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  /*@@
   @file      GRHydro_Marquina.f90
   @date      Thu Jan  11 11:03:32 2002
   @author    Pedro Montero, Toni Font    
   @desc 
   Routine to obtain the Marquina Fluxes. Note that this is the 
   MODIFIED Marquina formula as given by Aloy et.al. 
   (ApJ Supp 122 (1999) p.151) and not the full Marquina flux 
   of Donat and Marquina.
   @enddesc 
 @@*/

#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#include "cctk_Functions.h"

#include "GRHydro_Macros.h"
#include "SpaceMask.h"

 /*@@
   @routine    GRHydro_Marquina.f90 
   @date       Wed Feb 13 11:03:32 2002
   @author     Pedro Montero, Toni Font
   @desc 
   Routine to obtain the Marquina Fluxes
   @enddesc 
   @calls     
   @calledby   
   @history 
   Based on routines by Toni Font
   @endhistory 

@@*/


subroutine GRHydro_Marquina(CCTK_ARGUMENTS)
    
    implicit none


    DECLARE_CCTK_ARGUMENTS
    DECLARE_CCTK_PARAMETERS
    CCTK_REAL, dimension(5) :: marquinaflux, &
         consp,consm_i,fplus,fminus,f_marquina,primp,primm_i
    CCTK_REAL :: avg_alp,avg_beta,gxxh,gxyh,gxzh,gyyh,gyzh,gzzh, &
         avg_det,uxxh,uxyh,uxzh,uyyh,uyzh,uzzh,&
         pressp,pressm_i, &
         tmp_w_lorentzp, tmp_w_lorentzm_i, w_lorentzp,w_lorentzm_i, usendh, psi4h
    CCTK_REAL :: xtemp
    integer :: m
    integer :: i,j,k
    
    CCTK_INT :: type_bits, trivial, not_trivial

    if (flux_direction == 1) then
      call SpaceMask_GetTypeBits(type_bits, "Hydro_RiemannProblemX")
      call SpaceMask_GetStateBits(trivial, "Hydro_RiemannProblemX", &
           &"trivial")
    else if (flux_direction == 2) then
      call SpaceMask_GetTypeBits(type_bits, "Hydro_RiemannProblemY")
      call SpaceMask_GetStateBits(trivial, "Hydro_RiemannProblemY", &
           &"trivial")
    else if (flux_direction == 3) then
      call SpaceMask_GetTypeBits(type_bits, "Hydro_RiemannProblemZ")
      call SpaceMask_GetStateBits(trivial, "Hydro_RiemannProblemZ", &
           &"trivial")
    else
      !Keep this check in here, it is not checked again later
      call CCTK_WARN(0, "Flux direction not x,y,z")
    end if
    
    f_marquina = 0.d0
        
    !$OMP PARALLEL DO PRIVATE(i,j,consp,consm_i,primp,primm_i,&
    !$OMP marquinaflux,avg_beta,avg_alp,gxxh,gxyh,gxzh,gyyh,gyzh,gzzh,&
    !$OMP psi4h,f_marquina,uxxh,uxyh,uxzh,uyyh,uyzh,uzzh,usendh,&
    !$OMP tmp_w_lorentzp, tmp_w_lorentzm_i,w_lorentzp,w_lorentzm_i,&
    !$OMP fplus,fminus,m,avg_det)
    do k = GRHydro_stencil, cctk_lsh(3) - GRHydro_stencil
      do j = GRHydro_stencil, cctk_lsh(2) - GRHydro_stencil
        do i = GRHydro_stencil, cctk_lsh(1) - GRHydro_stencil

!!$        Set the left (p for plus) and right (m_i for minus, i+1) states

          consp(1)   = densplus(i,j,k) 
          consp(2)   = sxplus(i,j,k)
          consp(3)   = syplus(i,j,k)
          consp(4)   = szplus(i,j,k)
          consp(5)   = tauplus(i,j,k)
          
          consm_i(1) = densminus(i+xoffset,j+yoffset,k+zoffset)
          consm_i(2) = sxminus(i+xoffset,j+yoffset,k+zoffset)
          consm_i(3) = syminus(i+xoffset,j+yoffset,k+zoffset)
          consm_i(4) = szminus(i+xoffset,j+yoffset,k+zoffset)
          consm_i(5) = tauminus(i+xoffset,j+yoffset,k+zoffset) 
          
          primp(1)   = rhoplus(i,j,k) 
          primp(2)   = velxplus(i,j,k)
          primp(3)   = velyplus(i,j,k) 
          primp(4)   = velzplus(i,j,k)
          primp(5)   = epsplus(i,j,k)
          
          primm_i(1) = rhominus(i+xoffset,j+yoffset,k+zoffset)
          primm_i(2) = velxminus(i+xoffset,j+yoffset,k+zoffset)
          primm_i(3) = velyminus(i+xoffset,j+yoffset,k+zoffset)
          primm_i(4) = velzminus(i+xoffset,j+yoffset,k+zoffset)
          primm_i(5) = epsminus(i+xoffset,j+yoffset,k+zoffset) 

          marquinaflux = 0.d0
        
!!$        Set metric terms at interface
          
          if (shift_state .ne. 0) then
            if (flux_direction == 1) then
              avg_beta = 0.5d0 * (betax(i+xoffset,j+yoffset,k+zoffset) + &
                   betax(i,j,k))
            else if (flux_direction == 2) then
              avg_beta = 0.5d0 * (betay(i+xoffset,j+yoffset,k+zoffset) + &
                   betay(i,j,k))
            else
              avg_beta = 0.5d0 * (betaz(i+xoffset,j+yoffset,k+zoffset) + &
                   betaz(i,j,k))
            end if
          else
            avg_beta = 0.d0
          end if

          avg_alp = 0.5 * (alp(i,j,k) + alp(i+xoffset,j+yoffset,k+zoffset))

          gxxh = 0.5d0 * (gxx(i+xoffset,j+yoffset,k+zoffset) + &
               gxx(i,j,k))
          gxyh = 0.5d0 * (gxy(i+xoffset,j+yoffset,k+zoffset) + &
               gxy(i,j,k))
          gxzh = 0.5d0 * (gxz(i+xoffset,j+yoffset,k+zoffset) + &
               gxz(i,j,k))
          gyyh = 0.5d0 * (gyy(i+xoffset,j+yoffset,k+zoffset) + &
               gyy(i,j,k))
          gyzh = 0.5d0 * (gyz(i+xoffset,j+yoffset,k+zoffset) + &
               gyz(i,j,k))
          gzzh = 0.5d0 * (gzz(i+xoffset,j+yoffset,k+zoffset) + &
               gzz(i,j,k))

!!$ routine to calculate the determinant of the metric

         avg_det = SPATIAL_DETERMINANT(gxxh,gxyh,gxzh,gyyh,gyzh,gzzh)
          
!!$ If the Riemann problem is trivial, just calculate the fluxes from the 
!!$ left state and skip to the next cell

          if (SpaceMask_CheckStateBitsF90(space_mask, i, j, k, type_bits, trivial)) then

            if (flux_direction == 1) then
              call num_x_flux(consp(1),consp(2),consp(3),consp(4),consp(5),&
                   f_marquina(1),f_marquina(2),f_marquina(3),&
                   f_marquina(4),f_marquina(5),&
                   velxplus(i,j,k),pressplus(i,j,k),&
                   avg_det,avg_alp,avg_beta)
            else if (flux_direction == 2) then
              call num_x_flux(consp(1),consp(3),consp(4),consp(2),consp(5),&
                   f_marquina(1),f_marquina(3),f_marquina(4),&
                   f_marquina(2),f_marquina(5),&
                   velyplus(i,j,k),pressplus(i,j,k),&
                   avg_det,avg_alp,avg_beta)
            else
              call num_x_flux(consp(1),consp(4),consp(2),consp(3),consp(5),&
                   f_marquina(1),f_marquina(4),f_marquina(2),&
                   f_marquina(3),f_marquina(5),&
                   velzplus(i,j,k),pressplus(i,j,k),&
                   avg_det,avg_alp,avg_beta)
            end if
            
          else !!! The end of this branch is right at the bottom of the routine
            
            call UpperMetric(uxxh, uxyh, uxzh, uyyh, uyzh, uzzh, &
                 avg_det,gxxh, gxyh, gxzh, gyyh, gyzh, gzzh)
            
            if (flux_direction == 1) then
              usendh = uxxh
            else if (flux_direction == 2) then
              usendh = uyyh
            else
              usendh = uzzh
            end if

!!$left state

            tmp_w_lorentzp = gxxh*primp(2)*primp(2) + &
                 gyyh*primp(3)*primp(3) + gzzh*primp(4)*primp(4) + &
                 2*gxyh*primp(2)*primp(3) + 2*gxzh*primp(2) *primp(4) + &
                 2*gyzh*primp(3)*primp(4)
            if (tmp_w_lorentzp .ge. 1.d0) then
              w_lorentzp = GRHydro_lorentz_overshoot_cutoff
            else
              w_lorentzp = 1.d0 / sqrt(1.d0 - tmp_w_lorentzp);
            endif


!!$right state

            tmp_w_lorentzm_i = gxxh*primm_i(2)*primm_i(2) + &
                 gyyh*primm_i(3)*primm_i(3) + gzzh*primm_i(4)*primm_i(4) + &
                 2*gxyh*primm_i(2)*primm_i(3) + &
                 2*gxzh*primm_i(2) *primm_i(4)+ &
                 2*gyzh*primm_i(3)*primm_i(4)
            if (tmp_w_lorentzm_i .ge. 1.d0) then
              w_lorentzm_i = GRHydro_lorentz_overshoot_cutoff
            else
              w_lorentzm_i = 1.d0 / sqrt(1.d0 - tmp_w_lorentzm_i);
            endif

            
!!$eigenvalues and right eigenvectors
            
            if (flux_direction == 1) then

               if(evolve_temper.eq.0) then
                  call eigenproblem_marquina(GRHydro_eos_handle,&
                       primm_i(1),primm_i(2), & 
                       primm_i(3),primm_i(4),primm_i(5),primp(1), &
                       primp(2),primp(3),primp(4),primp(5), &
                       gxxh,gxyh,gxzh,gyyh,gyzh,gzzh, &
                       usendh,avg_det,avg_alp,avg_beta,consp(1),consp(2),&
                       consp(3), consp(4), consp(5),consm_i(1),consm_i(2), &
                       consm_i(3),consm_i(4),consm_i(5),marquinaflux(1), &
                       marquinaflux(2),marquinaflux(3),marquinaflux(4), &
                       marquinaflux(5))
               else
                  xtemp = temperature(i,j,k)
                  call eigenproblem_marquina_hot(GRHydro_eos_handle,&
                       primm_i(1),primm_i(2), & 
                       primm_i(3),primm_i(4),primm_i(5),primp(1), &
                       primp(2),primp(3),primp(4),primp(5), &
                       xtemp,y_e_minus(i+xoffset,j+yoffset,k+zoffset),y_e_plus(i,j,k),&
                       gxxh,gxyh,gxzh,gyyh,gyzh,gzzh, &
                       usendh,avg_det,avg_alp,avg_beta,consp(1),consp(2),&
                       consp(3), consp(4), consp(5),consm_i(1),consm_i(2), &
                       consm_i(3),consm_i(4),consm_i(5),marquinaflux(1), &
                       marquinaflux(2),marquinaflux(3),marquinaflux(4), &
                       marquinaflux(5))

               endif
              
            else if (flux_direction == 2) then

               if(evolve_temper.eq.0) then              
                  call eigenproblem_marquina(GRHydro_eos_handle,&
                       primm_i(1),primm_i(3), & 
                       primm_i(4),primm_i(2),primm_i(5),primp(1), &
                       primp(3),primp(4),primp(2),primp(5), &
                       gyyh,gyzh,gxyh,gzzh,gxzh,gxxh, &
                       usendh,avg_det,avg_alp,avg_beta,consp(1),consp(3),&
                       consp(4), consp(2), consp(5),consm_i(1),consm_i(3), &
                       consm_i(4),consm_i(2),consm_i(5),marquinaflux(1), &
                       marquinaflux(3),marquinaflux(4),marquinaflux(2), &
                       marquinaflux(5))
               else
                  xtemp = temperature(i,j,k)
                  call eigenproblem_marquina_hot(GRHydro_eos_handle,&
                       primm_i(1),primm_i(3), & 
                       primm_i(4),primm_i(2),primm_i(5),primp(1), &
                       primp(3),primp(4),primp(2),primp(5), &
                       xtemp,y_e_minus(i+xoffset,j+yoffset,k+zoffset),y_e_plus(i,j,k),&
                       gyyh,gyzh,gxyh,gzzh,gxzh,gxxh, &
                       usendh,avg_det,avg_alp,avg_beta,consp(1),consp(3),&
                       consp(4), consp(2), consp(5),consm_i(1),consm_i(3), &
                       consm_i(4),consm_i(2),consm_i(5),marquinaflux(1), &
                       marquinaflux(3),marquinaflux(4),marquinaflux(2), &
                       marquinaflux(5))

               endif
              
            else

               if(evolve_temper.eq.0) then
                  call eigenproblem_marquina(GRHydro_eos_handle,&
                       primm_i(1),primm_i(4), & 
                       primm_i(2),primm_i(3),primm_i(5),primp(1), &
                       primp(4),primp(2),primp(3),primp(5), &
                       gzzh,gxzh,gyzh,gxxh,gxyh,gyyh, &
                       usendh,avg_det,avg_alp,avg_beta,consp(1),consp(4),&
                       consp(2), consp(3), consp(5),consm_i(1),consm_i(4), &
                       consm_i(2),consm_i(3),consm_i(5),marquinaflux(1), &
                       marquinaflux(4),marquinaflux(2),marquinaflux(3), &
                       marquinaflux(5))
               else
                  xtemp = temperature(i,j,k)
                  call eigenproblem_marquina_hot(GRHydro_eos_handle,&
                       primm_i(1),primm_i(4), & 
                       primm_i(2),primm_i(3),primm_i(5),primp(1), &
                       primp(4),primp(2),primp(3),primp(5), &
                       xtemp,y_e_minus(i+xoffset,j+yoffset,k+zoffset),y_e_plus(i,j,k),&
                       gzzh,gxzh,gyzh,gxxh,gxyh,gyyh, &
                       usendh,avg_det,avg_alp,avg_beta,consp(1),consp(4),&
                       consp(2), consp(3), consp(5),consm_i(1),consm_i(4), &
                       consm_i(2),consm_i(3),consm_i(5),marquinaflux(1), &
                       marquinaflux(4),marquinaflux(2),marquinaflux(3), &
                       marquinaflux(5))
               endif
            end if
            
            fplus = 0.d0
            fminus = 0.d0
            
!!$calculate the fluxes
            
            if (flux_direction == 1) then
              
              call num_x_flux(consp(1),consp(2),consp(3),consp(4),consp(5), &
                   fplus(1),fplus(2),fplus(3),fplus(4), &
                   fplus(5),velxplus(i,j,k),pressplus(i,j,k), &
                   avg_det,avg_alp,avg_beta)
              
              call num_x_flux(consm_i(1),consm_i(2),consm_i(3), &
                   consm_i(4),consm_i(5),fminus(1),fminus(2),fminus(3), &
                   fminus(4), fminus(5), &
                   velxminus(i+xoffset,j+yoffset,k+zoffset), &
                   pressminus(i+xoffset,j+yoffset,k+zoffset), &
                   avg_det,avg_alp,avg_beta)
              
            else if (flux_direction == 2) then
              
              call num_x_flux(consp(1),consp(3),consp(4),consp(2),consp(5), &
                   fplus(1),fplus(3),fplus(4),fplus(2), &
                   fplus(5),velyplus(i,j,k),pressplus(i,j,k), &
                   avg_det,avg_alp,avg_beta)
              
              call num_x_flux(consm_i(1),consm_i(3),consm_i(4), &
                   consm_i(2),consm_i(5),fminus(1),fminus(3),fminus(4), &
                   fminus(2), fminus(5), &
                   velyminus(i+xoffset,j+yoffset,k+zoffset), &
                   pressminus(i+xoffset,j+yoffset,k+zoffset), &
                   avg_det,avg_alp,avg_beta)
              
              else
              
              call num_x_flux(consp(1),consp(4),consp(2),consp(3),consp(5), &
                   fplus(1),fplus(4),fplus(2),fplus(3), &
                   fplus(5),velzplus(i,j,k),pressplus(i,j,k),avg_det, &
                   avg_alp,avg_beta)
              
              call num_x_flux(consm_i(1),consm_i(4),consm_i(2), &
                   consm_i(3),consm_i(5),fminus(1),fminus(4),fminus(2), &
                   fminus(3), fminus(5), &
                   velzminus(i+xoffset,j+yoffset,k+zoffset), &
                   pressminus(i+xoffset,j+yoffset,k+zoffset), &
                   avg_det,avg_alp,avg_beta)
              
            end if
            
!!$ Marquina flux
            
            do m = 1,5
              
              f_marquina(m) = 0.5d0 * (fplus(m) + fminus(m) - marquinaflux(m))
              
            end do

          end if !!! The end of the SpaceMask check for a trivial RP.

          densflux(i,j,k) = f_marquina(1)
          sxflux(i,j,k)   = f_marquina(2)
          syflux(i,j,k)   = f_marquina(3)
          szflux(i,j,k)   = f_marquina(4)
          tauflux(i,j,k)  = f_marquina(5)

        enddo
      enddo
    enddo
      !$OMP END PARALLEL DO

    if (evolve_tracer .ne. 0) then

      !$OMP PARALLEL DO PRIVATE(i,j)
      do k = GRHydro_stencil, cctk_lsh(3) - GRHydro_stencil
        do j = GRHydro_stencil, cctk_lsh(2) - GRHydro_stencil
          do i = GRHydro_stencil, cctk_lsh(1) - GRHydro_stencil

            if (densflux(i, j, k) > 0.d0) then

              cons_tracerflux(i, j, k,:) = &
                   tracerplus(i, j, k,:) * &
                   densflux(i, j, k)

            else

              cons_tracerflux(i, j, k,:) = &
                   tracerminus(i + xoffset, j + yoffset, k + zoffset,:) * &
                   densflux(i, j, k)

            end if

          end do
        end do
      end do
      !$OMP END PARALLEL DO

    end if

    if (evolve_Y_e .ne. 0) then

      !$OMP PARALLEL DO PRIVATE(i,j)
      do k = GRHydro_stencil, cctk_lsh(3) - GRHydro_stencil
        do j = GRHydro_stencil, cctk_lsh(2) - GRHydro_stencil
          do i = GRHydro_stencil, cctk_lsh(1) - GRHydro_stencil

            if (densflux(i, j, k) > 0.d0) then

              Y_e_con_flux(i, j, k) = &
                   Y_e_plus(i, j, k) * &
                   densflux(i, j, k)

            else

              Y_e_con_flux(i, j, k) = &
                   Y_e_minus(i + xoffset, j + yoffset, k + zoffset) * &
                   densflux(i, j, k)

            end if

          end do
        end do
      end do
      !$OMP END PARALLEL DO

    end if
    
    return
end subroutine GRHydro_Marquina

 /*@@
   @routine    GRHydro_MarquinaGeneral 
   @date       Wed Feb 13 11:03:32 2002
   @author     Pedro Montero, Toni Font
   @desc 
   Routine to obtain the Marquina Fluxes
   @enddesc 
   @calls     
   @calledby   
   @history 
   Based on routines by Toni Font
   @endhistory 

@@*/


subroutine GRHydro_MarquinaGeneral(CCTK_ARGUMENTS)
    
  implicit none

  DECLARE_CCTK_ARGUMENTS
  DECLARE_CCTK_PARAMETERS
  DECLARE_CCTK_FUNCTIONS
  CCTK_REAL, dimension(5) :: cons_p,cons_m,&
       fplus,fminus,marquinaflux
  CCTK_REAL, dimension(6) :: prim_p, prim_m
  CCTK_REAL :: avg_alp,avg_beta,gxxh,gxyh,gxzh,gyyh,gyzh,gzzh, &
       avg_det,uxxh,uxyh,uxzh,uyyh,uyzh,uzzh, &
       cs2_p,cs2_m,dpdeps_p,dpdeps_m, &
       usendh, psi4h
  integer :: m
  integer :: i,j,k
  
  CCTK_INT :: type_bits, trivial, not_trivial, ierr
  
  if (flux_direction == 1) then
    call SpaceMask_GetTypeBits(type_bits, "Hydro_RiemannProblemX")
    call SpaceMask_GetStateBits(trivial, "Hydro_RiemannProblemX", &
         &"trivial")
  else if (flux_direction == 2) then
    call SpaceMask_GetTypeBits(type_bits, "Hydro_RiemannProblemY")
    call SpaceMask_GetStateBits(trivial, "Hydro_RiemannProblemY", &
         &"trivial")
  else if (flux_direction == 3) then
    call SpaceMask_GetTypeBits(type_bits, "Hydro_RiemannProblemZ")
    call SpaceMask_GetStateBits(trivial, "Hydro_RiemannProblemZ", &
         &"trivial")
  else
    call CCTK_WARN(0, "Flux direction not x,y,z")
  end if
  
  do k = GRHydro_stencil, cctk_lsh(3) - GRHydro_stencil
    do j = GRHydro_stencil, cctk_lsh(2) - GRHydro_stencil
      do i = GRHydro_stencil, cctk_lsh(1) - GRHydro_stencil
        
!!$        Set the left (p for plus) and right (m_i for minus, i+1) states
        
        cons_p(1)   = densplus(i,j,k) 
        cons_p(2)   = sxplus(i,j,k)
        cons_p(3)   = syplus(i,j,k)
        cons_p(4)   = szplus(i,j,k)
        cons_p(5)   = tauplus(i,j,k)
        
        cons_m(1) = densminus(i+xoffset,j+yoffset,k+zoffset)
        cons_m(2) = sxminus(i+xoffset,j+yoffset,k+zoffset)
        cons_m(3) = syminus(i+xoffset,j+yoffset,k+zoffset)
        cons_m(4) = szminus(i+xoffset,j+yoffset,k+zoffset)
        cons_m(5) = tauminus(i+xoffset,j+yoffset,k+zoffset) 
        
        prim_p(1)   = rhoplus(i,j,k) 
        prim_p(2)   = velxplus(i,j,k)
        prim_p(3)   = velyplus(i,j,k) 
        prim_p(4)   = velzplus(i,j,k)
        prim_p(5)   = epsplus(i,j,k)
        
        prim_m(1) = rhominus(i+xoffset,j+yoffset,k+zoffset)
        prim_m(2) = velxminus(i+xoffset,j+yoffset,k+zoffset)
        prim_m(3) = velyminus(i+xoffset,j+yoffset,k+zoffset)
        prim_m(4) = velzminus(i+xoffset,j+yoffset,k+zoffset)
        prim_m(5) = epsminus(i+xoffset,j+yoffset,k+zoffset) 
        
        prim_p(6) = pressplus(i,j,k)
        cs2_p     = eos_cs2_p(i,j,k)
        dpdeps_p  = eos_dpdeps_p(i,j,k)

        prim_m(6) = pressminus(i+xoffset,j+yoffset,k+zoffset)
        cs2_m     = eos_cs2_m(i+xoffset,j+yoffset,k+zoffset)
        dpdeps_m  = eos_dpdeps_m(i+xoffset,j+yoffset,k+zoffset)

        marquinaflux = 0.d0
        
!!$        Set metric terms at interface
        
        if (shift_state .ne. 0) then
          if (flux_direction == 1) then
            avg_beta = 0.5d0 * (betax(i+xoffset,j+yoffset,k+zoffset) + &
                 betax(i,j,k))
          else if (flux_direction == 2) then
            avg_beta = 0.5d0 * (betay(i+xoffset,j+yoffset,k+zoffset) + &
                 betay(i,j,k))
          else if (flux_direction == 3) then
            avg_beta = 0.5d0 * (betaz(i+xoffset,j+yoffset,k+zoffset) + &
                 betaz(i,j,k))
          else
            !$OMP CRITICAL
            call CCTK_WARN(0, "Flux direction not x,y,z")
            !$OMP END CRITICAL
          end if
        else
          avg_beta = 0.d0
        end if
        
        avg_alp = 0.5 * (alp(i,j,k) + alp(i+xoffset,j+yoffset,k+zoffset))
        
        gxxh = 0.5d0 * (gxx(i+xoffset,j+yoffset,k+zoffset) + &
             gxx(i,j,k))
        gxyh = 0.5d0 * (gxy(i+xoffset,j+yoffset,k+zoffset) + &
             gxy(i,j,k))
        gxzh = 0.5d0 * (gxz(i+xoffset,j+yoffset,k+zoffset) + &
             gxz(i,j,k))
        gyyh = 0.5d0 * (gyy(i+xoffset,j+yoffset,k+zoffset) + &
             gyy(i,j,k))
        gyzh = 0.5d0 * (gyz(i+xoffset,j+yoffset,k+zoffset) + &
             gyz(i,j,k))
        gzzh = 0.5d0 * (gzz(i+xoffset,j+yoffset,k+zoffset) + &
             gzz(i,j,k))
        
!!$ routine to calculate the determinant of the metric
        
        avg_det = SPATIAL_DETERMINANT(gxxh,gxyh,gxzh,gyyh,gyzh,gzzh)

!!$ If the Riemann problem is trivial the flux is already correct
        
        if (SpaceMask_CheckStateBitsF90(space_mask, i, j, k, type_bits, trivial)) then
          
        else !!! The end of this branch is right at the bottom of the routine
            
          call UpperMetric(uxxh, uxyh, uxzh, uyyh, uyzh, uzzh, &
               avg_det,gxxh, gxyh, gxzh, gyyh, gyzh, gzzh)
          
          if (flux_direction == 1) then
            usendh = uxxh
          else if (flux_direction == 2) then
            usendh = uyyh
          else if (flux_direction == 3) then
            usendh = uzzh
          else
            !$OMP CRITICAL
            call CCTK_WARN(0, "Flux direction not x,y,z")
            !$OMP END CRITICAL
          end if
          
!!$eigenvalues and right eigenvectors
          
          if (flux_direction == 1) then
            
            call eigenproblem_marquina_general(&
                 prim_m(1),prim_m(2),prim_m(3),prim_m(4),prim_m(5), &
                 prim_m(6),cs2_m,dpdeps_m, &
                 prim_p(1),prim_p(2),prim_p(3),prim_p(4),prim_p(5), &
                 prim_p(6),cs2_p,dpdeps_p, &
                 gxxh,gxyh,gxzh,gyyh,gyzh,gzzh, &
                 usendh,avg_det,avg_alp,avg_beta, &
                 cons_p(1),cons_p(2),cons_p(3),cons_p(4),cons_p(5), &
                 cons_m(1),cons_m(2),cons_m(3),cons_m(4),cons_m(5), &
                 marquinaflux(1),marquinaflux(2),marquinaflux(3), &
                 marquinaflux(4),marquinaflux(5))
            
          else if (flux_direction == 2) then
            
            call eigenproblem_marquina_general(&
                 prim_m(1),prim_m(3),prim_m(4),prim_m(2),prim_m(5), &
                 prim_m(6),cs2_m,dpdeps_m, &
                 prim_p(1),prim_p(3),prim_p(4),prim_p(2),prim_p(5), &
                 prim_p(6),cs2_p,dpdeps_p, &
                 gyyh,gyzh,gxyh,gzzh,gxzh,gxxh, &
                 usendh,avg_det,avg_alp,avg_beta,&
                 cons_p(1),cons_p(3),cons_p(4),cons_p(2),cons_p(5), &
                 cons_m(1),cons_m(3),cons_m(4),cons_m(2),cons_m(5), &
                 marquinaflux(1),marquinaflux(3),marquinaflux(4), &
                 marquinaflux(2),marquinaflux(5))
            
          else if (flux_direction == 3) then
            
            call eigenproblem_marquina_general(&
                 prim_m(1),prim_m(4),prim_m(2),prim_m(3),prim_m(5), &
                 prim_m(6),cs2_m,dpdeps_m, &
                 prim_p(1),prim_p(4),prim_p(2),prim_p(3),prim_p(5), &
                 prim_p(6),cs2_p,dpdeps_p, &
                 gzzh,gxzh,gyzh,gxxh,gxyh,gyyh, &
                 usendh,avg_det,avg_alp,avg_beta, &
                 cons_p(1),cons_p(4),cons_p(2),cons_p(3),cons_p(5), &
                 cons_m(1),cons_m(4),cons_m(2),cons_m(3),cons_m(5), &
                 marquinaflux(1),marquinaflux(4),marquinaflux(2), &
                 marquinaflux(3),marquinaflux(5))
            
          else
            !$OMP CRITICAL
            call CCTK_WARN(0, "Flux direction not x,y,z")
            !$OMP END CRITICAL
          end if
          
!!$ Marquina flux
          
          densflux(i,j,k) = densflux(i,j,k) - 0.5d0 * marquinaflux(1)
          sxflux(i,j,k)   = sxflux(i,j,k)   - 0.5d0 * marquinaflux(2)
          syflux(i,j,k)   = syflux(i,j,k)   - 0.5d0 * marquinaflux(3)
          szflux(i,j,k)   = szflux(i,j,k)   - 0.5d0 * marquinaflux(4)
          tauflux(i,j,k)  = tauflux(i,j,k)  - 0.5d0 * marquinaflux(5)
          
        end if !!! The end of the SpaceMask check for a trivial RP.
        
      enddo
    enddo
  enddo

  if (evolve_tracer .ne. 0) then

    do k = GRHydro_stencil, cctk_lsh(3) - GRHydro_stencil
      do j = GRHydro_stencil, cctk_lsh(2) - GRHydro_stencil
        do i = GRHydro_stencil, cctk_lsh(1) - GRHydro_stencil
          
          if (densflux(i, j, k) > 0.d0) then
            
            cons_tracerflux(i, j, k,:) = &
                 tracerplus(i, j, k,:) * &
                 densflux(i, j, k)
            
          else
            
            cons_tracerflux(i, j, k,:) = &
                 tracerminus(i + xoffset, j + yoffset, k + zoffset,:) * &
                 densflux(i, j, k)
            
          end if
          
        end do
      end do
    end do
      
  end if
      
end subroutine GRHydro_MarquinaGeneral