ccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c Solution of linear equation without inverting matrix
c using LU decomposition: 
c        AA * xx = bb         AA, bb: known
c                                 xx: to be found
c AA and bb are not modified in this subroutine
c                               
c MALV , Sep 2007
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

      subroutine LUdec(xx,aa,bb,m,n)

      implicit none

! Arguments 
      integer     m, n
      real*8      aa(m,m), bb(m), xx(m)


! Local variables
      real*8      a(n,n), b(n), x(n), d
      integer    i, j, indx(n)      


! Subrutinas utilizadas
!     ludcmp_dp, lubksb_dp

!!!!!!!!!!!!!!! Comienza el programa !!!!!!!!!!!!!!
      
      do i=1,n
        b(i) = bb(i+1)
        do j=1,n
           a(i,j) = aa(i+1,j+1)
        enddo
      enddo

      ! Descomposicion de auxm1
      call ludcmp_dp ( a, n, n, indx, d)

      ! Sustituciones foward y backwards para hallar la solucion
      do i=1,n
           x(i) = b(i)
      enddo
      call lubksb_dp( a, n, n, indx, x )

      do i=1,n
        xx(i+1) = x(i)
      enddo

      return
      end