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 3 entries in each of the rate and state variable arrays.
% There are a total of 11 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 (hour)');
    LEGEND_STATES(:,1) = strpad('PRL in component PRL (nanog_ml)');
    LEGEND_CONSTANTS(:,1) = strpad('kD in component PRL (nanog_ml)');
    LEGEND_CONSTANTS(:,2) = strpad('kO in component PRL (picog_ml)');
    LEGEND_CONSTANTS(:,3) = strpad('rP in component PRL (nanog_ml_hr)');
    LEGEND_CONSTANTS(:,4) = strpad('qP in component PRL (first_order_rate_constant)');
    LEGEND_STATES(:,2) = strpad('OT in component OT (picog_ml)');
    LEGEND_STATES(:,3) = strpad('DA in component DA (nanog_ml)');
    LEGEND_ALGEBRAIC(:,1) = strpad('vD in component DA (nanog_ml_hr)');
    LEGEND_CONSTANTS(:,5) = strpad('vDbar in component DA (nanog_ml_hr)');
    LEGEND_CONSTANTS(:,6) = strpad('DA_infinity in component DA (nanog_ml)');
    LEGEND_CONSTANTS(:,7) = strpad('qD in component DA (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,8) = strpad('kx in component OT (picog_ml)');
    LEGEND_ALGEBRAIC(:,2) = strpad('vO in component OT (picog_ml_hr)');
    LEGEND_CONSTANTS(:,9) = strpad('vObar in component OT (picog_ml_hr)');
    LEGEND_CONSTANTS(:,10) = strpad('rO in component OT (picog_ml_hr)');
    LEGEND_CONSTANTS(:,11) = strpad('qO in component OT (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,3) = strpad('x in component x (picog_ml)');
    LEGEND_RATES(:,1) = strpad('d/dt PRL in component PRL (nanog_ml)');
    LEGEND_RATES(:,3) = strpad('d/dt DA in component DA (nanog_ml)');
    LEGEND_RATES(:,2) = strpad('d/dt OT in component OT (picog_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 = [];
    STATES(:,1) = 20.0;
    CONSTANTS(:,1) = 300.0;
    CONSTANTS(:,2) = 9.0;
    CONSTANTS(:,3) = 300000.0;
    CONSTANTS(:,4) = 0.5;
    STATES(:,2) = 25.0;
    STATES(:,3) = 20000.0;
    CONSTANTS(:,5) = 10000.0;
    CONSTANTS(:,6) = 20000.0;
    CONSTANTS(:,7) = 0.2;
    CONSTANTS(:,8) = 50.0;
    CONSTANTS(:,9) = 500.0;
    CONSTANTS(:,10) = 1100.0;
    CONSTANTS(:,11) = 1.0;
    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(:,3).*(1.00000./(CONSTANTS(:,1)+STATES(:,3))).*power(STATES(:,2)./(CONSTANTS(:,2)+STATES(:,2)), 2.00000) -  CONSTANTS(:,4).*STATES(:,1);
    ALGEBRAIC(:,1) = piecewise({VOI>=2.00000&VOI<=4.00000, CONSTANTS(:,5) }, 0.00000);
    RATES(:,3) =  CONSTANTS(:,7).*(CONSTANTS(:,6) - STATES(:,3)) - ALGEBRAIC(:,1);
    ALGEBRAIC(:,2) = piecewise({VOI>=2.00000&VOI<=4.00000, CONSTANTS(:,9) }, 0.00000);
    ALGEBRAIC(:,3) = piecewise({VOI>=2.00000&VOI<=4.00000, 51.0000 , VOI>=16.0000&VOI<=18.0000, 51.0000 }, 1.00000);
    RATES(:,2) =  CONSTANTS(:,10).*(ALGEBRAIC(:,3)./(CONSTANTS(:,8)+ALGEBRAIC(:,3))) - ( CONSTANTS(:,11).*STATES(:,2)+ALGEBRAIC(:,2));
   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>=2.00000&VOI<=4.00000, CONSTANTS(:,5) }, 0.00000);
    ALGEBRAIC(:,2) = piecewise({VOI>=2.00000&VOI<=4.00000, CONSTANTS(:,9) }, 0.00000);
    ALGEBRAIC(:,3) = piecewise({VOI>=2.00000&VOI<=4.00000, 51.0000 , VOI>=16.0000&VOI<=18.0000, 51.0000 }, 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