
       read(*,*) zamin,zamax
     endif
-  endif
+  endif ! of if ((ztype.le.2).or.(ztype.le.4))
 
   ! Build corresponding vertical coordinates
@@ -512,5 +572,10 @@
     write(*,*) "Number of levels along vertical coordinate?"
     read(*,*) nblev
-    allocate(plevel(nblev))
+    allocate(plevel(nblev),stat=ierr)
+    if (ierr.ne.0) then
+      write(*,*) "Error: Failed to allocate plevel(nblev)"
+      write(*,*) "     nblev=",nblev
+      stop
+    endif
     if (nblev.eq.1) then ! in case only one level is asked for
       plevel(nblev)=pmin
@@ -525,5 +590,10 @@
     write(*,*) "Number of levels along vertical coordinate?"
     read(*,*) nblev
-    allocate(zareoid(nblev))
+    allocate(zareoid(nblev),stat=ierr)
+    if (ierr.ne.0) then
+      write(*,*) "Error: Failed to allocate zareoid(nblev)"
+      write(*,*) "     nblev=",nblev
+      stop
+    endif
     if (nblev.eq.1) then ! in case only one level is asked for
       zareoid(nblev)=zamin
@@ -533,10 +603,31 @@
       enddo
     endif
-  else ! above local surface
+  else if (ztype.eq.3) then ! above local surface
     ! set nblev to # of levels from input data files
     nblev=altlength
-    allocate(zsurface(nblev))
+    allocate(zsurface(nblev),stat=ierr)
+    if (ierr.ne.0) then
+      write(*,*) "Error: Failed to allocate zsurface(nblev)"
+      write(*,*) "     nblev=",nblev
+      stop
+    endif
     ! build specific above local surface altitudes
     call build_zs(nblev,have_sigma,sigma,aps,bps,zsurface)
+  else ! distance to center of planet
+   write(*,*) "Number of levels along vertical coordinate?"
+    read(*,*) nblev
+    allocate(zradius(nblev),stat=ierr)
+    if (ierr.ne.0) then
+      write(*,*) "Error: Failed to allocate zradius(nblev)"
+      write(*,*) "     nblev=",nblev
+      stop
+    endif
+    if (nblev.eq.1) then ! in case only one level is asked for
+      zradius(nblev)=zamin
+    else 
+      do i=1,nblev
+        zradius(i)=zamin+(real(i)-1.0)*((zamax-zamin)/(real(nblev)-1.0))
+      enddo
+    endif
   endif
 else ! auto_vert_levels=.false. ; user provides values
@@ -546,5 +637,10 @@
   read(*,*) nblev
   if (ztype.eq.1) then ! pressure coordinate
-    allocate(plevel(nblev))
+    allocate(plevel(nblev),stat=ierr)
+    if (ierr.ne.0) then
+      write(*,*) "Error: Failed to allocate plevel(nblev)"
+      write(*,*) "     nblev=",nblev
+      stop
+    endif
     write(*,*) "Enter Pressure (Pa) of levels, ordered"
     write(*,*) " from max (near-surface) to min (top of atmosphere),"
@@ -554,5 +650,10 @@
     enddo
   else if (ztype.eq.2) then ! above areoid heights
-    allocate(zareoid(nblev))
+    allocate(zareoid(nblev),stat=ierr)
+    if (ierr.ne.0) then
+      write(*,*) "Error: Failed to allocate zareoid(nblev)"
+      write(*,*) "     nblev=",nblev
+      stop
+    endif
     write(*,*) "Enter altitude (m) above areoid of levels, ordered"
     write(*,*) " from min to max (one value per line)"
@@ -560,10 +661,27 @@
       read(*,*) zareoid(i)
     enddo
-  else ! above local surface
-    allocate(zsurface(nblev))
+  else if (ztype.eq.2) then ! above local surface
+    allocate(zsurface(nblev),stat=ierr)
+    if (ierr.ne.0) then
+      write(*,*) "Error: Failed to allocate zsurface(nblev)"
+      write(*,*) "     nblev=",nblev
+      stop
+    endif
     write(*,*) "Enter altitude (m) above surface of levels, ordered"
     write(*,*) " from min to max (one value per line)"
     do i=1,nblev
       read(*,*) zsurface(i)
+    enddo
+  else ! distance to center of planet
+    allocate(zradius(nblev),stat=ierr)
+    if (ierr.ne.0) then
+      write(*,*) "Error: Failed to allocate zradius(nblev)"
+      write(*,*) "     nblev=",nblev
+      stop
+    endif
+    write(*,*) "Enter distance (m) to center of Mars of levels, ordered"
+    write(*,*) " from min to max (one value per line)"
+    do i=1,nblev
+      read(*,*) zradius(i)
     enddo
   endif
@@ -580,6 +698,8 @@
 else if (ztype.eq.2) then ! above areoid coordinate
   outfile=infile(1:len_trim(infile)-3)//"_A.nc"
-else ! above local surface
+else if (ztype.eq.3) then ! above local surface
   outfile=infile(1:len_trim(infile)-3)//"_S.nc"
+else ! radial distance to center of Mars
+  outfile=infile(1:len_trim(infile)-3)//"_R.nc"
 endif
 write(*,*) "Output file name is: "//trim(outfile)
@@ -596,5 +716,11 @@
   stop "Error: Failed to get ps ID"
 else
-  allocate(ps(lonlength,latlength,timelength))
+  allocate(ps(lonlength,latlength,timelength),stat=ierr)
+  if (ierr.ne.0) then
+    write(*,*) "Error: Failed to allocate ps(lonlength,latlength,timelength)"
+    write(*,*) "       lonlength=",lonlength," latlength=",latlength
+    write(*,*) "       timelength=",timelength
+    stop
+  endif
   ierr=NF_GET_VAR_REAL(infid,tmpvarid,ps)
   if (ierr.ne.NF_NOERR) then
@@ -606,5 +732,11 @@
 ! 2.1.2 Atmospheric pressure
 !===============================================================================
-allocate(press(lonlength,latlength,altlength,timelength))
+allocate(press(lonlength,latlength,altlength,timelength),stat=ierr)
+if (ierr.ne.0) then
+  write(*,*) "Error: Failed to allocate press(lonlength,latlength,altlength,timelength)"
+  write(*,*) "       lonlength=",lonlength," latlength=",latlength
+  write(*,*) "       altlength=",altlength," timelength=",timelength
+  stop
+endif
 
 if (have_sigma) then ! sigma coordinate
@@ -633,5 +765,11 @@
 ! 2.1.3 Atmospheric temperature
 !===============================================================================
-allocate(temp(lonlength,latlength,altlength,timelength))
+allocate(temp(lonlength,latlength,altlength,timelength),stat=ierr)
+if (ierr.ne.0) then
+  write(*,*) "Error: Failed to allocate temp(lonlength,latlength,altlength,timelength)"
+  write(*,*) "       lonlength=",lonlength," latlength=",latlength
+  write(*,*) "       altlength=",altlength," timelength=",timelength
+  stop
+endif
 
 ierr=NF_INQ_VARID(infid,"temp",tmpvarid)
@@ -665,5 +803,11 @@
 else
   have_rho=.true.
-  allocate(rho(lonlength,latlength,altlength,timelength))
+  allocate(rho(lonlength,latlength,altlength,timelength),stat=ierr)
+  if (ierr.ne.0) then
+    write(*,*) "Error: Failed to allocate rho(lonlength,latlength,altlength,timelength)"
+    write(*,*) "       lonlength=",lonlength," latlength=",latlength
+    write(*,*) "       altlength=",altlength," timelength=",timelength
+    stop
+  endif
   ierr=NF_GET_VAR_REAL(infid,tmpvarid,rho)
   if (ierr.ne.NF_NOERR) then
@@ -678,24 +822,92 @@
 if (have_rho) then
   if (ztype.le.2) then ! above areoid altitudes (also needed for ztype=1)
-    allocate(za_gcm(lonlength,latlength,altlength,timelength))
+    allocate(za_gcm(lonlength,latlength,altlength,timelength),stat=ierr)
+    if (ierr.ne.0) then
+      write(*,*) "Error: Failed to allocate za_gcm(lonlength,latlength,altlength,timelength)"
+      write(*,*) "       lonlength=",lonlength," latlength=",latlength
+      write(*,*) "       altlength=",altlength," timelength=",timelength
+      stop
+    endif
     call build_gcm_za(lonlength,latlength,altlength,timelength, &
                       phisinit,ps,press,temp,rho,za_gcm)
-  else ! above local surface altitudes
-    allocate(zs_gcm(lonlength,latlength,altlength,timelength))
+  else if (ztype.eq.3) then! above local surface altitudes
+    allocate(zs_gcm(lonlength,latlength,altlength,timelength),stat=ierr)
+    if (ierr.ne.0) then
+      write(*,*) "Error: Failed to allocate zs_gcm(lonlength,latlength,altlength,timelength)"
+      write(*,*) "       lonlength=",lonlength," latlength=",latlength
+      write(*,*) "       altlength=",altlength," timelength=",timelength
+      stop
+    endif
     call build_gcm_zs(lonlength,latlength,altlength,timelength, &
                       phisinit,ps,press,temp,rho,zs_gcm)
+  else ! radial distance to center of planet
+    allocate(za_gcm(lonlength,latlength,altlength,timelength),stat=ierr)
+    if (ierr.ne.0) then
+      write(*,*) "Error: Failed to allocate za_gcm(lonlength,latlength,altlength,timelength)"
+      write(*,*) "       lonlength=",lonlength," latlength=",latlength
+      write(*,*) "       altlength=",altlength," timelength=",timelength
+      stop
+    endif
+    allocate(ra_gcm(lonlength,latlength,altlength,timelength),stat=ierr)
+    if (ierr.ne.0) then
+      write(*,*) "Error: Failed to allocate ra_gcm(lonlength,latlength,altlength,timelength)"
+      write(*,*) "       lonlength=",lonlength," latlength=",latlength
+      write(*,*) "       altlength=",altlength," timelength=",timelength
+      stop
+    endif
+    call build_gcm_za(lonlength,latlength,altlength,timelength, &
+                      phisinit,ps,press,temp,rho,za_gcm)
+    ! and now convert the altitudes above areoid to radial distances
+    call build_gcm_ra(lonlength,latlength,altlength,timelength, &
+                      lon,lat,za_gcm,ra_gcm)
+   ! free za_gcm
+   deallocate(za_gcm)
   endif
 else
   write(*,*)"Warning: Using constant R to integrate hydrostatic equation"
   if (ztype.le.2) then ! above areoid altitudes (also needed for ztype=1)
-    allocate(za_gcm(lonlength,latlength,altlength,timelength))
+    allocate(za_gcm(lonlength,latlength,altlength,timelength),stat=ierr)
+    if (ierr.ne.0) then
+      write(*,*) "Error: Failed to allocate za_gcm(lonlength,latlength,altlength,timelength)"
+      write(*,*) "       lonlength=",lonlength," latlength=",latlength
+      write(*,*) "       altlength=",altlength," timelength=",timelength
+      stop
+    endif
     call crude_gcm_za(lonlength,latlength,altlength,timelength, &
                       phisinit,ps,press,temp,za_gcm)
-  else ! above local surface altitudes
-    allocate(zs_gcm(lonlength,latlength,altlength,timelength))
+  else if (ztype.eq.3) then ! above local surface altitudes
+    allocate(zs_gcm(lonlength,latlength,altlength,timelength),stat=ierr)
+    if (ierr.ne.0) then
+      write(*,*) "Error: Failed to allocate zs_gcm(lonlength,latlength,altlength,timelength)"
+      write(*,*) "       lonlength=",lonlength," latlength=",latlength
+      write(*,*) "       altlength=",altlength," timelength=",timelength
+      stop
+    endif
     call crude_gcm_zs(lonlength,latlength,altlength,timelength, &
                       phisinit,ps,press,temp,zs_gcm)
+  else ! radial distance to center of planet
+    allocate(za_gcm(lonlength,latlength,altlength,timelength),stat=ierr)
+    if (ierr.ne.0) then
+      write(*,*) "Error: Failed to allocate za_gcm(lonlength,latlength,altlength,timelength)"
+      write(*,*) "       lonlength=",lonlength," latlength=",latlength
+      write(*,*) "       altlength=",altlength," timelength=",timelength
+      stop
+    endif
+    allocate(ra_gcm(lonlength,latlength,altlength,timelength),stat=ierr)
+    if (ierr.ne.0) then
+      write(*,*) "Error: Failed to allocate ra_gcm(lonlength,latlength,altlength,timelength)"
+      write(*,*) "       lonlength=",lonlength," latlength=",latlength
+      write(*,*) "       altlength=",altlength," timelength=",timelength
+      stop
+    endif
+    call crude_gcm_za(lonlength,latlength,altlength,timelength, &
+                      phisinit,ps,press,temp,za_gcm)
+    ! and now convert the altitudes above areoid to radial distances
+    call build_gcm_ra(lonlength,latlength,altlength,timelength, &
+                      lon,lat,za_gcm,ra_gcm)
+   ! free za_gcm
+   deallocate(za_gcm)
   endif
-endif
+endif ! of if (have_rho)
 
 !===============================================================================
@@ -711,4 +923,5 @@
 if (ierr.ne.NF_NOERR) then
   write(*,*)"Error: could not create file ",outfile
+  write(*,*) NF_STRERROR(ierr)
   stop
 endif
@@ -720,5 +933,7 @@
 ierr=NF_DEF_DIM(outfid,"longitude",lonlength,lon_dimid)
 if (ierr.ne.NF_NOERR) then
-  stop "Error: Could not define longitude dimension"
+  write(*,*) "Error: Could not define longitude dimension"
+  write(*,*) NF_STRERROR(ierr)
+  stop
 endif
 
@@ -726,5 +941,7 @@
 ierr=NF_DEF_DIM(outfid,"latitude",latlength,lat_dimid)
 if (ierr.ne.NF_NOERR) then
-  stop "Error: Could not define latitude dimension"
+  write(*,*) "Error: Could not define latitude dimension"
+  write(*,*) NF_STRERROR(ierr)
+  stop
 endif
 
@@ -732,5 +949,7 @@
 ierr=NF_DEF_DIM(outfid,"altitude",nblev,alt_dimid)
 if (ierr.ne.NF_NOERR) then
-  stop "Error: Could not define altitude dimension"
+  write(*,*) "Error: Could not define altitude dimension"
+  write(*,*) NF_STRERROR(ierr)
+  stop
 endif
 
@@ -738,5 +957,7 @@
 ierr=NF_DEF_DIM(outfid,"Time",timelength,time_dimid)
 if (ierr.ne.NF_NOERR) then
-  stop "Error: Could not define latitude dimension"
+  write(*,*) "Error: Could not define Time dimension"
+  write(*,*) NF_STRERROR(ierr)
+  stop
 endif
 
@@ -744,5 +965,7 @@
 ierr=NF_DEF_DIM(outfid,"GCM_layers",altlength,gcm_layers_dimid)
 if (ierr.ne.NF_NOERR) then
-  stop "Error: Could not define GCM_layers dimension"
+  write(*,*) "Error: Could not define GCM_layers dimension"
+  write(*,*) NF_STRERROR(ierr)
+  stop
 endif
 
@@ -758,5 +981,7 @@
 ierr=NF_DEF_VAR(outfid,"longitude",NF_REAL,1,datashape(1),lon_varid)
 if (ierr.ne.NF_NOERR) then
-  stop "Error: Could not define longitude variable"
+  write(*,*) "Error: Could not define longitude variable"
+  write(*,*) NF_STRERROR(ierr)
+  stop
 endif
 
@@ -777,5 +1002,7 @@
 ierr=NF_DEF_VAR(outfid,"latitude",NF_REAL,1,datashape(2),lat_varid)
 if (ierr.ne.NF_NOERR) then
-  stop "Error: Could not define latitude variable"
+  write(*,*) "Error: Could not define latitude variable"
+  write(*,*) NF_STRERROR(ierr)
+  stop
 endif
 
@@ -796,5 +1023,7 @@
 ierr=NF_DEF_VAR(outfid,"altitude",NF_REAL,1,datashape(3),alt_varid)
 if (ierr.ne.NF_NOERR) then
-  stop "Error: Could not define altitude variable"
+  write(*,*) "Error: Could not define altitude variable"
+  write(*,*) NF_STRERROR(ierr)
+  stop
 endif
 
@@ -832,5 +1061,5 @@
     stop "Error: Problem writing positive for altitude"
   endif
-else ! above surface vertical coordinate
+else if (ztype.eq.3) then ! above surface vertical coordinate
   text='Altitude above local surface'
   ierr=NF_PUT_ATT_TEXT(outfid,alt_varid,'long_name',len_trim(text),text)
@@ -848,4 +1077,20 @@
     stop "Error: Problem writing positive for altitude"
   endif
+else ! radial distance to center of planet
+  text='Distance to center of Mars'
+  ierr=NF_PUT_ATT_TEXT(outfid,alt_varid,'long_name',len_trim(text),text)
+  if (ierr.ne.NF_NOERR) then
+    stop "Error: Problem writing long_name for altitude"
+  endif
+  text='m'
+  ierr=NF_PUT_ATT_TEXT(outfid,alt_varid,'units',len_trim(text),text)
+  if (ierr.ne.NF_NOERR) then
+    stop "Error: Problem writing units for altitude"
+  endif
+  text='up'
+  ierr=NF_PUT_ATT_TEXT(outfid,alt_varid,'positive',len_trim(text),text)
+  if (ierr.ne.NF_NOERR) then
+    stop "Error: Problem writing positive for altitude"
+  endif
 endif ! of if (have_sigma)
 
@@ -857,14 +1102,20 @@
   ierr=NF_DEF_VAR(outfid,"sigma",NF_REAL,1,gcm_layers_dimid,sigma_varid)
   if (ierr.ne.NF_NOERR) then
-    stop "Error: Could not define sigma variable"
+    write(*,*) "Error: Could not define sigma variable"
+    write(*,*) NF_STRERROR(ierr)
+    stop
   endif
 else ! hybrid coordinates
   ierr=NF_DEF_VAR(outfid,"aps",NF_REAL,1,gcm_layers_dimid,aps_varid)
   if (ierr.ne.NF_NOERR) then
-    stop "Error: Could not define aps variable"
+    write(*,*) "Error: Could not define aps variable"
+    write(*,*) NF_STRERROR(ierr)
+    stop
   endif
   ierr=NF_DEF_VAR(outfid,"bps",NF_REAL,1,gcm_layers_dimid,bps_varid)
   if (ierr.ne.NF_NOERR) then
-    stop "Error: Could not define bps variable"
+    write(*,*) "Error: Could not define bps variable"
+    write(*,*) NF_STRERROR(ierr)
+    stop
   endif
 endif
@@ -894,5 +1145,7 @@
 ierr=NF_DEF_VAR(outfid,"Time",NF_REAL,1,datashape(4),time_varid)
 if (ierr.ne.NF_NOERR) then
-  stop "Error: Could not define Time variable"
+  write(*,*) "Error: Could not define Time variable"
+  write(*,*) NF_STRERROR(ierr)
+  stop
 endif
 
@@ -917,5 +1170,7 @@
 ierr=NF_DEF_VAR(outfid,"ps",NF_REAL,3,surfdatashape,ps_varid)
 if (ierr.ne.NF_NOERR) then
-  stop "Error: Could not define ps variable"
+  write(*,*) "Error: Could not define ps variable"
+  write(*,*) NF_STRERROR(ierr)
+  stop
 endif
 
@@ -939,5 +1194,7 @@
   ierr=NF_DEF_VAR(outfid,"zareoid",NF_REAL,4,datashape,za_varid)
   if (ierr.ne.NF_NOERR) then
-    stop "Error: Could not define zareoid variable"
+    write(*,*) "Error: Could not define zareoid variable"
+    write(*,*) NF_STRERROR(ierr)
+    stop
   endif
   ! zareoid attributes
@@ -961,5 +1218,7 @@
   ierr=NF_DEF_VAR(outfid,"pressure",NF_REAL,4,datashape,p_varid)
   if (ierr.ne.NF_NOERR) then
-    stop "Error: Could not define pressure variable"
+    write(*,*) "Error: Could not define pressure variable"
+    write(*,*) NF_STRERROR(ierr)
+    stop
   endif
   ! pressure attributes
@@ -986,5 +1245,10 @@
 
 ! variables requested by user
-allocate(var_id(nbvar))
+allocate(var_id(nbvar),stat=ierr)
+if (ierr.ne.0) then
+  write(*,*) "Error: Failed to allocate var_id(nbvar)"
+  write(*,*) "       nbvar=",nbvar
+  stop
+endif
 do i=1,nbvar
   write(*,*) ""
@@ -994,5 +1258,6 @@
   if (ierr.ne.NF_NOERR) then
     write(*,*) 'Error, could not define variable ',trim(var(i))
-    stop ""
+    write(*,*) NF_STRERROR(ierr)
+    stop 
   endif
 
@@ -1002,5 +1267,6 @@
   if (ierr.ne.NF_NOERR) then
     write(*,*) 'Error, failed to get ID for variable ',trim(var(i))
-    stop ""
+    write(*,*) NF_STRERROR(ierr)
+    stop
   endif
   ierr=NF_INQ_VARNATTS(infid,tmpvarid,nbattr)
@@ -1008,5 +1274,6 @@
     write(*,*) 'Error, could not get number of attributes for variable ',&
                trim(var(i))
-    stop ""
+    write(*,*) NF_STRERROR(ierr)
+    stop
   endif
   ! inititialize j == number of attributes written to output
@@ -1099,5 +1366,7 @@
 ierr=NF_ENDDEF(outfid)
 if (ierr.ne.NF_NOERR) then
-  stop "Error: Could not switch out of define mode"
+  write(*,*) "Error: Could not switch out of define mode"
+  write(*,*) NF_STRERROR(ierr)
+  stop
 endif
 
@@ -1105,5 +1374,7 @@
 ierr=NF_PUT_VAR_REAL(outfid,lon_varid,lon)
 if (ierr.ne.NF_NOERR) then
-  stop "Error: Could not write longitude data to output file"
+  write(*,*) "Error: Could not write longitude data to output file"
+  write(*,*) NF_STRERROR(ierr)
+  stop
 endif
 
@@ -1111,5 +1382,7 @@
 ierr=NF_PUT_VAR_REAL(outfid,lat_varid,lat)
 if (ierr.ne.NF_NOERR) then
-  stop "Error: Could not write latitude data to output file"
+  write(*,*) "Error: Could not write latitude data to output file"
+  write(*,*) NF_STRERROR(ierr)
+  stop
 endif
 
@@ -1118,15 +1391,28 @@
   ierr=NF_PUT_VAR_REAL(outfid,alt_varid,plevel)
   if (ierr.ne.NF_NOERR) then
-    stop "Error: Could not write altitude data to output file"
+    write(*,*) "Error: Could not write altitude data to output file"
+    write(*,*) NF_STRERROR(ierr)
+    stop
   endif
 else if (ztype.eq.2) then ! above areoid altitude
   ierr=NF_PUT_VAR_REAL(outfid,alt_varid,zareoid)
   if (ierr.ne.NF_NOERR) then
-    stop "Error: Could not write altitude data to output file"
+    write(*,*) "Error: Could not write altitude data to output file"
+    write(*,*) NF_STRERROR(ierr)
+    stop
   endif
-else ! above local surface
+else if (ztype.eq.3) then ! above local surface
   ierr=NF_PUT_VAR_REAL(outfid,alt_varid,zsurface)
   if (ierr.ne.NF_NOERR) then
-    stop "Error: Could not write altitude data to output file"
+    write(*,*) "Error: Could not write altitude data to output file"
+    write(*,*) NF_STRERROR(ierr)
+    stop
+  endif
+else ! radial distance to center of Mars
+  ierr=NF_PUT_VAR_REAL(outfid,alt_varid,zradius)
+  if (ierr.ne.NF_NOERR) then
+    write(*,*) "Error: Could not write altitude data to output file"
+    write(*,*) NF_STRERROR(ierr)
+    stop
   endif
 endif
@@ -1136,14 +1422,20 @@
   ierr=NF_PUT_VAR_REAL(outfid,sigma_varid,sigma)
   if (ierr.ne.NF_NOERR) then
-    stop "Error: Could not write sigma data to output file"
+    write(*,*) "Error: Could not write sigma data to output file"
+    write(*,*) NF_STRERROR(ierr)
+    stop
   endif
 else ! hybrid coordinates
   ierr=NF_PUT_VAR_REAL(outfid,aps_varid,aps)
   if (ierr.ne.NF_NOERR) then
-    stop "Error: Could not write aps data to output file"
+    write(*,*) "Error: Could not write aps data to output file"
+    write(*,*) NF_STRERROR(ierr)
+    stop
   endif
   ierr=NF_PUT_VAR_REAL(outfid,bps_varid,bps)
   if (ierr.ne.NF_NOERR) then
-    stop "Error: Could not write bps data to output file"
+    write(*,*) "Error: Could not write bps data to output file"
+    write(*,*) NF_STRERROR(ierr)
+    stop
   endif
 endif
@@ -1152,5 +1444,7 @@
 ierr=NF_PUT_VAR_REAL(outfid,time_varid,time)
 if (ierr.ne.NF_NOERR) then
-  stop "Error: Could not write Time data to output file"
+  write(*,*) "Error: Could not write Time data to output file"
+  write(*,*) NF_STRERROR(ierr)
+  stop
 endif
 
@@ -1163,5 +1457,7 @@
 ierr=NF_PUT_VAR_REAL(outfid,ps_varid,ps)
 if (ierr.ne.NF_NOERR) then
-  stop "Error: Could not write ps data to output file"
+  write(*,*) "Error: Could not write ps data to output file"
+  write(*,*) NF_STRERROR(ierr)
+  stop
 endif
 
@@ -1172,7 +1468,19 @@
 ! 4.0 Allocations
 !indata() to store input (on GCM grid) data
-allocate(indata(lonlength,latlength,altlength,timelength))
+allocate(indata(lonlength,latlength,altlength,timelength),stat=ierr)
+if (ierr.ne.0) then
+  write(*,*) "Error: Failed to allocate indata(lonlength,latlength,altlength,timelength)"
+  write(*,*) "       lonlength=",lonlength," latlength=",latlength
+  write(*,*) "       altlength=",altlength," timelength=",timelength
+  stop
+endif
 ! outdata() to store output (on new vertical grid) data
-allocate(outdata(lonlength,latlength,nblev,timelength))
+allocate(outdata(lonlength,latlength,nblev,timelength),stat=ierr)
+if (ierr.ne.0) then
+  write(*,*) "Error: Failed to allocate outdata(lonlength,latlength,nblev,timelength)"
+  write(*,*) "       lonlength=",lonlength," latlength=",latlength
+  write(*,*) "       nblev=",nblev," timelength=",timelength
+  stop
+endif
 
 ! 4.1 If output is in pressure coordinate
@@ -1199,4 +1507,5 @@
   if (ierr.ne.NF_NOERR) then
     write(*,*)'Error, Failed to write variable ',var(i)
+    write(*,*) NF_STRERROR(ierr)
     stop
   endif
@@ -1210,5 +1519,7 @@
   ierr=NF_PUT_VAR_REAL(outfid,za_varid,outdata)
   if (ierr.ne.NF_NOERR) then
-    stop "Error, Failed to write zareoid to output file"
+    write(*,*) "Error, Failed to write zareoid to output file"
+    write(*,*) NF_STRERROR(ierr)
+    stop
   endif
 endif ! of if (ztype.eq.1)
@@ -1244,4 +1555,5 @@
   if (ierr.ne.NF_NOERR) then
     write(*,*)'Error, Failed to write variable ',var(i)
+    write(*,*) NF_STRERROR(ierr)
     stop
   endif
@@ -1258,5 +1570,7 @@
   ierr=NF_PUT_VAR_REAL(outfid,p_varid,outdata)
   if (ierr.ne.NF_NOERR) then
-    stop "Error, Failed to write pressure to output file"
+    write(*,*) "Error, Failed to write pressure to output file"
+    write(*,*) NF_STRERROR(ierr)
+    stop
   endif
 endif ! of if (ztype.eq.2)
@@ -1295,4 +1609,5 @@
     if (ierr.ne.NF_NOERR) then
       write(*,*)'Error, Failed to write variable ',var(i)
+      write(*,*) NF_STRERROR(ierr)
       stop
     endif
@@ -1309,13 +1624,67 @@
   ierr=NF_PUT_VAR_REAL(outfid,p_varid,outdata)
   if (ierr.ne.NF_NOERR) then
-    stop "Error, Failed to write pressure to output file"
+    write(*,*) "Error, Failed to write pressure to output file"
+    write(*,*) NF_STRERROR(ierr)
+    stop
   endif
 
 endif ! of if (ztype.eq.3)
 
-! 4.4 Close output file
+! 4.4 If output is in radial distance to center of planet
+if (ztype.eq.4) then
+  do i=1,nbvar ! loop on 4D variable to process
+  ! identify and read a dataset
+  ierr=NF_INQ_VARID(infid,var(i),tmpvarid)
+  if (ierr.ne.NF_NOERR) then
+    write(*,*) 'Error, failed to get ID for variable ',var(i)
+    stop
+  endif
+  ierr=NF_GET_VAR_REAL(infid,tmpvarid,indata)
+  if (ierr.ne.NF_NOERR) then
+    write(*,*) 'Error, failed to load variable ',var(i)
+    stop
+  endif
+  
+  ! interpolate dataset onto new grid
+  ! check if variable is "rho" (to set flag for interpolation below)
+  if (var(i).eq.'rho') then
+    j=1
+  else
+    j=0
+  endif
+  
+  call z_coord_interp(lonlength,latlength,altlength,timelength,nblev, &
+                      miss_val,ra_gcm,indata,j,zradius,outdata)
+
+  ! write new dataset to output file
+  ierr=NF_PUT_VAR_REAL(outfid,var_id(i),outdata)
+  if (ierr.ne.NF_NOERR) then
+    write(*,*)'Error, Failed to write variable ',var(i)
+    write(*,*) NF_STRERROR(ierr)
+    stop
+  endif
+
+  enddo ! of do i=1,nbvar
+  
+  ! interpolate pressure onto new grid
+  write(*,*) ""
+  write(*,*) "Processing pressure"
+  call z_coord_interp(lonlength,latlength,altlength,timelength,nblev, &
+                      miss_val,ra_gcm,press,1,zradius,outdata)
+
+  ! write result to output file
+  ierr=NF_PUT_VAR_REAL(outfid,p_varid,outdata)
+  if (ierr.ne.NF_NOERR) then
+    write(*,*) "Error, Failed to write pressure to output file"
+    write(*,*) NF_STRERROR(ierr)
+    stop
+  endif
+endif ! of if (ztype.eq.4)
+
+! 4.5 Close output file
 ierr=NF_CLOSE(outfid)
 if (ierr.ne.NF_NOERR) then
   write(*,*) 'Error, failed to close output file ',outfile
+  write(*,*) NF_STRERROR(ierr)
 endif
 
@@ -2238,2 +2607,6809 @@
 
 end subroutine interpolf
+
+!===============================================================================
+
+subroutine build_gcm_ra(lonlength,latlength,altlength,timelength, &
+                         lon,lat,za_gcm,ra_gcm)
+!==============================================================================
+! Purpose:  Build, from the "above areoid altitudes" of GCM levels,
+!           the corresponding "radial distance to center of Mars" values
+!==============================================================================
+implicit none
+!==============================================================================
+! Arguments:
+!==============================================================================
+integer,intent(in) :: lonlength ! # of points along longitude
+integer,intent(in) :: latlength ! # of points along latitude
+integer,intent(in) :: altlength ! # of points along altitude
+integer,intent(in) :: timelength ! # of stored time steps
+real,intent(in) :: lon(lonlength) ! GCM longitudes
+real,intent(in) :: lat(latlength) ! GCM latitudes
+!za_gcm: above areoid altitudes of GCM levels
+real,intent(in) :: za_gcm(lonlength,latlength,altlength,timelength)
+!ra_gcm: radial distance to center of planet of GCM levels
+real,intent(out) :: ra_gcm(lonlength,latlength,altlength,timelength)
+
+!===============================================================================
+! Local variables:
+!===============================================================================
+real :: rareoid(lonlength,latlength) ! radial position (ie: distance to the
+! center of Mars) of the reference areoid for GCM longitudes and latitudes
+integer :: iloop,jloop,kloop,tloop
+double precision :: dlon,dlat,dareoid ! double precision temp variables
+
+! common data shared with 'areoid_ini' and 'geoid' routines
+integer,parameter :: ndeg=90,ndeg2=2*ndeg,nd2p3=ndeg2+3
+! data structure of gravity field
+        double precision v0,omega,ae,gm
+	double precision clm(0:ndeg,0:ndeg),slm(0:ndeg,0:ndeg)
+	common /gmm1/v0,omega,ae,gm,clm,slm
+        integer lmin,lmax
+        double precision root(nd2p3)
+        double precision requator
+	common /sqr/ lmin,lmax,root,requator
+
+!===============================================================================
+! 1. Various initialisations
+!===============================================================================
+! initalize coefficients of areoid model
+call areoid_ini()
+
+! compute rareoid for GCM longitude/latitude grid
+do iloop=1,lonlength
+ dlon=lon(iloop) ! double precision version of lon
+ do jloop=1,latlength
+   dlat=lat(jloop) ! double precision version of lat
+   call geoid(dlon,dlat,dareoid)
+   rareoid(iloop,jloop)=dareoid
+ enddo
+enddo
+
+!===============================================================================
+! 1. Compute ra_gcm
+!===============================================================================
+!!! test:
+!rareoid(:,:)=0
+
+do tloop=1,timelength
+  do kloop=1,altlength
+    ra_gcm(:,:,kloop,tloop)=za_gcm(:,:,kloop,tloop)+rareoid(:,:)
+  enddo
+enddo
+
+end subroutine build_gcm_ra
+
+
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+! Routines corresponding to Lemoine et al. 2001 implementation.
+! Based on "areoid.f" program by G. Neumann, which is available at
+! ftp://ltpftp.gsfc.nasa.gov/projects/tharsis/MOLA/SOFTWARE/
+! uses the gravity field coefficients file 'mgm1025' available in
+! the same ftp directory
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+subroutine areoid_ini()
+implicit none
+!character(len=250) :: mgm="/u/emlmd/MCD_v4.3/data/mgm1025"
+
+!character(len=64) :: title ! first line of file
+!character(len=6) :: gcoef
+! data structure of gravity field
+         integer ndeg,ndeg2,nd2p3
+	  parameter (ndeg=90,ndeg2=2*ndeg,nd2p3=ndeg2+3)
+	  double precision c(0:ndeg,0:ndeg),s(0:ndeg,0:ndeg)
+	  double precision  v0,omega,ae,gm !,clm,slm
+	  double precision  plm(ndeg)
+	  common /gmm1/ v0,omega,ae,gm,c,s
+	  integer lmin,lmax
+          double precision root(nd2p3)
+          double precision r
+          common /sqr/ lmin,lmax, root,r
+!
+!        integer lcmax,mmax
+        integer k,l,m
+!        double precision coef
+        double precision x,xi,sum
+        
+	  ae= 3396000.d0
+	  gm =42828.37d9
+	  omega=0.70882181d-4
+! this value makes the equatorial mean radius equal to 3396 km.
+	do k=1,nd2p3
+	 root(k)=sqrt(dble(k))
+	enddo
+!  initialize coefficients c and s
+c(:,:)=0
+s(:,:)=0
+
+! fill in the values of c() and s() (extracted from mgm1025 file)
+c( 2, 0)=   -0.87450441550858D-03
+c( 3, 0)=   -0.11889205541698D-04
+c( 4, 0)=    0.51231389950069D-05
+c( 5, 0)=   -0.17246183479555D-05
+c( 6, 0)=    0.13442413561338D-05
+c( 7, 0)=    0.10568085417745D-05
+c( 8, 0)=    0.14344394468535D-06
+c( 9, 0)=   -0.28623030841535D-06
+c(10, 0)=    0.72517371380309D-06
+c(11, 0)=   -0.26515503657960D-06
+c(12, 0)=    0.25791004374137D-06
+c(13, 0)=   -0.48987732989967D-06
+c(14, 0)=    0.30149567154029D-06
+c(15, 0)=    0.49309755579596D-06
+c(16, 0)=    0.62303904221200D-06
+c(17, 0)=   -0.53940568680542D-07
+c(18, 0)=   -0.31286409396935D-06
+c(19, 0)=    0.66506982323697D-08
+c(20, 0)=    0.29800506646171D-06
+c(21, 0)=    0.12382554869535D-06
+c(22, 0)=   -0.11079454891980D-06
+c(23, 0)=    0.46651763615791D-07
+c(24, 0)=    0.26561879988827D-06
+c(25, 0)=   -0.14012911779311D-06
+c(26, 0)=   -0.17890980799686D-06
+c(27, 0)=   -0.22473934735542D-06
+c(28, 0)=    0.35017911372558D-07
+c(29, 0)=    0.96416933029589D-07
+c(30, 0)=    0.13454167912854D-07
+c(31, 0)=    0.11415389076391D-06
+c(32, 0)=    0.14309722973488D-06
+c(33, 0)=   -0.93613803420433D-07
+c(34, 0)=   -0.11634597651051D-06
+c(35, 0)=    0.17390073509388D-07
+c(36, 0)=    0.17980990446829D-06
+c(37, 0)=   -0.58813753768476D-07
+c(38, 0)=   -0.15639701438663D-06
+c(39, 0)=    0.67338858450205D-07
+c(40, 0)=    0.10015015531020D-06
+c(41, 0)=    0.65659089401047D-07
+c(42, 0)=   -0.32828754909310D-07
+c(43, 0)=    0.55320735747522D-07
+c(44, 0)=    0.10719796171993D-06
+c(45, 0)=   -0.24466821475646D-07
+c(46, 0)=    0.53066022003621D-07
+c(47, 0)=    0.18183459032733D-08
+c(48, 0)=   -0.90336249640171D-07
+c(49, 0)=    0.10172719809900D-07
+c(50, 0)=    0.14157647949966D-06
+c(51, 0)=   -0.13459597844273D-07
+c(52, 0)=   -0.10770557778749D-06
+c(53, 0)=    0.41656444281046D-07
+c(54, 0)=    0.23491811928996D-07
+c(55, 0)=    0.39514870435300D-07
+c(56, 0)=    0.17750185036483D-07
+c(57, 0)=   -0.16389790284882D-07
+c(58, 0)=    0.15924966924563D-07
+c(59, 0)=   -0.52269191539423D-07
+c(60, 0)=    0.22651535424788D-07
+c(61, 0)=   -0.22088875934791D-07
+c(62, 0)=   -0.89365975311230D-07
+c(63, 0)=   -0.22314891242664D-06
+c(64, 0)=   -0.10126090956466D-06
+c(65, 0)=    0.53472579669405D-07
+c(66, 0)=   -0.79239790651784D-07
+c(67, 0)=   -0.93403592836398D-07
+c(68, 0)=   -0.92958885757065D-07
+c(69, 0)=   -0.23268566991842D-06
+c(70, 0)=   -0.61104272230081D-07
+c(71, 0)=   -0.15227130308936D-06
+c(72, 0)=    0.44022260088073D-07
+c(73, 0)=   -0.18296622662986D-06
+c(74, 0)=   -0.21563284613746D-07
+c(75, 0)=   -0.14408830353913D-06
+c(76, 0)=   -0.31971691137664D-07
+c(77, 0)=   -0.96143919013694D-07
+c(78, 0)=   -0.14039664820363D-07
+c(79, 0)=   -0.56173045626134D-07
+c(80, 0)=   -0.42587385931103D-07
+c( 2, 1)=    0.94588820913966D-10
+c( 3, 1)=    0.38007291643504D-05
+c( 4, 1)=    0.42113282449449D-05
+c( 5, 1)=    0.48295248273193D-06
+c( 6, 1)=    0.17989300452431D-05
+c( 7, 1)=    0.13721377780493D-05
+c( 8, 1)=   -0.13172502269848D-06
+c( 9, 1)=    0.41968715869939D-06
+c(10, 1)=    0.92089843305934D-06
+c(11, 1)=   -0.81438583356007D-06
+c(12, 1)=   -0.11226169861948D-05
+c(13, 1)=   -0.56756560374700D-06
+c(14, 1)=    0.75140494090486D-06
+c(15, 1)=    0.23398249720387D-06
+c(16, 1)=   -0.23315134603590D-06
+c(17, 1)=   -0.37162884465144D-06
+c(18, 1)=   -0.18094168688736D-06
+c(19, 1)=    0.46181639714625D-07
+c(20, 1)=    0.18344606355547D-06
+c(21, 1)=   -0.14791536512739D-06
+c(22, 1)=   -0.40126140681542D-06
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+c(24, 1)=    0.18984659529516D-06
+c(25, 1)=   -0.77644847446303D-07
+c(26, 1)=   -0.18954371508813D-06
+c(27, 1)=    0.58215212507928D-07
+c(28, 1)=    0.15662107285173D-06
+c(29, 1)=    0.69848912908713D-07
+c(30, 1)=   -0.14594550925334D-06
+c(31, 1)=   -0.60978169516080D-07
+c(32, 1)=   -0.69857883539046D-07
+c(33, 1)=   -0.40910599890025D-07
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+c(35, 1)=    0.69051821175597D-07
+c(36, 1)=   -0.89123393751658D-07
+c(37, 1)=   -0.10308616478520D-06
+c(38, 1)=   -0.17953527802480D-07
+c(39, 1)=    0.13357163900313D-06
+c(40, 1)=    0.32997141656491D-07
+c(41, 1)=   -0.42770439863940D-07
+c(42, 1)=   -0.33815214882692D-07
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+c(44, 1)=    0.83199427365936D-07
+c(45, 1)=   -0.26716533044488D-08
+c(46, 1)=   -0.21968332747552D-07
+c(47, 1)=    0.26051927992496D-07
+c(48, 1)=   -0.20011329156204D-07
+c(49, 1)=   -0.46000606601472D-07
+c(50, 1)=   -0.50465401285307D-08
+c(51, 1)=   -0.21435559836597D-07
+c(52, 1)=   -0.79586940432080D-07
+c(53, 1)=   -0.21721909216360D-08
+c(54, 1)=    0.11211857004569D-07
+c(55, 1)=   -0.14572008323947D-07
+c(56, 1)=   -0.76165251339758D-07
+c(57, 1)=   -0.33685497326864D-07
+c(58, 1)=    0.29095996986081D-07
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+c(60, 1)=   -0.29984787445527D-07
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+c(63, 1)=   -0.44106457563710D-08
+c(64, 1)=   -0.11522745649087D-07
+c(65, 1)=    0.24452822525910D-07
+c(66, 1)=    0.39582110377419D-08
+c(67, 1)=   -0.16048574963929D-07
+c(68, 1)=   -0.10635293597363D-08
+c(69, 1)=   -0.25348757056472D-08
+c(70, 1)=   -0.13990070916062D-07
+c(71, 1)=   -0.21113532040349D-07
+c(72, 1)=    0.21388767403742D-07
+c(73, 1)=   -0.45295107975469D-07
+c(74, 1)=    0.11061952017768D-08
+c(75, 1)=   -0.20070701321975D-07
+c(76, 1)=   -0.81623263977223D-08
+c(77, 1)=   -0.48608889440242D-08
+c(78, 1)=    0.48605157923197D-08
+c(79, 1)=   -0.72265799247382D-08
+c(80, 1)=    0.12959728064204D-07
+c( 2, 2)=   -0.84585751018071D-04
+c( 3, 2)=   -0.15933741663502D-04
+c( 4, 2)=   -0.95107786023564D-06
+c( 5, 2)=   -0.42918839549229D-05
+c( 6, 2)=    0.85990806408567D-06
+c( 7, 2)=    0.28084893201890D-05
+c( 8, 2)=    0.18057628945403D-05
+c( 9, 2)=    0.11356212264308D-05
+c(10, 2)=    0.73405458338506D-08
+c(11, 2)=   -0.31264422685096D-06
+c(12, 2)=   -0.97454248928457D-07
+c(13, 2)=    0.19140550616679D-06
+c(14, 2)=    0.44883687385942D-06
+c(15, 2)=   -0.35213615909880D-06
+c(16, 2)=   -0.48079087360350D-06
+c(17, 2)=   -0.20190086133281D-06
+c(18, 2)=   -0.10432508924443D-06
+c(19, 2)=   -0.52238899978893D-07
+c(20, 2)=    0.69247343387462D-07
+c(21, 2)=   -0.93994254289733D-07
+c(22, 2)=    0.10295574560935D-06
+c(23, 2)=    0.19547803118600D-06
+c(24, 2)=    0.19407504646311D-07
+c(25, 2)=   -0.17219187149635D-06
+c(26, 2)=   -0.20135410709838D-06
+c(27, 2)=   -0.28273103642271D-08
+c(28, 2)=    0.30690987897186D-06
+c(29, 2)=    0.79628272547828D-07
+c(30, 2)=   -0.18900571342100D-06
+c(31, 2)=    0.83337491764168D-07
+c(32, 2)=    0.13315305225107D-06
+c(33, 2)=    0.58675965618782D-07
+c(34, 2)=   -0.10511750363253D-06
+c(35, 2)=   -0.41561363195631D-07
+c(36, 2)=    0.10803644254118D-06
+c(37, 2)=    0.57900788447265D-07
+c(38, 2)=   -0.10674339261125D-07
+c(39, 2)=    0.10267822284623D-08
+c(40, 2)=   -0.39409739046749D-07
+c(41, 2)=    0.48560442200681D-07
+c(42, 2)=    0.44295705013232D-08
+c(43, 2)=   -0.23863651808965D-07
+c(44, 2)=   -0.40529365741889D-07
+c(45, 2)=   -0.72544669649420D-07
+c(46, 2)=   -0.30840437495884D-07
+c(47, 2)=   -0.10134355839673D-07
+c(48, 2)=   -0.74066104086251D-07
+c(49, 2)=   -0.42575092353871D-07
+c(50, 2)=    0.38002915272366D-07
+c(51, 2)=    0.30850031943561D-08
+c(52, 2)=   -0.38896999892434D-07
+c(53, 2)=   -0.20811133913029D-08
+c(54, 2)=    0.60282320372300D-07
+c(55, 2)=    0.66842630552045D-08
+c(56, 2)=   -0.15054903643693D-07
+c(57, 2)=   -0.16272429639032D-07
+c(58, 2)=   -0.77062433134402D-08
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+c(60, 2)=    0.33331254807163D-07
+c(61, 2)=    0.47393585702229D-07
+c(62, 2)=    0.24590842039888D-07
+c(63, 2)=   -0.25081905036699D-07
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+c(65, 2)=    0.60565718726133D-09
+c(66, 2)=    0.13996463097736D-07
+c(67, 2)=    0.36801218056836D-07
+c(68, 2)=   -0.17804762229462D-07
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+c(73, 2)=   -0.20283358613253D-07
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+c(75, 2)=   -0.23260084626746D-07
+c(76, 2)=    0.99374517344100D-08
+c(77, 2)=   -0.32363754554167D-07
+c(78, 2)=    0.10856848087610D-07
+c(79, 2)=   -0.27919914518472D-07
+c(80, 2)=    0.16116790335365D-07
+c( 3, 3)=    0.35023491711606D-04
+c( 4, 3)=    0.64490745811941D-05
+c( 5, 3)=    0.33076885084810D-05
+c( 6, 3)=    0.95401012517447D-06
+c( 7, 3)=    0.87863220403753D-06
+c( 8, 3)=   -0.12040062428688D-05
+c( 9, 3)=   -0.99094051068927D-06
+c(10, 3)=   -0.29834384339389D-06
+c(11, 3)=   -0.12986012000905D-05
+c(12, 3)=   -0.14371536216267D-05
+c(13, 3)=    0.21515088011757D-06
+c(14, 3)=    0.42474467046937D-06
+c(15, 3)=   -0.55907478206270D-06
+c(16, 3)=   -0.53391027929080D-06
+c(17, 3)=   -0.45940051707924D-07
+c(18, 3)=   -0.29341890127158D-06
+c(19, 3)=   -0.52823002208831D-07
+c(20, 3)=    0.42381732878213D-06
+c(21, 3)=   -0.15864628605041D-06
+c(22, 3)=   -0.37694486993635D-06
+c(23, 3)=    0.10153362064588D-06
+c(24, 3)=    0.33326669401862D-06
+c(25, 3)=    0.10923543811362D-06
+c(26, 3)=   -0.15114438271846D-06
+c(27, 3)=    0.12204330344988D-06
+c(28, 3)=    0.19906682949500D-06
+c(29, 3)=    0.10324442774105D-06
+c(30, 3)=   -0.35165969895604D-07
+c(31, 3)=   -0.37695255894017D-07
+c(32, 3)=   -0.15441100504594D-06
+c(33, 3)=   -0.12566971141268D-06
+c(34, 3)=    0.86388483626716D-07
+c(35, 3)=    0.73898333015289D-07
+c(36, 3)=   -0.11654986577645D-06
+c(37, 3)=   -0.12337255642019D-06
+c(38, 3)=   -0.93452853607312D-07
+c(39, 3)=    0.15866384390936D-07
+c(40, 3)=    0.22621856963862D-07
+c(41, 3)=   -0.82261088157716D-07
+c(42, 3)=   -0.11509240581167D-06
+c(43, 3)=   -0.51209031157573D-07
+c(44, 3)=    0.87755823722094D-07
+c(45, 3)=   -0.32736783199659D-07
+c(46, 3)=   -0.44469896535062D-07
+c(47, 3)=    0.53202827198090D-07
+c(48, 3)=    0.31840012781999D-07
+c(49, 3)=   -0.39439367510789D-07
+c(50, 3)=   -0.24919100537213D-07
+c(51, 3)=    0.21683500372067D-07
+c(52, 3)=   -0.33140152676634D-08
+c(53, 3)=   -0.18205948135764D-07
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+c(55, 3)=    0.14256829781278D-07
+c(56, 3)=   -0.33010270260415D-07
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+c(58, 3)=    0.19680334210526D-07
+c(59, 3)=    0.49353515402636D-07
+c(60, 3)=   -0.32647840865208D-08
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+c(76, 3)=    0.30023266822151D-07
+c(77, 3)=   -0.65712049623256D-08
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+c(79, 3)=   -0.81982981193597D-09
+c(80, 3)=    0.14472986941000D-07
+c( 4, 4)=    0.30959206658010D-06
+c( 5, 4)=   -0.46336405889077D-05
+c( 6, 4)=    0.10065686648503D-05
+c( 7, 4)=    0.24640560610782D-05
+c( 8, 4)=    0.15844031607287D-05
+c( 9, 4)=    0.29405976756683D-06
+c(10, 4)=   -0.12101666736715D-05
+c(11, 4)=   -0.15688434008850D-05
+c(12, 4)=   -0.10108862643404D-06
+c(13, 4)=    0.17054914228551D-06
+c(14, 4)=    0.22728427855596D-06
+c(15, 4)=   -0.71711294666294D-06
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+c(19, 4)=    0.13800527907950D-06
+c(20, 4)=   -0.35839832070397D-06
+c(21, 4)=   -0.39829410795150D-06
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+c(23, 4)=    0.44405614702060D-06
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+c(25, 4)=   -0.61925818643782D-06
+c(26, 4)=   -0.37209534817516D-06
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+c(28, 4)=    0.40345026906393D-06
+c(29, 4)=   -0.18728923925709D-06
+c(30, 4)=   -0.26245016435872D-06
+c(31, 4)=   -0.31150685284646D-07
+c(32, 4)=    0.20037736081893D-06
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+c(34, 4)=   -0.29153815376169D-07
+c(35, 4)=   -0.17807633359855D-06
+c(36, 4)=   -0.15303133769982D-06
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+c(39, 4)=   -0.14539420941324D-07
+c(40, 4)=   -0.89280013487568D-07
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+c(44, 4)=    0.42197628209560D-07
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+c(46, 4)=   -0.75655211066113D-08
+c(47, 4)=    0.90026651213639D-07
+c(48, 4)=    0.93009448368906D-07
+c(49, 4)=   -0.23184611520205D-07
+c(50, 4)=   -0.20719026291426D-07
+c(51, 4)=    0.34422439963500D-07
+c(52, 4)=    0.21952192711957D-07
+c(53, 4)=   -0.21041597028035D-07
+c(54, 4)=   -0.24228687045471D-07
+c(55, 4)=    0.37895570193813D-08
+c(56, 4)=   -0.19352611895629D-07
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+c(58, 4)=    0.69419737541584D-07
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+c(60, 4)=   -0.18799793363085D-07
+c(61, 4)=    0.14374232953337D-07
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+c(66, 4)=   -0.37158460287582D-07
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+c(80, 4)=   -0.25351771157557D-08
+c( 5, 5)=   -0.44434141649300D-05
+c( 6, 5)=    0.16548025737626D-05
+c( 7, 5)=   -0.19096934491812D-06
+c( 8, 5)=   -0.27850787272597D-05
+c( 9, 5)=   -0.22656267960896D-05
+c(10, 5)=    0.42032262399202D-06
+c(11, 5)=    0.13520771564056D-05
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+c(14, 5)=   -0.45276921372495D-06
+c(15, 5)=   -0.93462951523554D-06
+c(16, 5)=   -0.34377637201001D-06
+c(17, 5)=    0.69789569926980D-06
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+c(19, 5)=   -0.28358145151180D-06
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+c(25, 5)=    0.28611650642088D-06
+c(26, 5)=    0.20360981554297D-06
+c(27, 5)=    0.96293497515718D-07
+c(28, 5)=   -0.47930164566393D-07
+c(29, 5)=   -0.12691726734393D-06
+c(30, 5)=   -0.93858451381326D-07
+c(31, 5)=    0.92431999857506D-07
+c(32, 5)=    0.93351803773724D-07
+c(33, 5)=   -0.15400246903553D-06
+c(34, 5)=   -0.14119500703571D-06
+c(35, 5)=    0.78736519330474D-07
+c(36, 5)=    0.83329148294896D-07
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+c(38, 5)=   -0.55893430456265D-07
+c(39, 5)=   -0.11157629707788D-06
+c(40, 5)=    0.54238258568734D-07
+c(41, 5)=    0.11263379495700D-06
+c(42, 5)=    0.41202421137030D-07
+c(43, 5)=   -0.59032315787153D-07
+c(44, 5)=    0.26883253020711D-07
+c(45, 5)=    0.51890763975186D-07
+c(46, 5)=    0.13952729851129D-07
+c(47, 5)=    0.83317364677177D-08
+c(48, 5)=   -0.13102674596668D-07
+c(49, 5)=   -0.21274731423140D-07
+c(50, 5)=   -0.54059556337886D-07
+c(51, 5)=   -0.18854105667823D-07
+c(52, 5)=    0.22621073263953D-07
+c(53, 5)=   -0.19805104368574D-07
+c(54, 5)=   -0.19550955358517D-07
+c(55, 5)=   -0.70267276107722D-08
+c(56, 5)=   -0.30278638914856D-07
+c(57, 5)=   -0.80729568890359D-08
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+s(34, 1)=   -0.51407090820137D-07
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+s( 3, 2)=    0.83539192403728D-05
+s( 4, 2)=   -0.89701777491190D-05
+s( 5, 2)=   -0.11641453008893D-05
+s( 6, 2)=    0.14667268956886D-05
+s( 7, 2)=   -0.62842100807606D-06
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+s( 9, 2)=    0.38142891566534D-06
+s(10, 2)=   -0.11124225282454D-05
+s(11, 2)=   -0.99100594960733D-06
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+s(14, 2)=   -0.52161616518213D-06
+s(15, 2)=   -0.78050858035765D-06
+s(16, 2)=   -0.87214358332511D-07
+s(17, 2)=    0.14579826763514D-06
+s(18, 2)=    0.43798807886695D-07
+s(19, 2)=    0.87664275315519D-07
+s(20, 2)=   -0.23739329968468D-06
+s(21, 2)=   -0.55617022532929D-06
+s(22, 2)=    0.74634801430613D-07
+s(23, 2)=    0.47058080251370D-06
+s(24, 2)=   -0.13833943024497D-06
+s(25, 2)=   -0.36206673055862D-06
+s(26, 2)=    0.13771086763274D-07
+s(27, 2)=    0.26908130569571D-06
+s(28, 2)=    0.25184065503879D-06
+s(29, 2)=    0.29109346693879D-08
+s(30, 2)=   -0.44165883077743D-07
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+s(32, 2)=    0.18305835915308D-06
+s(33, 2)=    0.20487537947298D-06
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+s(35, 2)=   -0.58882619512619D-07
+s(36, 2)=   -0.12311353910300D-06
+s(37, 2)=   -0.21919769425805D-07
+s(38, 2)=    0.11709291424090D-06
+s(39, 2)=    0.92699311123633D-07
+s(40, 2)=   -0.90368996680850D-07
+s(41, 2)=   -0.11102320608435D-06
+s(42, 2)=    0.85441307939682D-07
+s(43, 2)=    0.15019286440103D-06
+s(44, 2)=   -0.15758773652609D-07
+s(45, 2)=   -0.56546577893551D-07
+s(46, 2)=    0.46414838712203D-07
+s(47, 2)=    0.69440803211037D-07
+s(48, 2)=   -0.41543319320956D-07
+s(49, 2)=   -0.25453153619611D-07
+s(50, 2)=    0.61069806618382D-07
+s(51, 2)=   -0.21431871272039D-07
+s(52, 2)=   -0.27493738239856D-07
+s(53, 2)=    0.40499074786701D-07
+s(54, 2)=    0.16409989015642D-07
+s(55, 2)=   -0.46733116241997D-07
+s(56, 2)=   -0.49935750762261D-07
+s(57, 2)=    0.38916218999179D-07
+s(58, 2)=   -0.49768112095755D-08
+s(59, 2)=   -0.28668365214044D-07
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+s(61, 2)=   -0.15637139662540D-07
+s(62, 2)=   -0.20915792684197D-07
+s(63, 2)=   -0.54227075337162D-07
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+s(66, 2)=    0.10133225197098D-07
+s(67, 2)=   -0.22905770890077D-07
+s(68, 2)=   -0.22301580854256D-07
+s(69, 2)=   -0.92177350430440D-08
+s(70, 2)=   -0.18780903598666D-08
+s(71, 2)=   -0.75542782412997D-09
+s(72, 2)=    0.49577307486526D-08
+s(73, 2)=   -0.10826784880676D-07
+s(74, 2)=   -0.23224199983071D-07
+s(75, 2)=    0.19561774315674D-07
+s(76, 2)=   -0.30216464519069D-07
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+s(78, 2)=   -0.33399757719077D-07
+s(79, 2)=    0.18010662015649D-07
+s(80, 2)=   -0.32871462541030D-07
+s( 3, 3)=    0.25551471726737D-04
+s( 4, 3)=   -0.19274827646727D-06
+s( 5, 3)=    0.27140581800371D-06
+s( 6, 3)=    0.33222302672742D-06
+s( 7, 3)=   -0.39609564442357D-06
+s( 8, 3)=   -0.13382050309136D-05
+s( 9, 3)=   -0.10048343370863D-05
+s(10, 3)=    0.44208842620839D-06
+s(11, 3)=    0.76239768915178D-06
+s(12, 3)=    0.31335143763597D-06
+s(13, 3)=    0.18130002960504D-06
+s(14, 3)=   -0.31104921120362D-06
+s(15, 3)=   -0.29856958137367D-06
+s(16, 3)=    0.42481073247226D-06
+s(17, 3)=    0.19122120603783D-06
+s(18, 3)=   -0.46117693571270D-06
+s(19, 3)=   -0.20023496082877D-06
+s(20, 3)=    0.20997193488831D-06
+s(21, 3)=    0.24698772474013D-06
+s(22, 3)=    0.14526401968646D-07
+s(23, 3)=   -0.13094420881434D-06
+s(24, 3)=   -0.28724262482356D-06
+s(25, 3)=   -0.14705252644312D-06
+s(26, 3)=    0.12595891565708D-06
+s(27, 3)=    0.31207723482287D-06
+s(28, 3)=   -0.27650809086232D-06
+s(29, 3)=   -0.30671076129865D-06
+s(30, 3)=    0.84155662713398D-08
+s(31, 3)=    0.54069483045578D-07
+s(32, 3)=    0.37773579574019D-07
+s(33, 3)=   -0.11854623883255D-06
+s(34, 3)=   -0.16136229886968D-06
+s(35, 3)=   -0.59238139036980D-07
+s(36, 3)=    0.52705208366376D-07
+s(37, 3)=    0.61587862484921D-07
+s(38, 3)=   -0.11594308999457D-07
+s(39, 3)=   -0.21618306258924D-07
+s(40, 3)=   -0.14792502688220D-07
+s(41, 3)=    0.62343085836212D-07
+s(42, 3)=    0.25134346110112D-07
+s(43, 3)=    0.24424514891413D-07
+s(44, 3)=   -0.26996983351598D-07
+s(45, 3)=   -0.72534663934446D-08
+s(46, 3)=    0.29618360439917D-07
+s(47, 3)=    0.52654231743027D-08
+s(48, 3)=   -0.10583447514475D-07
+s(49, 3)=    0.37626191938029D-07
+s(50, 3)=    0.25596290670976D-07
+s(51, 3)=   -0.23932391975686D-07
+s(52, 3)=   -0.49857747681036D-07
+s(53, 3)=    0.95895058624665D-08
+s(54, 3)=    0.71293575106710D-07
+s(55, 3)=    0.14572395176144D-07
+s(56, 3)=   -0.46910828885870D-07
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+s(58, 3)=    0.31409118702607D-07
+s(59, 3)=   -0.14417701951018D-07
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+s(61, 3)=   -0.35334741851824D-08
+s(62, 3)=   -0.30324625813371D-07
+s(63, 3)=   -0.32787634088217D-07
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+s(66, 3)=   -0.18141161946838D-07
+s(67, 3)=    0.54521038956287D-09
+s(68, 3)=   -0.38138689619787D-08
+s(69, 3)=   -0.16093220344950D-07
+s(70, 3)=   -0.37036403872396D-07
+s(71, 3)=   -0.47186949728098D-08
+s(72, 3)=   -0.27956746206030D-07
+s(73, 3)=    0.85634852321390D-09
+s(74, 3)=   -0.38325087199963D-07
+s(75, 3)=    0.15398137020464D-07
+s(76, 3)=   -0.39023342002934D-07
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+s(78, 3)=   -0.35504514917566D-07
+s(79, 3)=    0.21761683080775D-07
+s(80, 3)=   -0.31625978448866D-07
+s( 4, 4)=   -0.12857823170070D-04
+s( 5, 4)=   -0.33773263335749D-05
+s( 6, 4)=    0.26339507884398D-05
+s( 7, 4)=   -0.42144144853044D-06
+s( 8, 4)=    0.14777413181852D-06
+s( 9, 4)=    0.16194710093435D-05
+s(10, 4)=   -0.69313507253819D-07
+s(11, 4)=   -0.64233300320774D-06
+s(12, 4)=    0.12301690995295D-06
+s(13, 4)=    0.68736009234055D-06
+s(14, 4)=   -0.95770079832859D-06
+s(15, 4)=   -0.83528061339268D-06
+s(16, 4)=   -0.54260378146251D-07
+s(17, 4)=   -0.93929405238052D-08
+s(18, 4)=    0.13191461217734D-06
+s(19, 4)=    0.25226344496632D-06
+s(20, 4)=    0.20621490254119D-06
+s(21, 4)=   -0.14043749966466D-06
+s(22, 4)=   -0.37858016062249D-06
+s(23, 4)=    0.73495913921712D-07
+s(24, 4)=    0.11779230311764D-06
+s(25, 4)=    0.15527691778753D-06
+s(26, 4)=    0.21058477382704D-06
+s(27, 4)=    0.89681836558224D-07
+s(28, 4)=    0.19622213253189D-07
+s(29, 4)=    0.47678131095151D-07
+s(30, 4)=    0.21380065806948D-06
+s(31, 4)=    0.75620818268705D-08
+s(32, 4)=    0.69970608136749D-07
+s(33, 4)=    0.31985403196957D-07
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+s(35, 4)=    0.79432952777437D-07
+s(36, 4)=   -0.22350132896334D-07
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+s(39, 4)=    0.36097324429760D-07
+s(40, 4)=    0.53798620841362D-07
+s(41, 4)=   -0.60633572489982D-08
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+s(44, 4)=    0.17136856044562D-07
+s(45, 4)=   -0.21172262663520D-07
+s(46, 4)=    0.15964270630663D-07
+s(47, 4)=    0.68319629051684D-07
+s(48, 4)=    0.22307463806329D-07
+s(49, 4)=   -0.22098747481583D-07
+s(50, 4)=   -0.13416105611403D-07
+s(51, 4)=   -0.28727639863575D-08
+s(52, 4)=    0.61362062327015D-08
+s(53, 4)=    0.28029179020574D-07
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+s(55, 4)=   -0.34076081538132D-07
+s(56, 4)=   -0.50027878148709D-07
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+s(58, 4)=    0.32984416637604D-07
+s(59, 4)=    0.46748302094913D-08
+s(60, 4)=   -0.28731083679469D-07
+s(61, 4)=   -0.12185426332213D-08
+s(62, 4)=    0.24196923372757D-07
+s(63, 4)=   -0.38300851302597D-07
+s(64, 4)=    0.23385333301277D-07
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+s(66, 4)=    0.24635886833335D-07
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+s(68, 4)=    0.11620271286385D-08
+s(69, 4)=    0.21844011370929D-07
+s(70, 4)=   -0.21954322860600D-07
+s(71, 4)=   -0.29656501717783D-08
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+s(73, 4)=   -0.33898434165158D-07
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+s(75, 4)=   -0.60657709996744D-08
+s(76, 4)=   -0.15629828556566D-07
+s(77, 4)=   -0.20599003025979D-08
+s(78, 4)=   -0.38749943891530D-08
+s(79, 4)=   -0.12713374207514D-07
+s(80, 4)=    0.22321713775651D-09
+s( 5, 5)=    0.37742550130119D-05
+s( 6, 5)=    0.16199010884387D-05
+s( 7, 5)=   -0.13557075249867D-05
+s( 8, 5)=   -0.16260186706174D-05
+s( 9, 5)=   -0.15457469241661D-05
+s(10, 5)=   -0.10600209030637D-05
+s(11, 5)=    0.89636346823903D-06
+s(12, 5)=    0.99814527374599D-06
+s(13, 5)=   -0.40334461020521D-06
+s(14, 5)=   -0.96150455430912D-06
+s(15, 5)=   -0.47286535275867D-06
+s(16, 5)=    0.58730941024010D-06
+s(17, 5)=    0.31152083265288D-06
+s(18, 5)=   -0.61825374203407D-06
+s(19, 5)=   -0.44472448343507D-06
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+s(21, 5)=    0.16628168439163D-06
+s(22, 5)=    0.31241402527141D-07
+s(23, 5)=    0.18854458337510D-06
+s(24, 5)=   -0.16489726638894D-06
+s(25, 5)=   -0.31845421512104D-06
+s(26, 5)=    0.22721950714351D-06
+s(27, 5)=    0.28299545652663D-06
+s(28, 5)=   -0.37389057002835D-07
+s(29, 5)=   -0.17226603663226D-06
+s(30, 5)=    0.14710390042110D-06
+s(31, 5)=    0.17561089328596D-06
+s(32, 5)=   -0.65422322261088D-07
+s(33, 5)=    0.54998698313070D-07
+s(34, 5)=   -0.58162952622315D-07
+s(35, 5)=   -0.21460608956987D-06
+s(36, 5)=    0.10197746868170D-07
+s(37, 5)=    0.12520063761894D-06
+s(38, 5)=   -0.35506011727971D-07
+s(39, 5)=   -0.19201531312844D-06
+s(40, 5)=   -0.12269200040578D-06
+s(41, 5)=    0.89778390439825D-07
+s(42, 5)=   -0.41913786741451D-07
+s(43, 5)=   -0.91520006488999D-07
+s(44, 5)=   -0.44920044599259D-07
+s(45, 5)=    0.11643541732227D-07
+s(46, 5)=   -0.26360725053581D-08
+s(47, 5)=   -0.44760884506842D-08
+s(48, 5)=   -0.21592819756822D-07
+s(49, 5)=   -0.60937408379074D-08
+s(50, 5)=    0.27401279526375D-08
+s(51, 5)=    0.15851055218607D-07
+s(52, 5)=   -0.39887968690482D-07
+s(53, 5)=   -0.18343774352404D-07
+s(54, 5)=    0.62372930417058D-08
+s(55, 5)=    0.20924085053186D-07
+s(56, 5)=   -0.30622186799619D-07
+s(57, 5)=   -0.11748953359707D-07
+s(58, 5)=    0.23880590247310D-07
+s(59, 5)=    0.20034896605191D-07
+s(60, 5)=   -0.16471279024280D-07
+s(61, 5)=   -0.11357411549884D-07
+s(62, 5)=   -0.18049010749233D-07
+s(63, 5)=   -0.65094139439041D-07
+s(64, 5)=   -0.20737977692137D-07
+s(65, 5)=   -0.29791542438761D-07
+s(66, 5)=    0.78550958031711D-09
+s(67, 5)=    0.98305589918783D-08
+s(68, 5)=    0.15360752910204D-07
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+s(70, 5)=    0.82258548517498D-08
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+s(73, 5)=    0.16308111802428D-08
+s(74, 5)=    0.14229372953148D-07
+s(75, 5)=   -0.82577367551857D-08
+s(76, 5)=    0.16419910665001D-07
+s(77, 5)=   -0.76141933727246D-08
+s(78, 5)=    0.15663078015234D-07
+s(79, 5)=   -0.38076118797541D-08
+s(80, 5)=    0.19338680156276D-07
+s( 6, 6)=    0.82048914571916D-06
+s( 7, 6)=   -0.18976252698758D-05
+s( 8, 6)=   -0.17859907392665D-05
+s( 9, 6)=    0.57635343927424D-06
+s(10, 6)=    0.11141482531981D-05
+s(11, 6)=    0.20520417204917D-07
+s(12, 6)=   -0.16241518863413D-05
+s(13, 6)=   -0.92898699384914D-06
+s(14, 6)=   -0.83030911917673D-07
+s(15, 6)=    0.63029479290680D-06
+s(16, 6)=    0.22377218327274D-06
+s(17, 6)=   -0.30803335024641D-06
+s(18, 6)=   -0.67899952282254D-06
+s(19, 6)=   -0.15250901091529D-06
+s(20, 6)=    0.37831534677241D-06
+s(21, 6)=    0.27709441869198D-06
+s(22, 6)=   -0.52996707240534D-06
+s(23, 6)=   -0.49676668701636D-06
+s(24, 6)=    0.36332436606584D-07
+s(25, 6)=    0.35015834406465D-06
+s(26, 6)=    0.58170241349480D-07
+s(27, 6)=   -0.32085152929534D-06
+s(28, 6)=   -0.26174056751663D-06
+s(29, 6)=    0.74912443471519D-08
+s(30, 6)=    0.36062403088968D-06
+s(31, 6)=    0.11445836997106D-06
+s(32, 6)=   -0.21026389477025D-06
+s(33, 6)=   -0.26176185843027D-06
+s(34, 6)=    0.27649159609722D-07
+s(35, 6)=    0.18659652364132D-06
+s(36, 6)=    0.64867610890407D-08
+s(37, 6)=   -0.12178155734875D-06
+s(38, 6)=   -0.11711628132855D-06
+s(39, 6)=   -0.54345146341479D-08
+s(40, 6)=    0.71059805395230D-07
+s(41, 6)=    0.46535261677561D-07
+s(42, 6)=   -0.19077964613060D-07
+s(43, 6)=   -0.61725941246726D-07
+s(44, 6)=    0.56827990615115D-07
+s(45, 6)=    0.49360626933475D-07
+s(46, 6)=   -0.44437585732807D-07
+s(47, 6)=   -0.16590532201585D-07
+s(48, 6)=    0.52118679119891D-07
+s(49, 6)=   -0.39270934787392D-07
+s(50, 6)=   -0.29200578663369D-07
+s(51, 6)=    0.71930752953130D-08
+s(52, 6)=   -0.55013112384309D-08
+s(53, 6)=   -0.41179828878416D-07
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+s(59, 6)=    0.12935720779420D-07
+s(60, 6)=   -0.11381909184848D-07
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+s(64, 6)=   -0.18345308909856D-07
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+s(66, 6)=   -0.12905439356089D-07
+s(67, 6)=   -0.19649164082368D-07
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+s(69, 6)=    0.98315960599906D-08
+s(70, 6)=   -0.36651513112467D-08
+s(71, 6)=   -0.31455261139310D-08
+s(72, 6)=    0.23442550631311D-07
+s(73, 6)=   -0.91447673426722D-08
+s(74, 6)=    0.12777811795930D-07
+s(75, 6)=   -0.38604892131951D-08
+s(76, 6)=    0.15707324950716D-07
+s(77, 6)=   -0.54637645120108D-08
+s(78, 6)=    0.12652007604582D-07
+s(79, 6)=    0.76513109485040D-08
+s(80, 6)=    0.80948836322871D-08
+s( 7, 7)=   -0.17718148905347D-05
+s( 8, 7)=    0.16408397974219D-05
+s( 9, 7)=    0.86647021106569D-06
+s(10, 7)=   -0.61835547459555D-06
+s(11, 7)=   -0.86232464665112D-06
+s(12, 7)=   -0.11248859759827D-06
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+s(17, 7)=   -0.24009029696849D-06
+s(18, 7)=   -0.16932094993760D-06
+s(19, 7)=    0.18821371044436D-06
+s(20, 7)=    0.40126716006775D-07
+s(21, 7)=   -0.30263479586734D-06
+s(22, 7)=    0.12697718689314D-07
+s(23, 7)=    0.28287048180980D-06
+s(24, 7)=    0.50713252130312D-06
+s(25, 7)=    0.26061153429560D-06
+s(26, 7)=   -0.23148709970149D-06
+s(27, 7)=   -0.11121282776403D-06
+s(28, 7)=    0.19604577315001D-06
+s(29, 7)=    0.16686812676659D-06
+s(30, 7)=    0.30214879537025D-07
+s(31, 7)=   -0.13377877566804D-06
+s(32, 7)=   -0.16610438475314D-06
+s(33, 7)=    0.28746228761159D-06
+s(34, 7)=    0.22764174789091D-06
+s(35, 7)=   -0.10676698900774D-06
+s(36, 7)=   -0.11823947886321D-06
+s(37, 7)=   -0.18761169597968D-07
+s(38, 7)=    0.15498239194539D-06
+s(39, 7)=   -0.39950543926411D-08
+s(40, 7)=   -0.43229921049524D-07
+s(41, 7)=    0.11412007712194D-06
+s(42, 7)=   -0.14466968510796D-07
+s(43, 7)=   -0.50395367209663D-07
+s(44, 7)=    0.10038828070189D-07
+s(45, 7)=    0.89846934942603D-07
+s(46, 7)=    0.26646513249887D-07
+s(47, 7)=   -0.10731318307303D-06
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+s(49, 7)=    0.75577709045872D-07
+s(50, 7)=   -0.42621912089417D-07
+s(51, 7)=   -0.16964770982555D-07
+s(52, 7)=    0.22999036083795D-07
+s(53, 7)=   -0.20887288050776D-07
+s(54, 7)=   -0.44108867497604D-07
+s(55, 7)=    0.13930811021967D-08
+s(56, 7)=   -0.83764704949305D-08
+s(57, 7)=   -0.69153676523682D-08
+s(58, 7)=    0.18007382119490D-08
+s(59, 7)=    0.33336892845039D-08
+s(60, 7)=   -0.41896555386511D-08
+s(61, 7)=   -0.17039520923528D-07
+s(62, 7)=   -0.16712720904900D-07
+s(63, 7)=    0.37298748429177D-07
+s(64, 7)=   -0.25654109191059D-07
+s(65, 7)=   -0.13749720601388D-07
+s(66, 7)=    0.26676806808541D-07
+s(67, 7)=    0.16476181922272D-07
+s(68, 7)=    0.83007982073902D-08
+s(69, 7)=    0.26847074426587D-07
+s(70, 7)=    0.18339215465452D-07
+s(71, 7)=   -0.12096493390590D-07
+s(72, 7)=    0.30873049918127D-07
+s(73, 7)=   -0.22948720255903D-08
+s(74, 7)=    0.42303559984739D-09
+s(75, 7)=   -0.31468500927299D-09
+s(76, 7)=   -0.78036646136261D-08
+s(77, 7)=   -0.15461825889251D-07
+s(78, 7)=    0.35576129993784D-08
+s(79, 7)=   -0.87002735760482D-08
+s(80, 7)=   -0.34389487185570D-09
+s( 8, 8)=   -0.24959849099076D-06
+s( 9, 8)=   -0.14580693512087D-06
+s(10, 8)=    0.81805036262635D-06
+s(11, 8)=    0.76433996425429D-06
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+s(78,71)=   -0.18887828748998D-07
+s(79,71)=   -0.30638177018873D-07
+s(80,71)=   -0.45786303998232D-07
+s(72,72)=    0.14619987101331D-07
+s(73,72)=   -0.28385543652245D-08
+s(74,72)=    0.20754818105081D-07
+s(75,72)=    0.91782741587554D-09
+s(76,72)=   -0.11348075853818D-07
+s(77,72)=   -0.16743464096756D-07
+s(78,72)=   -0.21718438590062D-07
+s(79,72)=    0.19282431527263D-07
+s(80,72)=   -0.18371376363970D-07
+s(73,73)=    0.28162386123265D-08
+s(74,73)=   -0.11088863947687D-07
+s(75,73)=    0.44883608270606D-08
+s(76,73)=   -0.10342902486516D-07
+s(77,73)=   -0.20982837873543D-07
+s(78,73)=   -0.44623528381893D-08
+s(79,73)=   -0.29457122452921D-07
+s(80,73)=    0.16518231847476D-07
+s(74,74)=   -0.90679068924709D-07
+s(75,74)=    0.11943656675702D-07
+s(76,74)=   -0.12287476815057D-07
+s(77,74)=   -0.86534126471312D-08
+s(78,74)=   -0.36699382529634D-07
+s(79,74)=    0.39699432381805D-07
+s(80,74)=    0.90511319573331D-08
+s(75,75)=    0.38068956857789D-08
+s(76,75)=   -0.11022066868994D-07
+s(77,75)=   -0.66351939341889D-08
+s(78,75)=    0.84753383878959D-08
+s(79,75)=    0.34003428729587D-07
+s(80,75)=    0.45474580203248D-08
+s(76,76)=   -0.47755842568499D-07
+s(77,76)=   -0.31455773211009D-07
+s(78,76)=   -0.12677631609515D-06
+s(79,76)=    0.75135393078467D-07
+s(80,76)=    0.29637278271697D-07
+s(77,77)=   -0.28273200616638D-07
+s(78,77)=   -0.30006709911530D-07
+s(79,77)=   -0.46078138454365D-07
+s(80,77)=    0.47083765379289D-07
+s(78,78)=   -0.27390694608716D-07
+s(79,78)=    0.10101212031673D-07
+s(80,78)=   -0.77640066465978D-07
+s(79,79)=    0.64488227584258D-07
+s(80,79)=   -0.72740512544236D-08
+s(80,80)=   -0.19642737190084D-07
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+	r = 3396000.d0 !  MOLA potential surface
+	xi = ae/r
+	m=0
+	x=0.
+	sum=0.
+	call lgndr(lmax,m,x,plm,root)
+	do l=2, lmax
+	  sum = sum + c(l,m) *xi**l *plm(l-m+1)
+	enddo
+	sum = sum+1.
+! centrifugal potential	
+	v0=(gm*sum/r + 0.5*omega**2 * r**2)
+!	write(out,*)'v0=', v0
+	return
+
+end subroutine areoid_ini
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+
+	subroutine geoid(dlon,dlat,rg)
+! marsgeoid.f
+! calculate radii of surface of constant gravity potential on rotating body
+! given spherical harmonic potential of body at lat,lon,elevation
+!
+! W = V +Phi = gm/r [1+ (R/r)**n [harmonics]] -1/2 omega**2 r**2
+
+        implicit none
+
+        double precision dlon,dlat
+        double precision rg
+        
+        double precision pi,d2r
+	parameter (pi=3.141592653589792D0, d2r=pi/180.d0)
+! data structure of gravity field
+        integer ndeg,ndeg1,ndeg2,nd2p3
+	parameter (ndeg=90,ndeg1=ndeg+1,ndeg2=2*ndeg,nd2p3=ndeg2+3)
+        double precision v0,omega,ae,gm
+	double precision c(0:ndeg,0:ndeg),s(0:ndeg,0:ndeg)
+	common /gmm1/v0,omega,ae,gm,c,s
+        integer lmin,lmax
+        double precision root(nd2p3)
+        double precision r
+	common /sqr/ lmin,lmax,root,r
+	double precision plm(ndeg1)
+	double precision tol
+        data tol /0.125d0/  ! tolerence on computed value of rg
+
+        integer i,m,l
+        double precision rlon,rlat
+        double precision x,cslt,xi,sum,cslm
+        double precision diff
+! save r
+	rg = r
+
+	rlon=dlon*d2r
+	rlat=dlat*d2r
+	x = sin(rlat)
+	cslt= cos(rlat)
+
+ 	do i=1,8 ! usually 3 iterations suffice
+
+	  xi = ae/r
+	  sum = 0.
+	  do m=0, lmax
+	   call lgndr(lmax,m,x,plm,root)
+	   do l=m, lmax
+	     cslm =  c(l,m)*cos(m*rlon) + s(l,m)*sin(m*rlon)
+	     sum = sum + cslm*xi**l *plm(l-m+1)
+	   enddo
+	  enddo
+	  sum=sum+1.
+! centrifugal potential	
+	  rg=(gm*sum+0.5*(omega**2)*(r**3)*(cslt**2))/v0
+!          write(out,*) i,r,rg
+          diff = r-rg
+          r = rg
+          if( abs(diff).lt. tol) goto 400
+	enddo ! do i=1,8
+
+ 400	continue
+
+	end subroutine geoid
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+      SUBROUTINE LGNDR(LMAX,M,X,PLM,SQR)
+! Return vector of plm's of degree from m to lmax, for order m
+      implicit none
+      integer LMAX
+      integer M
+      double precision X
+      double precision PLM(*),SQR(*)
+      integer IFACT,I,LL
+      double precision OM, PMM, PMMP1, PLL, SOMX2
+!  needs sqrt of integers from 1 to 2*L+3
+!  SIGN MODIF. OF NUM.REC. ALGORITHM, TO MATCH GEOPHYS. CONVENTION.
+!  AND NORMALIZATION TO MEAN SQUARE UNITY.
+
+      PMMP1=0 !dummy initialization to get rid of compiler warnings
+
+      OM = 1.
+      PMM=SQR(2*M+1)
+      IF(M.gt.0) then
+        PMM=SQR(2)*PMM
+        SOMX2=SQRT((1.-X)*(1.+X))
+        IFACT=1
+        do I=1,M
+          OM=-OM
+          PMM=-PMM*(SQR(IFACT)/SQR(IFACT+1))*SOMX2
+          IFACT=IFACT+2
+        enddo
+      ENDIF
+      PLM(1)=OM*PMM
+      if(LMAX.gt.M) then
+        PMMP1=X*SQR(2*M+3)*PMM
+        PLM(2)=OM*PMMP1
+      endif
+      if (LMAX.gt.M+1) then
+         DO LL=M+2,LMAX
+	   PLL=SQR(2*LL+1)*SQR(2*LL-1)/(SQR(LL+M)*SQR(LL-M)) &
+     & * (X*PMMP1-PMM*SQR(LL+M-1)*SQR(LL-M-1)/(SQR(2*LL-1)*SQR(2*LL-3)))
+           PLM(LL-M+1)=OM*PLL
+           PMM=PMMP1
+           PMMP1=PLL
+         ENDDO
+      endif
+      END SUBROUTINE LGNDR
+
