norm_response_coefficients.m

％The Metabolic Networks Toolbox contains functions to create, ％modify, display, and simulate bioche

function [R_S_norm,R_J_norm,R_S_2_norm,R_J_2_norm] = norm_response_coefficients(S,J,par,R_S,R_J,R_S_2,R_J_2,used_J)

%[R_S_norm,R_J_norm,R_S_2_norm,R_J_2_norm] = norm_response_coefficients(S,J,par,R_S,R_J,R_S_2,R_J_2,used_J)
%
% normalised response coefficients of 1st and 2nd order

n_met = length(S);
n_rea = length(J);

R_S_norm   = diag(1./S) * R_S * diag(par);

if exist('used_J','var'), J_inv = zeros(size(J)); J_inv(find(used_J)) = 1./J(find(used_J));
else, J_inv = 1./J; end

R_J_norm   = diag(J_inv) * R_J * diag(par);

if nargout>2,

for it=1:n_met,
  term1S(it,:,:) = R_S_norm(it,:)' * R_S_norm(it,:);
  term3S(it,:,:) = diag(R_S_norm(it,:));
end
term2S =  tensor_scale(tensor_scale(tensor_scale(R_S_2,1,(1./S)),2,par),3,par) ;

R_S_2_norm = - term1S + term2S  + term3S;

for it=1:n_rea,
  term1J(it,:,:) = R_J_norm(it,:)' * R_J_norm(it,:);
  term3J(it,:,:) = diag(R_J_norm(it,:));
end
term2J = tensor_scale(tensor_scale(tensor_scale(R_J_2,1,(J_inv)),2,par),3,par);

R_J_2_norm = - term1J + term2J + term3J;

end