function f=aslv3(a,s)
% solution of a system of linear equations for a symmetric, positive
% definite and tri-diagonal matrix.
% function f=aslv3(a,s)
% a : upper diagonal matrix coefficients. a(1,i) and a(2,i) contain
%     respectively the diagonal (i,i) and non-diagonal (i,i+1) terms.
% (c) 2006 Alain Hebert, Ecole Polytechnique de Montreal
   n=size(a,2) ;
   f=zeros(n,1) ;
   pmx=a(1,1) ;
   if pmx == 0.0, error('zero pivot(1).'), end
   f(1)=s(1)/pmx ;
   for i=2:n
      gar=a(2,i-1) ;
      a(2,i-1)=a(2,i-1)/pmx ;
      pmx=a(1,i)-gar*a(2,i-1) ;
      if pmx == 0.0, error('zero pivot(2).'), end
      f(i)=(s(i)-gar*f(i-1))/pmx ;
   end
   for i=n-1:-1:1
      f(i)=f(i)-a(2,i)*f(i+1) ;
   end