function retentostat_growth(V_B,Cs_chem, Cs_ret, Ysx_max, Ysp_max, ms_est, F_in, days, qp_func, qp_res)

% By putting two percent-signs (%%), one can mark parts of the code. 
%% Looping over the volume of the mixing vessel (Vessel A)

maxp = 20; % iterations over the volume of vessel A
maxi = 20; % iterations over the maintenance coefficient.
Fin_A = F_in;
Cx_end = zeros(maxp,maxi);
Cx_max = zeros(maxp,maxi);
V_Ass = [];
mu = [];

% Vectors for the final analysis, storing ALL datapoints over time
Cx_t = [];
mu_t = [];
Cs_t = [];
Cp_t = [];

for p = 1:maxp
    %% Process Parameters
    % Vessel A - Mixing Vessel
    %     Fin_A = 0.035; % L/h
    V_A = 0 + p*0.1; %L
    Fout_A = Fin_A; % L/h
    
    % Vessel B - Fermenter
    Fin_B = Fout_A;
    Fout_B = Fin_B;
    
    %% Storage matrices
    % Because of the loops used in this function, certain values are
    % required to be stored in matrices. When an ode-solver is in a loop,
    % the output will usually be stored in the output matrix (c in this
    % function), but will be overwritten once the loop is run again with a
    % new value. This would mean a loss of data if the data wouldn't be
    % stored in a 'storage matrix'. this is necessary when the data needs
    % to be accessed later.
    
    Cx = []; % storage matrix for biomass concentrations in vessel B
    Cs = []; % storage matrix for substrate concentrations in vessel A
    Cp = []; % storage matrix for product concentrations in vessel B
    mss = []; % Storage matrix for the ms-values (for the plotting)
    tss= []; % storage vector for the time-points (for plotting)
    
    %% Time span of the ode-solver in h
    
    tini= 0 ; % h
    tend= 24*days; % h
    dt  = 0.5; % the time steps that are used for the ode solver, [h]
    
    %% Initial concentrations for the ode-solver
    % In this model, these are the values that are obtained from the
    % chemostat phase. The time of 0 hours is when the chemostat is
    % switched to a retentostat.
    
    C_S0 = Cs_chem; %  g/L Substrate in the inflow of vessel A
    
    %% Looping over ms
        
    % Herbert Pirt Equation Parameters for product formation
    A = qp_func;
    B = (Ysp_max+Ysx_max*A)/(Ysx_max*Ysp_max);
    G = qp_res/Ysp_max;
    
    for i = 1:maxi
        
        ms = (ms_est-maxi/2*0.0001) + i*0.0001 % maintenance coefficient % gs/gx/h
        
        C_X0 = ((Fin_B/V_B)*C_S0)/(((Fin_B/V_B)*B)+ms + G);
        C_P0 = (A*(Fin_B/V_B)+qp_res)*C_X0*V_B/Fout_B;
        c0 = [C_X0 C_S0 C_P0];% C_SB0];
        
        %% ode solver
        opt = odeset('RelTol',1e-8, 'AbsTol',1e-8);
        [t,c] = ode45(@(t,c)dcdt(t,c,ms,Ysx_max,Ysp_max,Cs_ret,F_in,V_A,V_B, qp_res, B, A, G), tini:dt:tend, c0, opt);
        
        % there are several ode solvers available. ode45 is most common to
        % use for 'simple' problems
        
        % In order to keep the data available outside of the loop, the concentrations that are
        % yielded from the ode solver, they are stored in the
        % storage-matrices as defined above.
        
        Cx = [Cx c(:,1)]; Cx_t = [Cx_t c(:,1)];
        Cs = [Cs c(:,2)]; Cs_t = [Cs_t c(:,2)];
        Cp = [Cp c(:,3)]; Cp_t = [Cp_t c(:,3)];
        Cs_B = 0;
        
        %% Plotting & Data Handling
        % Calculate mu, qp, qs, Ysp qs(mu) and qs(ms) are calculated from the Herbert-pirt equation.
        for k = 1:1:length(t)
            qs(k,i) = ((Fin_B/V_B)*(Cs(k,i)-Cs_B))/Cx(k,i);
            qs_t(k,i+(p-1)*maxi) = qs(k,i);
            mu(k,i) = (qs(k,i)-G-ms)/B;  % based on substrate balance
            mu_t(k,i+(p-1)*maxi) = mu(k,i);
            qp(k,i) = A*mu(k,i)+qp_res;
            qp_t(k,i+(p-1)*maxi) = qp(k,i);
            Ysp(k,i) = qp(k,i)/qs(k,i);
            Ysp_t(k,i+(p-1)*maxi) = Ysp(k,i);
            qs_mu(k,i) = (mu(k,i)/Ysx_max)/qs(k,i);
            qs_mu_t(k,i+(p-1)*maxi) = qs_mu(k,i);
            qs_ms(k,i) = ms/qs(k,i);
            qs_ms_t(k,i+(p-1)*maxi) = qs_ms(k,i);
        end
        
        % as soon as the new loop starts, the data in matrices t and c and
        % the value for ms will be overwritten. Therefore, that data needs
        % to be stored in a nother matrix, that will contain all data of
        % all the loops.
        
        Cx_end(p,i) = c(end,1);
        Cx_max(p,i) = max(c(:,1));
        mss = [mss;ms];
        tss = [tss t];
        
    end
    
    V_Ass = [V_Ass V_A];
    
    %% Final data plotting
   
      
    figure(p*10)
    surf(mss,tss/24,Cx,'EdgeColor','none');
    xlabel(' m_s (g_{glucose}.g_x^{-1}.h^{-1})', 'FontSize',14 );
    ylabel('Time (d)', 'FontSize',14 );
    zlabel('C_x (g.L^{-1})', 'FontSize',14 );
    suptitle(['Volume_A = ' num2str(V_Ass(end)) ' L'])
    %when writing strings (of letters), an underscore (_) gives the next
    %letter as subscript OR whatever is between braces: {} 
    
end

%close all %closes small plots before final data plotting

%% Function Final Output

% The function should give the required answers on maximal volume of vessel A for maximal ms
% values as written output in the command window. to give written output,
% the commands fprintf are used. The constraint on Volume of vessel A is
% defined by the maximal volume for which the biomass specific growth rate
% remains non-negative (= starvation).
Cx_eval = Cx_max./Cx_end; % evaluate whether Cx max is at the end of the
% retentostat
mu_thres = ones(length(t),1)*1e-3; % This vector is created to have a
% threshold line for the growth rate (has to be below 0.001 h-1

for p = 1:maxp;
    if Cx_eval(p,maxi) > 1
        % It is easiest to have the output in an easily accessible format,
        % here a sentence.
        fprintf(['The maximal volume of mixing vessel A for ' ...
            'which a robust set-up can be guaranteed \n based on this model, ' ...
            'up to an ms of ' num2str(mss(maxi)) ' is a volume of '...
            num2str(V_Ass(p-1)) ' L. \n' ])
        % It has to be p-1, because if p is used for the volume, the Cx_eval
        % is already > 1.
        
        % but a visual check of the conclusion is required as well.
        for a = 0:1 % plot for the first 'wrong'  V_A and the last ' good' V_A.
         
            figure((p-a)*101);% suptitle(['Volume_A = ' num2str(V_Ass(p-a)) ' L'])
            Fontsize = 15;
            % Biomass concentration
            subplot(3,3,1)
            plot(t/24,Cx_t(:,1+((p-a)-1)*maxi),'r',t/24,Cx_t(:,(maxi+((p-a)-1)*maxi)),'k-', 'LineWidth', 1.5);
            hold on;
            xlabel(' Time (d)', 'FontSize',15 );
            ylabel('C_x (g.L^{-1})', 'FontSize',15 );
            title('a','FontSize',Fontsize);
            % Specific growth rate
            subplot(3,3,4)
            plot(t/24,mu_t(:,1+((p-a)-1)*maxi),'r',t/24,mu_t(:,maxi+((p-a)-1)*maxi),'k-', 'LineWidth', 1.5);
            hold on; 
            xlabel(' Time (d)', 'FontSize',15  );
            ylabel('\mu (h^{-1})', 'FontSize',15 );
            title('d','FontSize',Fontsize);
            % Substrate inflow concentration
            subplot(3,3,2)
            plot(t/24,Cs_t(:,1+((p-a)-1)*maxi),'r',t/24,Cs_t(:,maxi+((p-a)-1)*maxi),...
                'k-', 'LineWidth', 1.5);
            hold on; 
            xlabel(' Time (d)', 'FontSize',15  );
            ylabel('C_{s,}_{in} (g.L^{-1})', 'FontSize',15 );
            title('b','FontSize',Fontsize);
            % Specific growth rate (logarithmic scale)
            subplot(3,3,7)
            semilogy(t/24,mu_t(:,1+((p-a)-1)*maxi),'r',t/24,mu_t(:,maxi+((p-a)-1)*maxi),...
                'k-',t/24,mu_thres,'g', 'LineWidth', 1.5);
            hold on;
            xlabel(' Time (d)', 'FontSize',15  );
            ylabel('\mu (h^{-1})', 'FontSize',15 );
            title('g','FontSize',Fontsize);
            % specific product formation rate
            subplot(3,3,6)
            plot(t/24,qp_t(:,1+((p-a)-1)*maxi),'r',t/24,qp_t(:,maxi+((p-a)-1)*maxi),...
                'k-', 'LineWidth', 1.5);
            hold on; 
            xlabel(' Time (d)', 'FontSize',15  );
            ylabel('q_p (g_{p}.g_{x}^{-1}.h^{-1})', 'FontSize',15 );
            title('f','FontSize',Fontsize);
            % product concentration
            subplot(3,3,3)
            plot(t/24,Cp_t(:,1+((p-a)-1)*maxi),'r',t/24,Cp_t(:,maxi+((p-a)-1)*maxi),...
                'k-', 'LineWidth', 1.5);
            hold on; 
            xlabel(' Time (d)', 'FontSize',15  );
            ylabel('C_p (g.L^{-1})', 'FontSize',15 );
            title('c','FontSize',Fontsize);
            % specific substrate consumption rate
            subplot(3,3,5)
            plot(t/24,qs_t(:,1+((p-a)-1)*maxi),'r',t/24,qs_t(:,maxi+((p-a)-1)*maxi),...
                'k-', 'LineWidth', 1.5);
            hold on; 
            xlabel(' Time (d)', 'FontSize',15  );
            ylabel('q_s (g_{s}.g_x^{-1}.h^{-1})', 'FontSize',15 );
            title('e','FontSize',Fontsize);
            axis([0,1,0 , 0.07], 'auto x')
            
            subplot(3,3,8)
            plot(t/24,qs_mu_t(:,1+((p-a)-1)*maxi)*100,'r',t/24,qs_ms_t(:,1+((p-a)-1)*maxi)*100, 'k','LineWidth', 1.5);
            hold on
            plot(t/24,qs_mu_t(:,maxi+((p-a)-1)*maxi)*100,'g',t/24,qs_ms_t(:,maxi+((p-a)-1)*maxi)*100, 'b','LineWidth', 1.5);
            xlabel(' Time (d)', 'FontSize',Fontsize );
            ylabel('Gluc. distr. (%)', 'FontSize',Fontsize );
            title('h','FontSize',Fontsize );
            

            % Product on substrate yield
            subplot(3,3,9)
            plot(t/24,Ysp_t(:,1+((p-a)-1)*maxi),'r',t/24,Ysp_t(:,maxi+((p-a)-1)*maxi),...
                'k-', 'LineWidth', 1.5);
            hold on;
            xlabel(' Time (d)', 'FontSize',15  );
            ylabel('Y_{sp} (g_p.g_s^{-1})', 'FontSize',15 );
            title('i','FontSize',Fontsize);
      
            
        end
        
        break
        
    end
end


end

function dc = dcdt(t,c,ms,Ysx_max,Ysp_max,Cs_ret,F_in,V_A,V_B, qp_res, B, A, G)
% global Fin_A V_A Fout_A ms Ysx_max Ysp_max qp V_B


%% Variables
Cx_B = c(1);
Cs_A = c(2);
Cp_B = c(3);
Cs_B = 0;

%% Model Parameters

% Vessel A - Mixing Vessel

Cs_R = Cs_ret; % the concentration in the second medium vessel; eventually the concentration in vessel A.

% Vessel B - Fermentor
Fin_A = F_in;
Fout_A = Fin_A;
Fin_B = Fout_A;
Fout_B = Fin_B;

qs = ((Fin_B/V_B)*(Cs_A-Cs_B))/Cx_B;
mu = (qs - G - ms)/B;
qp = A * mu + qp_res; 

%% Equations
dc(1) = mu*Cx_B; % Balance of Cx_B
dc(2) = Fin_A/V_A*Cs_R - Fout_A/V_A*Cs_A; %  % Balance of Cs_A
dc(3) = qp*Cx_B-Fout_B*Cp_B; % Balance of Cp_B: Product formation

dc = dc';
end