function [VOI, STATES, ALGEBRAIC, CONSTANTS] = mainFunction()
    % This is the "main function".  In Matlab, things work best if you rename this function to match the filename.
   [VOI, STATES, ALGEBRAIC, CONSTANTS] = solveModel();
end

function [algebraicVariableCount] = getAlgebraicVariableCount() 
    % Used later when setting a global variable with the number of algebraic variables.
    % Note: This is not the "main method".  
    algebraicVariableCount =5;
end
% There are a total of 2 entries in each of the rate and state variable arrays.
% There are a total of 20 entries in the constant variable array.
%

function [VOI, STATES, ALGEBRAIC, CONSTANTS] = solveModel()
    % Create ALGEBRAIC of correct size
    global algebraicVariableCount;  algebraicVariableCount = getAlgebraicVariableCount();
    % Initialise constants and state variables
    [INIT_STATES, CONSTANTS] = initConsts;

    % Set timespan to solve over 
    tspan = [0, 10];

    % Set numerical accuracy options for ODE solver
    options = odeset('RelTol', 1e-06, 'AbsTol', 1e-06, 'MaxStep', 1);

    % Solve model with ODE solver
    [VOI, STATES] = ode15s(@(VOI, STATES)computeRates(VOI, STATES, CONSTANTS), tspan, INIT_STATES, options);

    % Compute algebraic variables
    [RATES, ALGEBRAIC] = computeRates(VOI, STATES, CONSTANTS);
    ALGEBRAIC = computeAlgebraic(ALGEBRAIC, CONSTANTS, STATES, VOI);

    % Plot state variables against variable of integration
    [LEGEND_STATES, LEGEND_ALGEBRAIC, LEGEND_VOI, LEGEND_CONSTANTS] = createLegends();
    figure();
    plot(VOI, STATES);
    xlabel(LEGEND_VOI);
    l = legend(LEGEND_STATES);
    set(l,'Interpreter','none');
end

function [LEGEND_STATES, LEGEND_ALGEBRAIC, LEGEND_VOI, LEGEND_CONSTANTS] = createLegends()
    LEGEND_STATES = ''; LEGEND_ALGEBRAIC = ''; LEGEND_VOI = ''; LEGEND_CONSTANTS = '';
    LEGEND_VOI = strpad('time in component environment (minute)');
    LEGEND_STATES(:,1) = strpad('G in component G (mg_l)');
    LEGEND_CONSTANTS(:,1) = strpad('Vg in component G (litre)');
    LEGEND_CONSTANTS(:,2) = strpad('Gin in component G (mg_l_min)');
    LEGEND_ALGEBRAIC(:,1) = strpad('f2_G in component G (mg_min)');
    LEGEND_ALGEBRAIC(:,3) = strpad('f3_G in component G (per_l)');
    LEGEND_ALGEBRAIC(:,4) = strpad('f4_I in component G (mg_min)');
    LEGEND_ALGEBRAIC(:,5) = strpad('f5_I in component G (mg_min)');
    LEGEND_CONSTANTS(:,3) = strpad('C2 in component G (mg_l)');
    LEGEND_CONSTANTS(:,4) = strpad('C3 in component G (mg_l)');
    LEGEND_CONSTANTS(:,5) = strpad('C4 in component G (mU_l)');
    LEGEND_CONSTANTS(:,6) = strpad('C5 in component G (mU_l)');
    LEGEND_CONSTANTS(:,7) = strpad('U0 in component G (mg_min)');
    LEGEND_CONSTANTS(:,8) = strpad('Um in component G (mg_min)');
    LEGEND_CONSTANTS(:,9) = strpad('Ub in component G (mg_min)');
    LEGEND_CONSTANTS(:,10) = strpad('beta in component G (dimensionless)');
    LEGEND_CONSTANTS(:,11) = strpad('Rg in component G (mg_min)');
    LEGEND_CONSTANTS(:,12) = strpad('alpha in component G (l_mU)');
    LEGEND_CONSTANTS(:,13) = strpad('ti in component G (minute)');
    LEGEND_CONSTANTS(:,14) = strpad('E in component G (l_min)');
    LEGEND_CONSTANTS(:,15) = strpad('Vp in component G (litre)');
    LEGEND_CONSTANTS(:,16) = strpad('Vi in component G (litre)');
    LEGEND_STATES(:,2) = strpad('I in component I (mU_l)');
    LEGEND_ALGEBRAIC(:,2) = strpad('f1_G in component I (mU_min)');
    LEGEND_CONSTANTS(:,17) = strpad('Rm in component I (mU_min)');
    LEGEND_CONSTANTS(:,18) = strpad('C1 in component I (mg_l)');
    LEGEND_CONSTANTS(:,19) = strpad('a1 in component I (mg_l)');
    LEGEND_CONSTANTS(:,20) = strpad('di in component I (first_order_rate_constant)');
    LEGEND_RATES(:,1) = strpad('d/dt G in component G (mg_l)');
    LEGEND_RATES(:,2) = strpad('d/dt I in component I (mU_l)');
    LEGEND_STATES  = LEGEND_STATES';
    LEGEND_ALGEBRAIC = LEGEND_ALGEBRAIC';
    LEGEND_RATES = LEGEND_RATES';
    LEGEND_CONSTANTS = LEGEND_CONSTANTS';
end

function [STATES, CONSTANTS] = initConsts()
    VOI = 0; CONSTANTS = []; STATES = []; ALGEBRAIC = [];
    STATES(:,1) = 1000.0;
    CONSTANTS(:,1) = 10.0;
    CONSTANTS(:,2) = 0.54;
    CONSTANTS(:,3) = 144.0;
    CONSTANTS(:,4) = 1000.0;
    CONSTANTS(:,5) = 80.0;
    CONSTANTS(:,6) = 26.0;
    CONSTANTS(:,7) = 40.0;
    CONSTANTS(:,8) = 940.0;
    CONSTANTS(:,9) = 72.0;
    CONSTANTS(:,10) = 1.77;
    CONSTANTS(:,11) = 180.0;
    CONSTANTS(:,12) = 0.29;
    CONSTANTS(:,13) = 100;
    CONSTANTS(:,14) = 0.2;
    CONSTANTS(:,15) = 3.0;
    CONSTANTS(:,16) = 11.0;
    STATES(:,2) = 9000.0;
    CONSTANTS(:,17) = 210.0;
    CONSTANTS(:,18) = 2000.0;
    CONSTANTS(:,19) = 300.0;
    CONSTANTS(:,20) = 0.06;
    if (isempty(STATES)), warning('Initial values for states not set');, end
end

function [RATES, ALGEBRAIC] = computeRates(VOI, STATES, CONSTANTS)
    global algebraicVariableCount;
    statesSize = size(STATES);
    statesColumnCount = statesSize(2);
    if ( statesColumnCount == 1)
        STATES = STATES';
        ALGEBRAIC = zeros(1, algebraicVariableCount);
        utilOnes = 1;
    else
        statesRowCount = statesSize(1);
        ALGEBRAIC = zeros(statesRowCount, algebraicVariableCount);
        RATES = zeros(statesRowCount, statesColumnCount);
        utilOnes = ones(statesRowCount, 1);
    end
    ALGEBRAIC(:,2) = CONSTANTS(:,17)./(1.00000+exp(((CONSTANTS(:,18) - STATES(:,1))./( 1.00000.*CONSTANTS(:,1)))./CONSTANTS(:,19)));
    RATES(:,2) =  1.00000.*ALGEBRAIC(:,2) -  CONSTANTS(:,20).*STATES(:,2);
    ALGEBRAIC(:,1) =  CONSTANTS(:,9).*(1.00000 - exp( 1.00000.*( - STATES(:,1)./( CONSTANTS(:,3).*CONSTANTS(:,1)))));
    ALGEBRAIC(:,3) = STATES(:,1)./( CONSTANTS(:,4).*CONSTANTS(:,1));
    ALGEBRAIC(:,4) = CONSTANTS(:,7)+(CONSTANTS(:,8) - CONSTANTS(:,7))./(1.00000+exp(  - CONSTANTS(:,10).*log( 1.00000.*(STATES(:,2)./( CONSTANTS(:,5).*(1.00000./CONSTANTS(:,16)+1.00000./( CONSTANTS(:,14).*CONSTANTS(:,13))))))));
    ALGEBRAIC(:,5) = CONSTANTS(:,11)./(1.00000+exp( CONSTANTS(:,12).*(STATES(:,2)./( 1.00000.*CONSTANTS(:,15) -  1.00000.*CONSTANTS(:,6)))));
    RATES(:,1) = CONSTANTS(:,2)+ 1.00000.*ALGEBRAIC(:,5)+ - ( 1.00000.*ALGEBRAIC(:,1)+ ALGEBRAIC(:,3).*ALGEBRAIC(:,4));
   RATES = RATES';
end

% Calculate algebraic variables
function ALGEBRAIC = computeAlgebraic(ALGEBRAIC, CONSTANTS, STATES, VOI)
    statesSize = size(STATES);
    statesColumnCount = statesSize(2);
    if ( statesColumnCount == 1)
        STATES = STATES';
        utilOnes = 1;
    else
        statesRowCount = statesSize(1);
        utilOnes = ones(statesRowCount, 1);
    end
    ALGEBRAIC(:,2) = CONSTANTS(:,17)./(1.00000+exp(((CONSTANTS(:,18) - STATES(:,1))./( 1.00000.*CONSTANTS(:,1)))./CONSTANTS(:,19)));
    ALGEBRAIC(:,1) =  CONSTANTS(:,9).*(1.00000 - exp( 1.00000.*( - STATES(:,1)./( CONSTANTS(:,3).*CONSTANTS(:,1)))));
    ALGEBRAIC(:,3) = STATES(:,1)./( CONSTANTS(:,4).*CONSTANTS(:,1));
    ALGEBRAIC(:,4) = CONSTANTS(:,7)+(CONSTANTS(:,8) - CONSTANTS(:,7))./(1.00000+exp(  - CONSTANTS(:,10).*log( 1.00000.*(STATES(:,2)./( CONSTANTS(:,5).*(1.00000./CONSTANTS(:,16)+1.00000./( CONSTANTS(:,14).*CONSTANTS(:,13))))))));
    ALGEBRAIC(:,5) = CONSTANTS(:,11)./(1.00000+exp( CONSTANTS(:,12).*(STATES(:,2)./( 1.00000.*CONSTANTS(:,15) -  1.00000.*CONSTANTS(:,6)))));
end

% Pad out or shorten strings to a set length
function strout = strpad(strin)
    req_length = 160;
    insize = size(strin,2);
    if insize > req_length
        strout = strin(1:req_length);
    else
        strout = [strin, blanks(req_length - insize)];
    end
end