function f=alldls(ldlt,mu1,s)
% solution of a symmetric linear system where the coefficient matrix
% have been factorized by a preceding call to alldlf.
% function f=alldls(ldlt,mu1,s)
% where ldlt and mu1 are row vectors and f and s are column vectors.
% (c) 2006 Alain Hebert, Ecole Polytechnique de Montreal
   n=size(s,1) ; f=zeros(n,1) ;
   if n == 1
      f(1)=s(1)*ldlt(mu1(1)) ;
      return
   end
   f(1)=s(1) ;
   k1=mu1(1)+1 ;
   for i=2:n
      k2=mu1(i) ;
      kj=i-k2+k1 ;
      f(i)=s(i)-sum(f(kj:i-1).*ldlt(k1:k2-1)') ;
      k1=k2+1 ;
   end
   f(1:n)=f(1:n).*ldlt(mu1(1:n))' ;
   k2=mu1(n) ;
   for i=n:-1:2
      k1=mu1(i-1)+1 ;
      kj=i-k2+k1 ;
      f(kj:i-1)=f(kj:i-1)-f(i)*ldlt(k1:k2-1)' ;
      k2=k1-1 ;
   end