lp_s(p,set)

function [max_r,ind] = lp_s(p,set)
%
% Computation of the maximal magnitude of the rational ADI function over
% a discrete subset of the left complex half plane.
%
%   Calling sequence:
%
%     [max_r,ind] = lp_s(p,set)
%
%   Input:
%
%     p        vector of ADI parameters;
%     set      vector representing the discrete set.
%
%   Output:
%
%     max_r    maximal magnitude of the rational ADI function over set;
%     ind      index - maximum is attained for set(ind). 
%
%   
%   LYAPACK 1.0 (Thilo Penzl, Jan 1999)
%

max_r = -1;
ind = 0;
  
for i = 1:length(set)
  
  x = set(i);
  
  rr = 1;
  for j = 1:length(p)

    rr = rr*abs(p(j)-x)/abs(p(j)+x);
    
  end  
    
  if rr > max_r
    
    max_r = rr;
    ind = i;
   
  end
  
end