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***s/r vdfds - Computes the first difference g of a function f
*              at unevenly spaced points (vectorized version)
*

      subroutine vdfds (F_g, F_f, F_hr, np, n, F_alfa, F_beta) 1
#include "impnone.cdk"
*
      integer n,np
      real    F_g(np,n), F_f(np,n), F_hr(n), F_alfa, F_beta
*
*AUTHOR
*
*REVISION
* v2_30   L. Corbeil             - Version parallele
*
*OBJECT
*        - GIVEN A FUNCTION F AT N UNEVENLY SPACED POINTS, THIS ROUTINE
*        - CALCULATES ITS FIRST DIFFERENCE G AT THESE POINTS.
*        - HR MUST CONTAIN THE INVERSE OF THE INTERVAL LENGTHS.
*        - BOUNDARY CONDITIONS SPECIFIED BY ALFA,BETA, (SEE BELOW). 
*
*ARGUMENTS
*  Name        I/O                 Description
*----------------------------------------------------------------
*   F_g         O         Result
*   F_f         I         Function to be differenced
*   F_hr        I         Inverse of the interval lengths 
*   F_alfa      I         Used for boundary conditions
*   F_beta      I         Used for boundary conditions
*----------------------------------------------------------------------
*
**
      integer i, pt
      real    a(np)
*
*     ---------------------------------------------------------------
*
      do i=1,n-1
      do pt=1,np
         F_g(pt,i+1) = F_hr(i)*(F_f(pt,i+1)-F_f(pt,i))
      enddo
      enddo
*
      do pt=1,np
        a(pt) = F_g(pt,2)
      enddo
*
      do i=2,n-1
      do pt=1,np
         F_g(pt,i) = (F_hr(i)*F_g(pt,i+1)+F_hr(i-1)*F_g(pt,i))
     $               /(F_hr(i)+F_hr(i-1))
      enddo
      enddo
*
*     BOUNDARIES
      do pt=1,np
         F_g(pt,1) = F_alfa*a(pt)     +(1.-F_alfa)*F_g(pt,2)
         F_g(pt,n) = F_beta*F_g(pt,n) +(1.-F_beta)*F_g(pt,n-1)
      enddo
*
*     ---------------------------------------------------------------
*
      return
      end