subroutine  recos_qL(q_im1, q_i, q_ip1, 
     &                        r_im1, r_i, r_ip1,
     &                        rqL_iph )

c------------------------------------------------------------
c Calculates the reconstructed variables
c from the LEFT using a minmod slope limiter.
c Note that the input coordinates are the coordinates
c of the cell centres (x_(i-1), x_(i) and x_(i+1)), 
c the output is at the cell boundary x_(i+1/2).
c------------------------------------------------------------

         implicit      none

         character*8   cdnm
         parameter   ( cdnm = 'recos_qL' ) 

         logical       ltrace
         parameter   ( ltrace = .false. )

         real*8        q_im1,  q_i,   q_ip1
         real*8        r_im1,  r_i,   r_ip1

         real*8        rqL_iph

         real*8        s_iph,    s_imh   
         real*8        sigma_i

         real*8        minmod 
         
c============================================================
c============================================================

         if ( ltrace ) then
            write(0,*) cdnm,':  q_im1=', q_im1
            write(0,*) cdnm,':    q_i=', q_i
            write(0,*) cdnm,':  q_ip1=', q_ip1
            write(0,*) cdnm,':  '
            write(0,*) cdnm,':  r_im1=', r_im1
            write(0,*) cdnm,':    r_i=', r_i
            write(0,*) cdnm,':  r_ip1=', r_ip1
            write(0,*) cdnm,':  '
         endif
         s_iph = (q_ip1 - q_i) / (r_ip1 - r_i)
         s_imh = (q_i - q_im1) / (r_i - r_im1)
         sigma_i = minmod(s_imh, s_iph) 
         rqL_iph = q_i + sigma_i * 0.5d0 * (r_ip1 - r_i)
         if ( ltrace ) then
            write(0,*) cdnm,':    rqL_iph=', rqL_iph
         endif
         return
         end