dom_dec_compute_projection_error.m

function proj_err = dom_dec_compute_projection_error(...
    detailed_data,XN,K,base_sim_data)
%function proj_err = dom_dec_compute_projection_error(...
%    detailed_data,XN,K,base_sim_data)
%
% if XN is a cell: K is assumed to be a cell and the projections
% on the subdomains are computed

% IM, 06.03.2012

proj_err = 0;

if iscell(XN)

  ehPROJ = cell(1,2);
  for i = 1:2
    
    uh = base_sim_data.uh.dofs(detailed_data.masks{i});
    
    if ~isempty(XN{i})
      ehPROJ{i} = uh - XN{i} * (XN{i}' * K{i} * uh);
    else
      ehPROJ{i} = uh;
    end;
    
    norm = ehPROJ{i}' * K{i} * ehPROJ{i};
    if (norm < 0)
      norm = 0;
    end;
    
    proj_err = proj_err + norm;    
    
  end;
  
  proj_err = sqrt(proj_err);
    
else
  
  if ~isempty(XN)
    ehPROJ = base_sim_data.uh.dofs - XN * (XN' * K * ...
                                           base_sim_data.uh.dofs);
  else
    ehPROJ = base_sim_data.uh.dofs;
  end;
  
  proj_err = ehPROJ' * K * ehPROJ;
  
  if proj_err < 0
    proj_err = 0;
  end;
  
  proj_err = sqrt(proj_err);  
  
end;