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 2 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_CONSTANTS(:,1) = strpad('s in component uninfected (per_day_mm3)');
    LEGEND_CONSTANTS(:,2) = strpad('p in component uninfected (per_day)');
    LEGEND_CONSTANTS(:,3) = strpad('gamma in component uninfected (per_day)');
    LEGEND_CONSTANTS(:,14) = strpad('beta in component uninfected (dimensionless)');
    LEGEND_CONSTANTS(:,4) = strpad('N in component free_virus_particle (dimensionless)');
    LEGEND_CONSTANTS(:,5) = strpad('k_1 in component latently_infected (mm3_per_day)');
    LEGEND_CONSTANTS(:,6) = strpad('k_2 in component actively_infected (per_day)');
    LEGEND_CONSTANTS(:,7) = strpad('k_3 in component latently_infected (per_day)');
    LEGEND_CONSTANTS(:,8) = strpad('mu_V in component free_virus_particle (per_day)');
    LEGEND_STATES(:,1) = strpad('T_1 in component latently_infected (per_mm3)');
    LEGEND_CONSTANTS(:,9) = strpad('mu_b in component actively_infected (per_day)');
    LEGEND_STATES(:,2) = strpad('T in component uninfected (per_mm3)');
    LEGEND_CONSTANTS(:,10) = strpad('k_4 in component latently_infected (per_day)');
    LEGEND_CONSTANTS(:,11) = strpad('T_0 in component latently_infected (per_mm3)');
    LEGEND_CONSTANTS(:,12) = strpad('V_0 in component latently_infected (per_mm3)');
    LEGEND_CONSTANTS(:,13) = strpad('t_min in component latently_infected (day)');
    LEGEND_ALGEBRAIC(:,1) = strpad('T_1_t in component latently_infected (per_mm3)');
    LEGEND_ALGEBRAIC(:,2) = strpad('T_2 in component actively_infected (per_mm3)');
    LEGEND_ALGEBRAIC(:,3) = strpad('V in component free_virus_particle (per_mm3)');
    LEGEND_RATES(:,2) = strpad('d/dt T in component uninfected (per_mm3)');
    LEGEND_RATES(:,1) = strpad('d/dt T_1 in component latently_infected (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) = 0.01;
    CONSTANTS(:,3) = 2E-5;
    CONSTANTS(:,4) = 1000;
    CONSTANTS(:,5) = 2.4E-5;
    CONSTANTS(:,6) = 3E-3;
    CONSTANTS(:,7) = 0.023;
    CONSTANTS(:,8) = 2.4;
    STATES(:,1) = 0;
    CONSTANTS(:,9) = 0.24;
    STATES(:,2) = 1000;
    CONSTANTS(:,10) = 2.424;
    CONSTANTS(:,11) = 1000;
    CONSTANTS(:,12) = 1E-3;
    CONSTANTS(:,13) = 2;
    CONSTANTS(:,14) =  (CONSTANTS(:,3)./CONSTANTS(:,7)).*(1.00000+CONSTANTS(:,6)./CONSTANTS(:,9));
    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(:,2) = ((CONSTANTS(:,1)+ CONSTANTS(:,2).*STATES(:,2)) -  CONSTANTS(:,3).*power(STATES(:,2), 2.00000)) -  ( CONSTANTS(:,7).*CONSTANTS(:,14)+( CONSTANTS(:,4).*CONSTANTS(:,5).*CONSTANTS(:,6))./( CONSTANTS(:,5).*STATES(:,2)+CONSTANTS(:,8))).*STATES(:,2).*STATES(:,1);
    ALGEBRAIC(:,1) =  (( CONSTANTS(:,5).*CONSTANTS(:,11).*CONSTANTS(:,12))./(CONSTANTS(:,10) - CONSTANTS(:,7))).*(exp(  - CONSTANTS(:,7).*VOI) - exp(  - CONSTANTS(:,10).*VOI));
    RATES(:,1) = piecewise({VOI<=CONSTANTS(:,13), ALGEBRAIC(:,1) },  (( CONSTANTS(:,4).*CONSTANTS(:,5).*CONSTANTS(:,6))./( CONSTANTS(:,5).*STATES(:,2)+CONSTANTS(:,8))).*STATES(:,2).*STATES(:,1) -  CONSTANTS(:,7).*STATES(:,1));
   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) =  (( CONSTANTS(:,5).*CONSTANTS(:,11).*CONSTANTS(:,12))./(CONSTANTS(:,10) - CONSTANTS(:,7))).*(exp(  - CONSTANTS(:,7).*VOI) - exp(  - CONSTANTS(:,10).*VOI));
    ALGEBRAIC(:,2) = ( CONSTANTS(:,6).*STATES(:,1))./CONSTANTS(:,9);
    ALGEBRAIC(:,3) = ( CONSTANTS(:,4).*CONSTANTS(:,6).*STATES(:,1))./( CONSTANTS(:,5).*STATES(:,2)+CONSTANTS(:,8));
end

% Compute result of a piecewise function
function x = piecewise(cases, default)
    set = [0];
    for i = 1:2:length(cases)
        if (length(cases{i+1}) == 1)
            x(cases{i} & ~set,:) = cases{i+1};
        else
            x(cases{i} & ~set,:) = cases{i+1}(cases{i} & ~set);
        end
        set = set | cases{i};
        if(set), break, end
    end
    if (length(default) == 1)
        x(~set,:) = default;
    else
        x(~set,:) = default(~set);
    end
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