!-------------------------------------- LICENCE BEGIN ------------------------------------
!Environment Canada - Atmospheric Science and Technology License/Disclaimer,
!                     version 3; Last Modified: May 7, 2008.
!This is free but copyrighted software; you can use/redistribute/modify it under the terms
!of the Environment Canada - Atmospheric Science and Technology License/Disclaimer
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!-------------------------------------- LICENCE END --------------------------------------
!
C
C  X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X
C

      subroutine cyclic(x,r,a,b,c,n) 2,4
*
*Author: Luc Fillion - MSC- 9 march 04
*           
*
      IMPLICIT NONE
#include "taglam4d.cdk"
#include "comlun.cdk"
      integer n
      real*8 a(n),b(n),c(n),r(n),x(n)
!
      integer i
      real*8 fact,alpha,beta,gamma,bb(n),u(n),z(n)
!
!!
      if(n.le.2) then
        call abort3d(nulout,'CYCLIC: n too small')
      endif
      gamma=-b(1)
      if(gamma.eq.0.0) then
        call abort3d(nulout,'CYCLIC: gamma = 0.0')
      endif
!
      beta=a(1)
      alpha=beta  ! Luc approximation
!
      bb(1)=b(1)-gamma
      bb(n)=b(n)-alpha*beta/gamma
      do i=2,n-1
        bb(i)=b(i)
      enddo
!
      call tridiag(x,r,a,bb,c,n)
      u(1)=gamma
      u(n)=alpha
      do i=2,n-1
        u(i)=0.
      enddo
      call tridiag(z,u,a,bb,c,n)
!
      fact=(x(1)+beta*x(n)/gamma)/(1.+z(1)+beta*z(n)/gamma)
      do i=1,n
        x(i)=x(i)-fact*z(i)
      enddo
!
      return
      end