c
c     12/96
c
c     a subroutine for testing all divergence and ivnerse divergence routines
c
c     (1) first set an irrotational vector field v,w
c
c     (2) compute the coefficients br,bi,cr,ci of (v,w) using vector analysis
c
c     (3) compute the divergence of (v,w) using divec,dives,divgc,divgs
c
c     (4) analystically compute the divergence and compare with (3)
c
c     (5) invert the divergence and compare with the irrotational (v,w)
c
      program tdiv
c
c     set dimensions with parameter statements
c
      parameter(nnlat= 15,nnlon=  9, nnt = 2)
c *** be sure to set
c     mmdb = min0(nlat,(nlon+1)/2), mmdab = min0(nlat,(nnlon+2)/2)
      parameter (mmdab = (nnlon+2)/2, mmdb = (nnlon+1)/2)
      parameter (lleng= 5*nnlat*nnlat*nnlon,llsav=15*nnlat*nnlat*nnlon)
      parameter (lldwork = 4*nnlat*nnlat)
      dimension work(lleng),wsave(llsav)
      dimension br(mmdb,nnlat,nnt),bi(mmdb,nnlat,nnt)
      dimension dwork(lldwork)
      dimension cr(mmdb,nnlat,nnt),ci(mmdb,nnlat,nnt)
      dimension a(mmdab,nnlat,nnt),b(mmdab,nnlat,nnt)
      dimension dv(nnlat,nnlon,nnt)
      dimension thetag(nnlat),dtheta(nnlat),dwts(nnlat)
      dimension v(nnlat,nnlon,nnt),w(nnlat,nnlon,nnt)
      dimension pertrb(nnt)
      double precision dtheta, dwts
c
c     set dimension variables
c
      nlat = nnlat
      nlon = nnlon
      nmax = max0(nlat,nlon)
      mdab = mmdab
      mdb = mmdb

      lwork = lleng
      lsave = llsav
      nt = nnt
      call iout(nlat,4hnlat)
      call iout(nlon,4hnlon)
      call iout(nt,4h  nt)
      isym = 0
      ityp = 0
c
c     set equally spaced colatitude and longitude increments
c
      pi = 4.0*atan(1.0)
      dphi = (pi+pi)/nlon
      dlat = pi/(nlat-1)
c
c     compute nlat gaussian points in thetag
c
      ldwork = lldwork
      call gaqd(nlat,dtheta,dwts,dwork,ldwork,ier)
      do  i=1,nlat
	thetag(i) = dtheta(i)
      end do
      call name(4hgaqd)
      call iout(ier,4h ier)
      call vecout(thetag,4hthtg,nlat)
c
c     test all divergence and inverse divergence subroutines
c
      do icase=1,4
      call name(4h****)
      call name(4h****)
      call iout(icase,4hicas)
c
c     set vector field v,w
c
      do k=1,nt
	do j=1,nlon
	  phi = (j-1)*dphi
	  sinp = sin(phi)
	  cosp = cos(phi)
	  do i=1,nlat
	    theta = (i-1)*dlat
	    if (icase.gt.2) theta=thetag(i)
	    cost = cos(theta)
	    sint = sin(theta)
	    x = sint*cosp
	    y = sint*sinp
	    z = cost
	    dxdt = cost*cosp
	    d2xdt2 = -sint*cosp
	    dxdp = -sint*sinp
	    d2xdp2 = -sint*cosp
	    dydt = cost*sinp
	    d2ydt2 = -sint*sinp
	    dydp = sint*cosp
	    d2ydp2 = -sint*sinp
	    dzdt = -sint
	    d2zdt2 = -cost
	    dzdp = 0.0
	    d2zdp2 = 0.0
	    if (k.eq.1) then
	       sf = x*y
	       dsfdt = x*dydt+y*dxdt
	       dsfdp = x*dydp+y*dxdp
	       v(i,j,k) = dsfdt
	       w(i,j,k) = cosp*dydp+sinp*dxdp
c              dv = 1/sint*(d(sint*v)/dt + dw/dp)
	       dvdt = x*d2ydt2 + 2.*dxdt*dydt + y*d2xdt2
c              1/sint*dwdp = 1/sint*(cosp*d2ydp2-sinp*dydp+sinp*d2xdp2+cosp*dxdp)
c                          = -4.*sinp*cosp
	       dv(i,j,k) = dvdt + cost*(cosp*dydt+sinp*dxdt) - 4.*cosp*sinp
	    else if (k.eq.2) then
	       sf = x*z
	       dsfdt = x*dzdt+z*dxdt
	       dsfdp = x*dzdp+z*dxdp
	       v(i,j,k) = dsfdt
	       w(i,j,k) = -cost*sinp
	       dvdt = x*d2zdt2+2.*dzdt*dxdt + z*dx2dt2
c              dv = 1/sint*(d(sint*v)/dt + dw/dp)
	       dv(i,j,k) = -6.*cost*sint*cosp
	    else if (k.eq.3) then
	       sf = y*z
	       dsfdt = y*dzdt+z*dydt
	       dsfdp = y*dzdp+z*dydp
	       v(i,j,k) = dsfdt
	       w(i,j,k) = z*cosp
	       dv(i,j,k) = -6.*cost*sint*sinp
	    end if
	  end do
	end do
      end do

c     if (nmax.lt.10) then
c     do kk=1,nt
c     call iout(kk,4h**kk)
c     call aout(v(1,1,kk),4h   v,nlat,nlon)
c     call aout(w(1,1,kk),4h   w,nlat,nlon)
c     call aout(dv(1,1,kk),4h  dv,nlat,nlon)
c     end do
c     end if

      if (icase.eq.1) then

      call name(4h**ec)
c
c     analyze vector field
c
      call vhaeci(nlat,nlon,wsave,lsave,dwork,ldwork,ierror)
      call name(4hshs )
      call iout(ierror,4hierr)

      call vhaec(nlat,nlon,isym,nt,v,w,nlat,nlon,br,bi,cr,ci,mdb,
     +nlat,wsave,lsave,work,lwork,ierror)
      call name(4hvha )
      call iout(ierror,4hierr)

      if (nmax.lt.10) then
      do kk=1,nt
      call iout(kk,4h**kk)
      call aout(br(1,1,kk),4h  br,mdb,nlat)
      call aout(bi(1,1,kk),4h  bi,mdb,nlat)
      call aout(cr(1,1,kk),4h  cr,mdb,nlat)
      call aout(ci(1,1,kk),4h  ci,mdb,nlat)
      end do
      end if
c
c     compute divergence of (v,w) in dv
c

      call shseci(nlat,nlon,wsave,lsave,dwork,ldwork,ierror)
      call name(4hshsi)
      call iout(ierror,4hierr)

      call divec(nlat,nlon,isym,nt,dv,nlat,nlon,br,bi,mdb,nlat,
     +wsave,lsave,work,lwork,ierror)
      call name(4hdiv )
      call iout(ierror,4hierr)
      call iout(nlat,4hnlat)
      call iout(nlon,4hnlon)


      else if (icase.eq.2) then

      call name(4h**es)
      call shsesi(nlat,nlon,wsave,lsave,work,lwork,dwork,ldwork,ierror)
      call name(4hshsi)
      call iout(ierror,4hierr)

      call dives(nlat,nlon,isym,nt,dv,nlat,nlon,br,bi,mdb,nlat,
     +wsave,lsave,work,lwork,ierror)

      call name(4hdiv )
      call iout(ierror,4hierr)

      else if (icase .eq. 3) then

      call name(4h**gc)

      call shsgci(nlat,nlon,wsave,lsave,dwork,ldwork,ierror)
      call name(4hshsi)
      call iout(ierror,4hierr)

      call divgc(nlat,nlon,isym,nt,dv,nlat,nlon,br,bi,mdb,nlat,
     +wsave,lsave,work,lwork,ierror)
      call name(4hdiv )
      call iout(ierror,4hierr)

      else if (icase .eq. 4) then

      call name(4h**gs)

      call shsgsi(nlat,nlon,wsave,lsave,work,lwork,dwork,ldwork,ierror)
      call name(4hshsi)
      call iout(ierror,4hierr)

      call divgs(nlat,nlon,isym,nt,dv,nlat,nlon,br,bi,mdb,nlat,
     +wsave,lsave,work,lwork,ierror)
      call name(4hdiv )
      call iout(ierror,4hierr)

      end if

c     if (nmax.lt.10) then
c     do kk=1,nt
c     call iout(kk,4h**kk)
c     call aout(dv(1,1,kk),4h  dv,nlat,nlon)
c     end do
c     end if
c
c     compute "error" in dv
c
      err2 = 0.0
      do k=1,nt
	do j=1,nlon
	  phi = (j-1)*dphi
	  sinp = sin(phi)
	  cosp = cos(phi)
	  do i=1,nlat
	    theta = (i-1)*dlat
	    if (icase.gt.2) theta=thetag(i)
	    cost = cos(theta)
	    sint = sin(theta)
	    x = sint*cosp
	    y = sint*sinp
	    z = cost
	    dxdt = cost*cosp
	    d2xdt2 = -sint*cosp
	    dxdp = -sint*sinp
	    d2xdp2 = -sint*cosp
	    dydt = cost*sinp
	    d2ydt2 = -sint*sinp
	    dydp = sint*cosp
	    d2ydp2 = -sint*sinp
	    dzdt = -sint
	    d2zdt2 = -cost
	    dzdp = 0.0
	    d2zdp2 = 0.0
	    if (k.eq.1) then
	       sf = x*y
	       dvdt = x*d2ydt2 + 2.*dxdt*dydt + y*d2xdt2
	       dve = dvdt + cost*(cosp*dydt+sinp*dxdt) - 4.*cosp*sinp
	    else if (k.eq.2) then
c              sf = x*z
	       dve = -6.*sint*cost*cosp
	    else if (k.eq.3) then
c              sf = y*z
	       dve = -6.*cost*sint*sinp
	    end if
	       err2 = err2 + (dv(i,j,k)-dve)**2
	  end do
	end do
      end do
c
c     set and print least squares error in dv
c
      err2 = sqrt(err2/(nt*nlat*nlon))
      call vout(err2,4herr2)
c
c     now recompute (v,w) inverting dv using idiv(ec,es,gc,gs)
c
      do kk=1,nt
      do j=1,nlon
      do i=1,nlat
      v(i,j,kk) = 0.0
      w(i,j,kk) = 0.0
      end do
      end do
      end do


      if (icase.eq.1) then

      call name(4h**ec)


      call shaeci(nlat,nlon,wsave,lsave,dwork,ldwork,ierror)
      call name(4hshai)
      call iout(ierror,4hierr)

      call shaec(nlat,nlon,isym,nt,dv,nlat,nlon,a,b,
     +mdab,nlat,wsave,lsave,work,lwork,ierror)
      call name(4hsha )
      call iout(ierror,4hierr)
      call iout(lsave,4hlsav)
      call iout(lwork,4hlwrk)

c     if (nmax.lt.10) then
c     do kk=1,nt
c     call iout(kk,4h**kk)
c     call aout(a(1,1,kk),4h   a,nlat,nlat)
c     call aout(b(1,1,kk),4h   b,nlat,nlat)
c     end do
c     end if

      call vhseci(nlat,nlon,wsave,lsave,dwork,ldwork,ierror)
      call name(4hidvi)
      call iout(ierror,4hierr)

      call idivec(nlat,nlon,isym,nt,v,w,nlat,nlon,a,b,
     +mdab,nlat,wsave,lsave,work,lwork,pertrb,ierror)
      call name(4hidiv)
      call iout(ierror,4hierr)
      call vecout(pertrb,4hprtb,nt)

      else if (icase.eq.2) then

      call name(4h**es)


      call shaesi(nlat,nlon,wsave,lsave,work,lwork,dwork,ldwork,ierror)
      call name(4hshai)
      call iout(ierror,4hierr)

      call shaes(nlat,nlon,isym,nt,dv,nlat,nlon,a,b,
     +mdab,nlat,wsave,lsave,work,lwork,ierror)
      call name(4hsha )
      call iout(ierror,4hierr)
      call iout(lsave,4hlsav)
      call iout(lwork,4hlwrk)

      call vhsesi(nlat,nlon,wsave,lsave,work,lwork,dwork,ldwork,ierror)
      call name(4hidvi)
      call iout(ierror,4hierr)

      call idives(nlat,nlon,isym,nt,v,w,nlat,nlon,a,b,
     +mdab,nlat,wsave,lsave,work,lwork,pertrb,ierror)
      call name(4hidiv)
      call iout(ierror,4hierr)
      call vecout(pertrb,4hprtb,nt)

      else if (icase.eq.3) then

      call name(4h**gc)


      call shagci(nlat,nlon,wsave,lsave,dwork,ldwork,ierror)
      call name(4hshai)
      call iout(ierror,4hierr)

      call shagc(nlat,nlon,isym,nt,dv,nlat,nlon,a,b,
     +mdab,nlat,wsave,lsave,work,lwork,ierror)
      call name(4hsha )
      call iout(ierror,4hierr)
      call iout(lsave,4hlsav)
      call iout(lwork,4hlwrk)

      call vhsgci(nlat,nlon,wsave,lsave,dwork,ldwork,ierror)
      call name(4hidvi)
      call iout(ierror,4hierr)

      call idivgc(nlat,nlon,isym,nt,v,w,nlat,nlon,a,b,
     +mdab,nlat,wsave,lsave,work,lwork,pertrb,ierror)
      call name(4hidiv)
      call iout(ierror,4hierr)
      call vecout(pertrb,4hprtb,nt)

      else if (icase.eq.4) then

      call name(4h**gs)


      call shagsi(nlat,nlon,wsave,lsave,work,lwork,dwork,ldwork,ierror)
      call name(4hshai)
      call iout(ierror,4hierr)

      call shags(nlat,nlon,isym,nt,dv,nlat,nlon,a,b,
     +mdab,nlat,wsave,lsave,work,lwork,ierror)
      call name(4hsha )
      call iout(ierror,4hierr)
      call iout(lsave,4hlsav)
      call iout(lwork,4hlwrk)

      call vhsgsi(nlat,nlon,wsave,lsave,work,lwork,dwork,ldwork,ierror)
      call name(4hidvi)
      call iout(ierror,4hierr)

      call idivgs(nlat,nlon,isym,nt,v,w,nlat,nlon,a,b,
     +mdab,nlat,wsave,lsave,work,lwork,pertrb,ierror)
      call name(4hidiv)
      call iout(ierror,4hierr)
      call vecout(pertrb,4hprtb,nt)

      end if


c     if (nmax.lt.10) then
c     do kk=1,nt
c     call iout(kk,4h**kk)
c     call aout(v(1,1,kk),4h   v,nlat,nlon)
c     call aout(w(1,1,kk),4h   w,nlat,nlon)
c     end do
c     end if

c
c     compare this v,w with original
c
      err2v = 0.0
      err2w = 0.0
      do k=1,nt
	do j=1,nlon
	  phi = (j-1)*dphi
	  sinp = sin(phi)
	  cosp = cos(phi)
	  do i=1,nlat
	    theta = (i-1)*dlat
	    if (icase.gt.2) theta=thetag(i)
	    cost = cos(theta)
	    sint = sin(theta)
	    x = sint*cosp
	    y = sint*sinp
	    z = cost
	    dxdt = cost*cosp
	    dxdp = -sint*sinp
	    dydt = cost*sinp
	    dydp = sint*cosp
	    dzdt = -sint
	    dzdp = 0.0
	    if (k.eq.1) then
	       sf = x*y
	       dsfdt = x*dydt+y*dxdt
	       dsfdp = x*dydp+y*dxdp
	       ve = dsfdt
	       we = cosp*dydp+sinp*dxdp
	    else if (k.eq.2) then
	       sf = x*z
	       dsfdt = x*dzdt+z*dxdt
	       dsfdp = x*dzdp+z*dxdp
	       ve = dsfdt
	       we = -cost*sinp
	    else if (k.eq.3) then
	       sf = y*z
	       dsfdt = y*dzdt+z*dydt
	       dsfdp = y*dzdp+z*dydp
	       ve = dsfdt
	       we = z*cosp
	    else if (k.eq.4) then
	    end if
	    err2v = err2v + (v(i,j,k)-ve)**2
	    err2w = err2w + (w(i,j,k)-we)**2
	  end do
	end do
      end do
      err2v = sqrt(err2v/(nlat*nlon*nt))
      err2w = sqrt(err2w/(nlat*nlon*nt))
      call vout(err2v,4herrv)
      call vout(err2w,4herrw)

c
c     end of icase loop
c
      end do
      end