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 =6;
end
% There are a total of 2 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 (minute)');
    LEGEND_STATES(:,1) = strpad('G in component G (mg_per_litre)');
    LEGEND_ALGEBRAIC(:,1) = strpad('Gin in component G (mg_per_litre_minute)');
    LEGEND_ALGEBRAIC(:,3) = strpad('f2_G in component f2_G (mg_per_minute)');
    LEGEND_ALGEBRAIC(:,4) = strpad('f3_G in component f3_G (per_litre)');
    LEGEND_ALGEBRAIC(:,5) = strpad('f4_I in component f4_I (mg_per_minute)');
    LEGEND_ALGEBRAIC(:,6) = strpad('f5_I in component f5_I (mg_per_minute)');
    LEGEND_STATES(:,2) = strpad('I in component I (mU_per_litre)');
    LEGEND_ALGEBRAIC(:,2) = strpad('Iin in component I (mU_per_litre_minute)');
    LEGEND_CONSTANTS(:,1) = strpad('di in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,2) = strpad('C2 in component model_parameters (mg_per_litre)');
    LEGEND_CONSTANTS(:,3) = strpad('Ub in component model_parameters (mg_per_minute)');
    LEGEND_CONSTANTS(:,4) = strpad('Vg in component model_parameters (litre)');
    LEGEND_CONSTANTS(:,5) = strpad('C3 in component model_parameters (mg_per_litre)');
    LEGEND_CONSTANTS(:,6) = strpad('C4 in component model_parameters (mU_per_litre)');
    LEGEND_CONSTANTS(:,7) = strpad('Vi in component model_parameters (litre)');
    LEGEND_CONSTANTS(:,8) = strpad('U0 in component model_parameters (mg_per_minute)');
    LEGEND_CONSTANTS(:,9) = strpad('Um in component model_parameters (mg_per_minute)');
    LEGEND_CONSTANTS(:,10) = strpad('beta in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,11) = strpad('ti in component model_parameters (minute)');
    LEGEND_CONSTANTS(:,12) = strpad('Vp in component model_parameters (litre)');
    LEGEND_CONSTANTS(:,13) = strpad('C5 in component model_parameters (mU_per_litre)');
    LEGEND_CONSTANTS(:,14) = strpad('Rg in component model_parameters (mg_per_minute)');
    LEGEND_CONSTANTS(:,15) = strpad('alpha in component model_parameters (litre_per_mU)');
    LEGEND_RATES(:,1) = strpad('d/dt G in component G (mg_per_litre)');
    LEGEND_RATES(:,2) = strpad('d/dt I in component I (mU_per_litre)');
    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) = 150.0;
    STATES(:,2) = 5.0;
    CONSTANTS(:,1) = 0.0107;
    CONSTANTS(:,2) = 144;
    CONSTANTS(:,3) = 72.0;
    CONSTANTS(:,4) = 10.0;
    CONSTANTS(:,5) = 1000.0;
    CONSTANTS(:,6) = 80.0;
    CONSTANTS(:,7) = 11.0;
    CONSTANTS(:,8) = 40.0;
    CONSTANTS(:,9) = 940.0;
    CONSTANTS(:,10) = 1.77;
    CONSTANTS(:,11) = 100.0;
    CONSTANTS(:,12) = 3.0;
    CONSTANTS(:,13) = 26.0;
    CONSTANTS(:,14) = 180.0;
    CONSTANTS(:,15) = 0.29;
    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
    ALGEBRAIC(:,2) = piecewise({VOI<=30.0000&VOI>=0.00000, 0.250000 , VOI<120.000&VOI>=30.0000, 0.250000+ 1.00000.*(1.00000+(VOI - 120.000)./90.0000) , VOI<240.000&VOI>=120.000, 0.250000+ 1.00000.*(1.00000 -  0.500000.*((VOI - 120.000)./120.000)) , VOI<=480.000&VOI>=240.000, 0.250000+ 0.500000.*(1.00000 - (VOI - 240.000)./240.000) , VOI<530.000&VOI>480.000, 0.250000 , VOI<620.000&VOI>=530.000, 0.250000+ 1.00000.*(1.00000+(VOI - 620.000)./90.0000) , VOI<740.000&VOI>=620.000, 0.250000+ 1.00000.*(1.00000 -  0.500000.*((VOI - 620.000)./120.000)) , VOI<=980.000&VOI>=740.000, 0.250000+ 0.500000.*(1.00000 - (VOI - 740.000)./240.000) }, NaN);
    RATES(:,2) = ALGEBRAIC(:,2) -  CONSTANTS(:,1).*STATES(:,2);
    ALGEBRAIC(:,1) = piecewise({VOI<15.0000&VOI>=0.00000, 0.0500000+ (5.00000./15.0000).*VOI , VOI<45.0000&VOI>=15.0000, 0.0500000+ 5.00000.*((45.0000 - VOI)./(45.0000 - 15.0000)) , VOI<=240.000&VOI>=45.0000, 0.0500000 , VOI>240.000&VOI<255.000, 0.0500000+ (5.00000./255.000).*VOI , VOI<285.000&VOI>=255.000, 0.0500000+ 5.00000.*((285.000 - VOI)./(285.000 - 255.000)) , VOI<=480.000&VOI>=285.000, 0.0500000 , VOI<495.000&VOI>480.000, 0.0500000+ (5.00000./495.000).*VOI , VOI<525.000&VOI>=495.000, 0.0500000+ 5.00000.*((525.000 - VOI)./(525.000 - 495.000)) , VOI<=720.000&VOI>=525.000, 0.0500000 , VOI>720.000&VOI<735.000, 0.0500000+ (5.00000./735.000).*VOI , VOI<765.000&VOI>=735.000, 0.0500000+ 5.00000.*((765.000 - VOI)./(765.000 - 735.000)) , VOI<=960.000&VOI>=765.000, 0.0500000 }, NaN);
    ALGEBRAIC(:,3) =  CONSTANTS(:,3).*(1.00000 - exp( - STATES(:,1)./( CONSTANTS(:,2).*CONSTANTS(:,4).*1.00000)));
    ALGEBRAIC(:,4) = STATES(:,1)./( CONSTANTS(:,5).*CONSTANTS(:,4));
    ALGEBRAIC(:,5) = CONSTANTS(:,8)+(CONSTANTS(:,9) - CONSTANTS(:,8))./(1.00000+exp(  - CONSTANTS(:,10).*log(STATES(:,2)./( CONSTANTS(:,6).*(1.00000./CONSTANTS(:,7)+1.00000./( 0.200000.*CONSTANTS(:,11)))))));
    ALGEBRAIC(:,6) = CONSTANTS(:,14)./(1.00000+exp( CONSTANTS(:,15).*(STATES(:,2)./( 1.00000.*( 1.00000.*CONSTANTS(:,12) - CONSTANTS(:,13))))));
    RATES(:,1) = (ALGEBRAIC(:,1)+ 1.00000.*ALGEBRAIC(:,6)) - ( 1.00000.*ALGEBRAIC(:,3)+ ALGEBRAIC(:,4).*ALGEBRAIC(:,5));
   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(:,2) = piecewise({VOI<=30.0000&VOI>=0.00000, 0.250000 , VOI<120.000&VOI>=30.0000, 0.250000+ 1.00000.*(1.00000+(VOI - 120.000)./90.0000) , VOI<240.000&VOI>=120.000, 0.250000+ 1.00000.*(1.00000 -  0.500000.*((VOI - 120.000)./120.000)) , VOI<=480.000&VOI>=240.000, 0.250000+ 0.500000.*(1.00000 - (VOI - 240.000)./240.000) , VOI<530.000&VOI>480.000, 0.250000 , VOI<620.000&VOI>=530.000, 0.250000+ 1.00000.*(1.00000+(VOI - 620.000)./90.0000) , VOI<740.000&VOI>=620.000, 0.250000+ 1.00000.*(1.00000 -  0.500000.*((VOI - 620.000)./120.000)) , VOI<=980.000&VOI>=740.000, 0.250000+ 0.500000.*(1.00000 - (VOI - 740.000)./240.000) }, NaN);
    ALGEBRAIC(:,1) = piecewise({VOI<15.0000&VOI>=0.00000, 0.0500000+ (5.00000./15.0000).*VOI , VOI<45.0000&VOI>=15.0000, 0.0500000+ 5.00000.*((45.0000 - VOI)./(45.0000 - 15.0000)) , VOI<=240.000&VOI>=45.0000, 0.0500000 , VOI>240.000&VOI<255.000, 0.0500000+ (5.00000./255.000).*VOI , VOI<285.000&VOI>=255.000, 0.0500000+ 5.00000.*((285.000 - VOI)./(285.000 - 255.000)) , VOI<=480.000&VOI>=285.000, 0.0500000 , VOI<495.000&VOI>480.000, 0.0500000+ (5.00000./495.000).*VOI , VOI<525.000&VOI>=495.000, 0.0500000+ 5.00000.*((525.000 - VOI)./(525.000 - 495.000)) , VOI<=720.000&VOI>=525.000, 0.0500000 , VOI>720.000&VOI<735.000, 0.0500000+ (5.00000./735.000).*VOI , VOI<765.000&VOI>=735.000, 0.0500000+ 5.00000.*((765.000 - VOI)./(765.000 - 735.000)) , VOI<=960.000&VOI>=765.000, 0.0500000 }, NaN);
    ALGEBRAIC(:,3) =  CONSTANTS(:,3).*(1.00000 - exp( - STATES(:,1)./( CONSTANTS(:,2).*CONSTANTS(:,4).*1.00000)));
    ALGEBRAIC(:,4) = STATES(:,1)./( CONSTANTS(:,5).*CONSTANTS(:,4));
    ALGEBRAIC(:,5) = CONSTANTS(:,8)+(CONSTANTS(:,9) - CONSTANTS(:,8))./(1.00000+exp(  - CONSTANTS(:,10).*log(STATES(:,2)./( CONSTANTS(:,6).*(1.00000./CONSTANTS(:,7)+1.00000./( 0.200000.*CONSTANTS(:,11)))))));
    ALGEBRAIC(:,6) = CONSTANTS(:,14)./(1.00000+exp( CONSTANTS(:,15).*(STATES(:,2)./( 1.00000.*( 1.00000.*CONSTANTS(:,12) - CONSTANTS(:,13))))));
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