% Exemplo da aula sobre balancos - Producao de 3HB e HHx sem crescimento
% Slide 27
% Balanco de carbono

% 
% Ordem dos compostos: Glicose, Ac Hex, O2, 3HB, HHx, CO2

nC = [6 6 0 4 6 1];
v = [-1.54; -0.18; -3.16; 1.4; 0.09; 3.29];

dif = nC*v;
bal = 100*(nC(4:6)*v(4:6))/-(nC(1:3)*v(1:3))
vC = nC'.*v;

% Balanco redox
nNR = [24 32 -4 18 30 0];

dif_r = nNR*v;
bal_r = 100*(nNR(4:6)*v(4:6))/-(nNR(1:3)*v(1:3))
vNR = nNR'.*v;

% Reconciliacao dos fluxos
A = [nC; nNR];
var = 2,5/100*abs(v);
S = diag(var);

v_rec = v - S*A'*(A*S*A')^(-1)*A*v;

% Verificacao
difc_rec = nC*v_rec
balc_rec = 100*(nC(4:6)*v_rec(4:6))/-(nC(1:3)*v_rec(1:3))

difnr_rec = nNR*v_rec
balnr_rec = 100*(nNR(4:6)*v_rec(4:6))/-(nNR(1:3)*v_rec(1:3))