function [iter,eval,delta]=alfse(a,b,evect,adect,sour,eps)
% find the solution of a fixed source eigenvalue problem defined as
% (a-eval*b)*delta=sour using the inverse power method. The associated
% eigenvalue problem is
%    (a-eval*b)*evect=0
%    (a'-eval*b')*adect=0
% function [iter,eval,delta]=alfse(a,b,evect,adect,sour,eps)
% (c) 2007 Alain Hebert, Polytechnique Montreal
   check=adect'*sour ;
   if abs(check) > eps
      error('the fixed source is not orthogonal to the adjoint eigenvector')
   end
   znum=adect'*a*evect ; zden=adect'*b*evect ;
   try
      a=inv(a) ;
   catch
      error('singular matrix')
   end
   % perform power iterations.
   iter=0 ;
   eval=znum/zden ;
   sour=a*sour ;
   n=size(a,2) ; delta=zeros(n,1) ;
   while true
      iter=iter+1 ;
      if iter > 300, error('unable to converge.'), end
      s1=adect'*b*delta ;
      gar=sour-(s1/zden)*evect+eval*a*b*delta ;
      err1=max(abs(gar)) ; err2=max(abs(gar-delta)) ;
      delta=gar ;
      if err2 <= err1*eps, break, end
   end