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 =2;
end
% There are a total of 7 entries in each of the rate and state variable arrays.
% There are a total of 13 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(:,10) = strpad('T in component T (per_ml)');
    LEGEND_CONSTANTS(:,1) = strpad('k in component kinetic_parameters (ml_per_day)');
    LEGEND_CONSTANTS(:,2) = strpad('p in component kinetic_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,3) = strpad('c in component kinetic_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,4) = strpad('delta in component kinetic_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,1) = strpad('I in component I (per_ml)');
    LEGEND_CONSTANTS(:,11) = strpad('I_0 in component I (per_ml)');
    LEGEND_CONSTANTS(:,12) = strpad('k_ in component kinetic_parameters (ml_per_day)');
    LEGEND_STATES(:,2) = strpad('E4 in component E4 (per_ml)');
    LEGEND_CONSTANTS(:,5) = strpad('VI_0 in component VI (per_ml)');
    LEGEND_STATES(:,3) = strpad('VI in component VI (per_ml)');
    LEGEND_ALGEBRAIC(:,1) = strpad('h in component Heavyside_function (dimensionless)');
    LEGEND_STATES(:,4) = strpad('VNI in component VNI (per_ml)');
    LEGEND_ALGEBRAIC(:,2) = strpad('V in component virus_total (per_ml)');
    LEGEND_STATES(:,5) = strpad('E1 in component E1 (per_ml)');
    LEGEND_CONSTANTS(:,13) = strpad('b_ in component kinetic_parameters (day)');
    LEGEND_STATES(:,6) = strpad('E2 in component E2 (per_ml)');
    LEGEND_STATES(:,7) = strpad('E3 in component E3 (per_ml)');
    LEGEND_CONSTANTS(:,6) = strpad('tau_p in component Heavyside_function (day)');
    LEGEND_CONSTANTS(:,7) = strpad('b in component kinetic_parameters (day)');
    LEGEND_CONSTANTS(:,8) = strpad('m in component kinetic_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,9) = strpad('n in component kinetic_parameters (dimensionless)');
    LEGEND_RATES(:,1) = strpad('d/dt I in component I (per_ml)');
    LEGEND_RATES(:,3) = strpad('d/dt VI in component VI (per_ml)');
    LEGEND_RATES(:,4) = strpad('d/dt VNI in component VNI (per_ml)');
    LEGEND_RATES(:,5) = strpad('d/dt E1 in component E1 (per_ml)');
    LEGEND_RATES(:,6) = strpad('d/dt E2 in component E2 (per_ml)');
    LEGEND_RATES(:,7) = strpad('d/dt E3 in component E3 (per_ml)');
    LEGEND_RATES(:,2) = strpad('d/dt E4 in component E4 (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) = 2.4e-5;
    CONSTANTS(:,2) = 774;
    CONSTANTS(:,3) = 3;
    CONSTANTS(:,4) = 0.5;
    STATES(:,1) = 0.1;
    STATES(:,2) = 0;
    CONSTANTS(:,5) = 200000;
    STATES(:,3) = 200000;
    STATES(:,4) = 0;
    STATES(:,5) = 0;
    STATES(:,6) = 0;
    STATES(:,7) = 0;
    CONSTANTS(:,6) = 0;
    CONSTANTS(:,7) = 0.25;
    CONSTANTS(:,8) = 0.01;
    CONSTANTS(:,9) = 4;
    CONSTANTS(:,10) = ( CONSTANTS(:,3).*CONSTANTS(:,4))./( CONSTANTS(:,1).*CONSTANTS(:,2));
    CONSTANTS(:,11) =  (CONSTANTS(:,3)./CONSTANTS(:,2)).*CONSTANTS(:,5);
    CONSTANTS(:,12) = CONSTANTS(:,1)./power(1.00000+ CONSTANTS(:,8).*CONSTANTS(:,7), CONSTANTS(:,9));
    CONSTANTS(:,13) = CONSTANTS(:,7)./(1.00000+ CONSTANTS(:,8).*CONSTANTS(:,7));
    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(:,12).*CONSTANTS(:,10).*STATES(:,2) -  CONSTANTS(:,4).*STATES(:,1);
    RATES(:,5) = (STATES(:,3) - STATES(:,5))./CONSTANTS(:,13);
    RATES(:,6) = (STATES(:,5) - STATES(:,6))./CONSTANTS(:,13);
    RATES(:,7) = (STATES(:,6) - STATES(:,7))./CONSTANTS(:,13);
    RATES(:,2) = (STATES(:,7) - STATES(:,2))./CONSTANTS(:,13);
    ALGEBRAIC(:,1) = piecewise({VOI<CONSTANTS(:,6), 0.00000 }, 1.00000);
    RATES(:,3) =  (1.00000 - ALGEBRAIC(:,1)).*CONSTANTS(:,2).*STATES(:,1) -  CONSTANTS(:,3).*STATES(:,3);
    RATES(:,4) =  ALGEBRAIC(:,1).*CONSTANTS(:,2).*STATES(:,1) -  CONSTANTS(:,3).*STATES(:,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(:,1) = piecewise({VOI<CONSTANTS(:,6), 0.00000 }, 1.00000);
    ALGEBRAIC(:,2) = STATES(:,3)+STATES(:,4);
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