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 =9;
end
% There are a total of 2 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 (hour)');
    LEGEND_CONSTANTS(:,1) = strpad('Ado in component Ado (micromolar)');
    LEGEND_ALGEBRAIC(:,1) = strpad('Met in component Met (micromolar)');
    LEGEND_ALGEBRAIC(:,2) = strpad('Hcy in component Hcy (micromolar)');
    LEGEND_STATES(:,1) = strpad('AdoHcy in component AdoHcy (micromolar)');
    LEGEND_CONSTANTS(:,2) = strpad('K_AHC in component K_AHC (micromolar)');
    LEGEND_STATES(:,2) = strpad('AdoMet in component AdoMet (micromolar)');
    LEGEND_ALGEBRAIC(:,7) = strpad('V_MET in component V_MET (flux)');
    LEGEND_ALGEBRAIC(:,8) = strpad('V_GNMT in component V_GNMT (flux)');
    LEGEND_ALGEBRAIC(:,3) = strpad('V_MATI in component V_MATI (flux)');
    LEGEND_ALGEBRAIC(:,5) = strpad('V_MATIII in component V_MATIII (flux)');
    LEGEND_ALGEBRAIC(:,9) = strpad('V_D in component V_D (flux)');
    LEGEND_CONSTANTS(:,3) = strpad('V_MATImax in component V_MATI (flux)');
    LEGEND_CONSTANTS(:,4) = strpad('Km_MATI in component V_MATI (micromolar)');
    LEGEND_CONSTANTS(:,5) = strpad('Ki_MATI in component V_MATI (micromolar)');
    LEGEND_CONSTANTS(:,6) = strpad('V_MATIIImax in component V_MATIII (flux)');
    LEGEND_ALGEBRAIC(:,4) = strpad('Km1_MATIII in component V_MATIII (micromolar)');
    LEGEND_CONSTANTS(:,7) = strpad('Km2_MATIII in component V_MATIII (micromolar)');
    LEGEND_CONSTANTS(:,8) = strpad('V_METmax in component V_MET (flux)');
    LEGEND_ALGEBRAIC(:,6) = strpad('Km1_MET in component V_MET (micromolar)');
    LEGEND_CONSTANTS(:,9) = strpad('Km2_MET_A in component V_MET (dimensionless)');
    LEGEND_CONSTANTS(:,10) = strpad('V_GNMTmax in component V_GNMT (flux)');
    LEGEND_CONSTANTS(:,11) = strpad('Km_GNMT in component V_GNMT (micromolar)');
    LEGEND_CONSTANTS(:,12) = strpad('Ki_GNMT in component V_GNMT (micromolar)');
    LEGEND_CONSTANTS(:,13) = strpad('alpha_d in component V_D (first_order_rate_constant)');
    LEGEND_RATES(:,2) = strpad('d/dt AdoMet in component AdoMet (micromolar)');
    LEGEND_RATES(:,1) = strpad('d/dt AdoHcy in component AdoHcy (micromolar)');
    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) = 1;
    STATES(:,1) = 3;
    CONSTANTS(:,2) = 0.1;
    STATES(:,2) = 60;
    CONSTANTS(:,3) = 561;
    CONSTANTS(:,4) = 41;
    CONSTANTS(:,5) = 50;
    CONSTANTS(:,6) = 22870;
    CONSTANTS(:,7) = 21.1;
    CONSTANTS(:,8) = 4544;
    CONSTANTS(:,9) = 10;
    CONSTANTS(:,10) = 10600;
    CONSTANTS(:,11) = 4500;
    CONSTANTS(:,12) = 20;
    CONSTANTS(:,13) = 1333;
    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(:,6) =  10.0000.*(1.00000+STATES(:,1)./4.00000);
    ALGEBRAIC(:,7) = CONSTANTS(:,8)./(1.00000+ALGEBRAIC(:,6)./STATES(:,2)+CONSTANTS(:,9)+( CONSTANTS(:,9).*ALGEBRAIC(:,6))./STATES(:,2));
    ALGEBRAIC(:,8) = ( (CONSTANTS(:,10)./(1.00000+power(CONSTANTS(:,11)./STATES(:,2), 2.30000))).*1.00000)./(1.00000+STATES(:,1)./CONSTANTS(:,12));
    ALGEBRAIC(:,1) = piecewise({VOI>=0.00000&VOI<5.00000, 45.0000 , VOI>=5.00000&VOI<15.0000, 52.0000 , VOI>=15.0000&VOI<60.0000, 55.0000 , VOI>=60.0000&VOI<75.0000, 52.0000 , VOI>=75.0000, 45.0000 }, NaN);
    ALGEBRAIC(:,3) = CONSTANTS(:,3)./(1.00000+ (CONSTANTS(:,4)./ALGEBRAIC(:,1)).*(1.00000+STATES(:,2)./CONSTANTS(:,5)));
    ALGEBRAIC(:,4) = 20000.0./(1.00000+ 5.70000.*power(STATES(:,2)./(STATES(:,2)+600.000), 2.00000));
    ALGEBRAIC(:,5) = CONSTANTS(:,6)./(1.00000+( ALGEBRAIC(:,4).*CONSTANTS(:,7))./(power(ALGEBRAIC(:,1), 2.00000)+ ALGEBRAIC(:,1).*CONSTANTS(:,7)));
    RATES(:,2) = (ALGEBRAIC(:,3)+ALGEBRAIC(:,5)) - (ALGEBRAIC(:,7)+ALGEBRAIC(:,8));
    ALGEBRAIC(:,2) = ( STATES(:,1).*CONSTANTS(:,2))./CONSTANTS(:,1);
    ALGEBRAIC(:,9) =  CONSTANTS(:,13).*ALGEBRAIC(:,2);
    RATES(:,1) = ((ALGEBRAIC(:,7)+ALGEBRAIC(:,8)) - ALGEBRAIC(:,9))./(1.00000+CONSTANTS(:,2)./CONSTANTS(:,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(:,6) =  10.0000.*(1.00000+STATES(:,1)./4.00000);
    ALGEBRAIC(:,7) = CONSTANTS(:,8)./(1.00000+ALGEBRAIC(:,6)./STATES(:,2)+CONSTANTS(:,9)+( CONSTANTS(:,9).*ALGEBRAIC(:,6))./STATES(:,2));
    ALGEBRAIC(:,8) = ( (CONSTANTS(:,10)./(1.00000+power(CONSTANTS(:,11)./STATES(:,2), 2.30000))).*1.00000)./(1.00000+STATES(:,1)./CONSTANTS(:,12));
    ALGEBRAIC(:,1) = piecewise({VOI>=0.00000&VOI<5.00000, 45.0000 , VOI>=5.00000&VOI<15.0000, 52.0000 , VOI>=15.0000&VOI<60.0000, 55.0000 , VOI>=60.0000&VOI<75.0000, 52.0000 , VOI>=75.0000, 45.0000 }, NaN);
    ALGEBRAIC(:,3) = CONSTANTS(:,3)./(1.00000+ (CONSTANTS(:,4)./ALGEBRAIC(:,1)).*(1.00000+STATES(:,2)./CONSTANTS(:,5)));
    ALGEBRAIC(:,4) = 20000.0./(1.00000+ 5.70000.*power(STATES(:,2)./(STATES(:,2)+600.000), 2.00000));
    ALGEBRAIC(:,5) = CONSTANTS(:,6)./(1.00000+( ALGEBRAIC(:,4).*CONSTANTS(:,7))./(power(ALGEBRAIC(:,1), 2.00000)+ ALGEBRAIC(:,1).*CONSTANTS(:,7)));
    ALGEBRAIC(:,2) = ( STATES(:,1).*CONSTANTS(:,2))./CONSTANTS(:,1);
    ALGEBRAIC(:,9) =  CONSTANTS(:,13).*ALGEBRAIC(:,2);
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