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 =1;
end
% There are a total of 4 entries in each of the rate and state variable arrays.
% There are a total of 9 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_CONSTANTS(:,1) = strpad('s in component uninfected (per_day_mm3)');
    LEGEND_CONSTANTS(:,2) = strpad('r in component uninfected (per_day)');
    LEGEND_CONSTANTS(:,3) = strpad('T_max in component uninfected (per_mm3)');
    LEGEND_CONSTANTS(:,4) = strpad('mu_T in component uninfected (per_day)');
    LEGEND_CONSTANTS(:,5) = strpad('k_1 in component latently_infected (mm3_per_day)');
    LEGEND_STATES(:,1) = strpad('T_1 in component latently_infected (per_mm3)');
    LEGEND_STATES(:,2) = strpad('T_2 in component actively_infected (per_mm3)');
    LEGEND_STATES(:,3) = strpad('V in component free_virus_particle (per_mm3)');
    LEGEND_STATES(:,4) = strpad('T in component uninfected (per_mm3)');
    LEGEND_CONSTANTS(:,6) = strpad('k_2 in component actively_infected (per_day)');
    LEGEND_CONSTANTS(:,7) = strpad('mu_b in component actively_infected (per_day)');
    LEGEND_CONSTANTS(:,8) = strpad('mu_V in component free_virus_particle (per_day)');
    LEGEND_CONSTANTS(:,9) = strpad('N in component free_virus_particle (dimensionless)');
    LEGEND_ALGEBRAIC(:,1) = strpad('T_tot in component T_cell_population (per_mm3)');
    LEGEND_RATES(:,4) = strpad('d/dt T in component uninfected (per_mm3)');
    LEGEND_RATES(:,1) = strpad('d/dt T_1 in component latently_infected (per_mm3)');
    LEGEND_RATES(:,2) = strpad('d/dt T_2 in component actively_infected (per_mm3)');
    LEGEND_RATES(:,3) = strpad('d/dt V in component free_virus_particle (per_mm3)');
    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 = [];
    CONSTANTS(:,1) = 10;
    CONSTANTS(:,2) = 0.03;
    CONSTANTS(:,3) = 1500;
    CONSTANTS(:,4) = 0.02;
    CONSTANTS(:,5) = 2.4E-5;
    STATES(:,1) = 0;
    STATES(:,2) = 0;
    STATES(:,3) = 1.0E-3;
    STATES(:,4) = 1000;
    CONSTANTS(:,6) = 3E-3;
    CONSTANTS(:,7) = 0.24;
    CONSTANTS(:,8) = 2.4;
    CONSTANTS(:,9) = 1400;
    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(:,4) = ((CONSTANTS(:,1) -  CONSTANTS(:,4).*STATES(:,4))+ CONSTANTS(:,2).*STATES(:,4).*(1.00000 - (STATES(:,4)+STATES(:,1)+STATES(:,2))./CONSTANTS(:,3))) -  CONSTANTS(:,5).*STATES(:,3).*STATES(:,4);
    RATES(:,1) = ( CONSTANTS(:,5).*STATES(:,3).*STATES(:,4) -  CONSTANTS(:,4).*STATES(:,1)) -  CONSTANTS(:,6).*STATES(:,1);
    RATES(:,2) =  CONSTANTS(:,6).*STATES(:,1) -  CONSTANTS(:,7).*STATES(:,2);
    RATES(:,3) = ( CONSTANTS(:,9).*CONSTANTS(:,7).*STATES(:,2) -  CONSTANTS(:,5).*STATES(:,3).*STATES(:,4)) -  CONSTANTS(:,8).*STATES(:,3);
   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(:,1) = STATES(:,4)+STATES(:,1)+STATES(:,2);
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