c ***********************************************************************

      subroutine update_vector(n) 
c  update the Euler vectors.

      implicit double precision(a-h, o-z)
      parameter(maxa=500,maxn=maxa*3)
      integer nout, nn
      double precision ft(3),du(3),newu(3)
       common/matrix/x(maxa,3),bangle(maxa),rz(maxa)
       common/matrix2/ r(maxa,maxa)
       common/bf_coords/f(maxa,3),v(maxa,3),u(maxa,3)
        common/ddx/d_x(maxa,3)



        do i = 1, n 
             ii = i+1
	     if (i.eq.n) then
	      ii=1
	     endif
         do j = 1, 3
            newu(j) =   (x(ii,j)-x(i,j))/r(i,ii)
            du(j) = newu(j) - u(i,j)
         enddo

 
         du_f = du(1)*f(i,1)+du(2)*f(i,2)+du(3)*f(i,3) 
         do j = 1, 3
	    ft(j) = f(i,j) - du_f*u(i,j)
            u(i,j) = newu(j)
         enddo

c project out any component of ft that is paralle to u
c    newf = ft (dot) (I - uu)
c where I and uu are 3x3 tensors.

         xy = newu(1)*newu(2)
         xz = newu(1)*newu(3)
         yz = newu(2)*newu(3)
         f1=ft(1)*(1.d0-newu(1)*newu(1))-ft(2)*xy-ft(3)*xz
         f2=ft(2)*(1.d0-newu(2)*newu(2))-ft(1)*xy-ft(3)*yz
         f3=ft(3)*(1.d0-newu(3)*newu(3))-ft(1)*xz-ft(2)*yz

c normalize vector f
         ftotal = dsqrt(f1*f1+f2*f2+f3*f3)
         f(i,1)=f1/ftotal
         f(i,2)=f2/ftotal
         f(i,3)=f3/ftotal

c calculate vector: v = u x f
         v(i,1)=u(i,2)*f(i,3)-f(i,2)*u(i,3)
         v(i,2)=-u(i,1)*f(i,3)+f(i,1)*u(i,3)
         v(i,3)=u(i,1)*f(i,2)-f(i,1)*u(i,2)
      enddo

      return
      end