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 5 entries in each of the rate and state variable arrays.
% There are a total of 15 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('lambda in component uninfected (per_ml_day)');
    LEGEND_CONSTANTS(:,2) = strpad('d_T in component uninfected (per_day)');
    LEGEND_CONSTANTS(:,3) = strpad('efficacy in component drug_efficacy (dimensionless)');
    LEGEND_CONSTANTS(:,4) = strpad('k in component uninfected (ml_per_day)');
    LEGEND_STATES(:,1) = strpad('V in component viral_load (per_ml)');
    LEGEND_STATES(:,2) = strpad('T in component uninfected (per_ml)');
    LEGEND_CONSTANTS(:,5) = strpad('eta in component latently_infected (dimensionless)');
    LEGEND_CONSTANTS(:,6) = strpad('d_0 in component latently_infected (per_day)');
    LEGEND_ALGEBRAIC(:,1) = strpad('f in component activated (dimensionless)');
    LEGEND_CONSTANTS(:,7) = strpad('a in component latently_infected (per_day)');
    LEGEND_CONSTANTS(:,8) = strpad('rho in component latently_infected (per_day)');
    LEGEND_STATES(:,3) = strpad('L_a in component activated (per_ml)');
    LEGEND_STATES(:,4) = strpad('L_0 in component latently_infected (per_ml)');
    LEGEND_CONSTANTS(:,9) = strpad('p in component activated (per_day)');
    LEGEND_CONSTANTS(:,10) = strpad('a_L in component activated (per_day)');
    LEGEND_CONSTANTS(:,11) = strpad('T_off in component activated (day)');
    LEGEND_CONSTANTS(:,12) = strpad('T_on in component activated (day)');
    LEGEND_CONSTANTS(:,13) = strpad('delta in component productively_infected (per_day)');
    LEGEND_STATES(:,5) = strpad('T_star in component productively_infected (per_ml)');
    LEGEND_CONSTANTS(:,14) = strpad('p_v in component viral_load (per_day)');
    LEGEND_CONSTANTS(:,15) = strpad('c in component viral_load (per_day)');
    LEGEND_RATES(:,2) = strpad('d/dt T in component uninfected (per_ml)');
    LEGEND_RATES(:,4) = strpad('d/dt L_0 in component latently_infected (per_ml)');
    LEGEND_RATES(:,3) = strpad('d/dt L_a in component activated (per_ml)');
    LEGEND_RATES(:,5) = strpad('d/dt T_star in component productively_infected (per_ml)');
    LEGEND_RATES(:,1) = strpad('d/dt V in component viral_load (per_ml)');
    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) = 1E4;
    CONSTANTS(:,2) = 0.01;
    CONSTANTS(:,3) = 0.85;
    CONSTANTS(:,4) = 2.4E-8;
    STATES(:,1) = 50;
    STATES(:,2) = 600000;
    CONSTANTS(:,5) = 0.001;
    CONSTANTS(:,6) = 0.001;
    CONSTANTS(:,7) = 0.03;
    CONSTANTS(:,8) = 0.01;
    STATES(:,3) = 0;
    STATES(:,4) = 2;
    CONSTANTS(:,9) = 1.4;
    CONSTANTS(:,10) = 0.1;
    CONSTANTS(:,11) = 54;
    CONSTANTS(:,12) = 50;
    CONSTANTS(:,13) = 1;
    STATES(:,5) = 0.3;
    CONSTANTS(:,14) = 2000;
    CONSTANTS(:,15) = 23;
    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)) -  (1.00000 - CONSTANTS(:,3)).*CONSTANTS(:,4).*STATES(:,1).*STATES(:,2);
    RATES(:,5) = ( (1.00000 - CONSTANTS(:,5)).*(1.00000 - CONSTANTS(:,3)).*CONSTANTS(:,4).*STATES(:,1).*STATES(:,2) -  1.00000.*CONSTANTS(:,13).*STATES(:,5).*STATES(:,5))+ CONSTANTS(:,10).*STATES(:,3);
    RATES(:,1) =  CONSTANTS(:,14).*STATES(:,5) -  CONSTANTS(:,15).*STATES(:,1);
    ALGEBRAIC(:,1) = piecewise({CONSTANTS(:,11)<VOI, 0.00000 , VOI<CONSTANTS(:,12), 0.00000 }, 1.00000);
    RATES(:,4) = (( CONSTANTS(:,5).*(1.00000 - CONSTANTS(:,3)).*CONSTANTS(:,4).*STATES(:,1).*STATES(:,2) -  CONSTANTS(:,6).*STATES(:,4)) -  ALGEBRAIC(:,1).*CONSTANTS(:,7).*STATES(:,4))+ (1.00000 - ALGEBRAIC(:,1)).*CONSTANTS(:,8).*STATES(:,3);
    RATES(:,3) = ( ALGEBRAIC(:,1).*( CONSTANTS(:,7).*STATES(:,4)+ CONSTANTS(:,9).*STATES(:,3)) -  (1.00000 - ALGEBRAIC(:,1)).*(CONSTANTS(:,7)+CONSTANTS(:,8)).*STATES(:,3)) -  CONSTANTS(:,10).*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) = piecewise({CONSTANTS(:,11)<VOI, 0.00000 , VOI<CONSTANTS(:,12), 0.00000 }, 1.00000);
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