function w = letrfm1(N, v, x, s, iflag)

%  The function w =  letrfm1(N,x,s,iflag) computes the Legendre
%  tranforms w.r.t. to the Legendre-Gauss-Lobatto nodes.
%
%  Input:
%  N:          Degree of polynomials, must be even
%  v:          Sequence to be transformed
%  x,s:        output of leinit.m (x:  LGL nodes, s_jk=L_k(x_j))
%  iflag=1:    Spectral  to Physical
%  iflag.ne.1: Physical  to Spectral
%
%
%  Output:
%  w:       transformed sequence
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if (iflag==1)

     w=s*v;

else

     for i=1:N+1
         v(i)=v(i)/(s(i,N+1)^2);
     end

     w=s'*v;
     for i=1:N
         w(i)=w(i)*(2*i-1)/(N*(N+1));
     end

     w(N+1)=w(N+1)/(N+1);

end