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 =3;
end
% There are a total of 5 entries in each of the rate and state variable arrays.
% There are a total of 14 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 (day)');
    LEGEND_STATES(:,1) = strpad('X in component X (dimensionless)');
    LEGEND_CONSTANTS(:,1) = strpad('mu0 in component X (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,2) = strpad('lamda in component X (first_order_rate_constant)');
    LEGEND_STATES(:,2) = strpad('K in component K (first_order_rate_constant)');
    LEGEND_STATES(:,3) = strpad('V in component V (dimensionless)');
    LEGEND_STATES(:,4) = strpad('Y in component Y (dimensionless)');
    LEGEND_CONSTANTS(:,3) = strpad('mu1 in component Y (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,4) = strpad('a in component Y (dimensionless)');
    LEGEND_STATES(:,5) = strpad('Z in component Z (dimensionless)');
    LEGEND_ALGEBRAIC(:,1) = strpad('CD4 in component CD4 (dimensionless)');
    LEGEND_CONSTANTS(:,5) = strpad('mu2 in component V (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,6) = strpad('beta in component V (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,7) = strpad('b in component V (dimensionless)');
    LEGEND_CONSTANTS(:,8) = strpad('theta in component Z (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,9) = strpad('rho in component Z (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,2) = strpad('f_X in component Z (dimensionless)');
    LEGEND_ALGEBRAIC(:,3) = strpad('g_V in component Z (dimensionless)');
    LEGEND_CONSTANTS(:,10) = strpad('C1 in component Z (dimensionless)');
    LEGEND_CONSTANTS(:,11) = strpad('C2 in component Z (dimensionless)');
    LEGEND_CONSTANTS(:,12) = strpad('X0 in component Z (dimensionless)');
    LEGEND_CONSTANTS(:,13) = strpad('omega in component K (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,14) = strpad('Kmax in component K (first_order_rate_constant)');
    LEGEND_RATES(:,1) = strpad('d/dt X in component X (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt Y in component Y (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt V in component V (dimensionless)');
    LEGEND_RATES(:,5) = strpad('d/dt Z in component Z (dimensionless)');
    LEGEND_RATES(:,2) = strpad('d/dt K in component K (first_order_rate_constant)');
    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) = 1.0E11;
    CONSTANTS(:,1) = 4.0E-3;
    CONSTANTS(:,2) = 4.0E8;
    STATES(:,2) = 1.35E-14;
    STATES(:,3) = 1.0;
    STATES(:,4) = 1.0;
    CONSTANTS(:,3) = 0.30;
    CONSTANTS(:,4) = 1.0;
    STATES(:,5) = 0.0;
    CONSTANTS(:,5) = 1.0;
    CONSTANTS(:,6) = 1.0E3;
    CONSTANTS(:,7) = 1.0;
    CONSTANTS(:,8) = 1.0E-6;
    CONSTANTS(:,9) = 0.50;
    CONSTANTS(:,10) = 0.04;
    CONSTANTS(:,11) = 1.0E3;
    CONSTANTS(:,12) = 1.0E11;
    CONSTANTS(:,13) = 1.0E-16;
    CONSTANTS(:,14) = 20.0;
    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
    RATES(:,1) = CONSTANTS(:,2) - ( CONSTANTS(:,1).*STATES(:,1)+ STATES(:,2).*STATES(:,3).*STATES(:,1));
    RATES(:,4) =  STATES(:,2).*STATES(:,3).*STATES(:,4) -  CONSTANTS(:,3).*(1.00000+ CONSTANTS(:,4).*STATES(:,5)).*STATES(:,4);
    RATES(:,3) =  CONSTANTS(:,6).*STATES(:,4) -  CONSTANTS(:,5).*(1.00000+ CONSTANTS(:,7).*STATES(:,5)).*STATES(:,3);
    RATES(:,2) =  CONSTANTS(:,13).*STATES(:,3).*(CONSTANTS(:,14) - STATES(:,2));
    ALGEBRAIC(:,2) = ( (1.00000+CONSTANTS(:,10)).*power(STATES(:,1)./CONSTANTS(:,12), 2.00000))./(CONSTANTS(:,10)+power(STATES(:,1)./CONSTANTS(:,12), 2.00000));
    ALGEBRAIC(:,3) = STATES(:,3)./(CONSTANTS(:,11)+STATES(:,3));
    RATES(:,5) =  CONSTANTS(:,8).*ALGEBRAIC(:,3)+ CONSTANTS(:,9).*(ALGEBRAIC(:,2) - STATES(:,5)).*STATES(:,5);
   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) = ( (1.00000+CONSTANTS(:,10)).*power(STATES(:,1)./CONSTANTS(:,12), 2.00000))./(CONSTANTS(:,10)+power(STATES(:,1)./CONSTANTS(:,12), 2.00000));
    ALGEBRAIC(:,3) = STATES(:,3)./(CONSTANTS(:,11)+STATES(:,3));
    ALGEBRAIC(:,1) = (STATES(:,1)+STATES(:,4))./1.00000e+11;
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