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 =11;
end
% There are a total of 4 entries in each of the rate and state variable arrays.
% There are a total of 21 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_ALGEBRAIC(:,1) = strpad('Metin in component environment (flux)');
    LEGEND_STATES(:,1) = strpad('Met in component Met (micromolar)');
    LEGEND_ALGEBRAIC(:,8) = strpad('V_MS in component V_MS (flux)');
    LEGEND_ALGEBRAIC(:,11) = strpad('V_BHMT in component V_BHMT (flux)');
    LEGEND_ALGEBRAIC(:,2) = strpad('V_MATI in component V_MATI (flux)');
    LEGEND_ALGEBRAIC(:,4) = strpad('V_MATIII in component V_MATIII (flux)');
    LEGEND_STATES(:,2) = strpad('AdoMet in component AdoMet (micromolar)');
    LEGEND_ALGEBRAIC(:,7) = strpad('V_METH in component V_METH (flux)');
    LEGEND_ALGEBRAIC(:,5) = strpad('V_GNMT in component V_GNMT (flux)');
    LEGEND_STATES(:,3) = strpad('AdoHcy in component AdoHcy (micromolar)');
    LEGEND_ALGEBRAIC(:,9) = strpad('V_AH in component V_AH (flux)');
    LEGEND_STATES(:,4) = strpad('Hcy in component Hcy (micromolar)');
    LEGEND_ALGEBRAIC(:,10) = strpad('V_CBS in component V_CBS (flux)');
    LEGEND_CONSTANTS(:,1) = strpad('V_MATImax in component V_MATI (flux)');
    LEGEND_CONSTANTS(:,2) = strpad('Km_MATI in component V_MATI (micromolar)');
    LEGEND_CONSTANTS(:,3) = strpad('Ki_MATI in component V_MATI (micromolar)');
    LEGEND_CONSTANTS(:,4) = strpad('V_MATIIImax in component V_MATIII (flux)');
    LEGEND_ALGEBRAIC(:,3) = strpad('Km1_MATIII in component V_MATIII (micromolar)');
    LEGEND_CONSTANTS(:,5) = strpad('Km2_MATIII in component V_MATIII (micromolar)');
    LEGEND_CONSTANTS(:,6) = strpad('V_GNMTmax in component V_GNMT (flux)');
    LEGEND_CONSTANTS(:,7) = strpad('Km_GNMT in component V_GNMT (micromolar)');
    LEGEND_CONSTANTS(:,8) = strpad('Ki_GNMT in component V_GNMT (micromolar)');
    LEGEND_CONSTANTS(:,9) = strpad('V_METHmax in component V_METH (flux)');
    LEGEND_ALGEBRAIC(:,6) = strpad('Km1_METH in component V_METH (micromolar)');
    LEGEND_CONSTANTS(:,10) = strpad('Km2_METH_A in component V_METH (dimensionless)');
    LEGEND_CONSTANTS(:,11) = strpad('five_mTHF in component V_MS (micromolar)');
    LEGEND_CONSTANTS(:,12) = strpad('V_MSmax in component V_MS (flux)');
    LEGEND_CONSTANTS(:,13) = strpad('Kd_MS in component V_MS (micromolar)');
    LEGEND_CONSTANTS(:,14) = strpad('Km_Hcy_MS in component V_MS (micromolar)');
    LEGEND_CONSTANTS(:,15) = strpad('Km_five_mTHF_MS in component V_MS (micromolar)');
    LEGEND_CONSTANTS(:,16) = strpad('alpha1 in component V_AH (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,17) = strpad('alpha2 in component V_AH (dimensionless)');
    LEGEND_CONSTANTS(:,18) = strpad('beta1 in component V_CBS (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,19) = strpad('beta2 in component V_CBS (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,20) = strpad('V_BHMTmax in component V_BHMT (flux)');
    LEGEND_CONSTANTS(:,21) = strpad('Km_BHMT in component V_BHMT (micromolar)');
    LEGEND_RATES(:,1) = strpad('d/dt Met in component Met (micromolar)');
    LEGEND_RATES(:,2) = strpad('d/dt AdoMet in component AdoMet (micromolar)');
    LEGEND_RATES(:,3) = strpad('d/dt AdoHcy in component AdoHcy (micromolar)');
    LEGEND_RATES(:,4) = strpad('d/dt Hcy in component Hcy (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 = [];
    STATES(:,1) = 53.5;
    STATES(:,2) = 137.6;
    STATES(:,3) = 13.2;
    STATES(:,4) = 0.88;
    CONSTANTS(:,1) = 561;
    CONSTANTS(:,2) = 41;
    CONSTANTS(:,3) = 50;
    CONSTANTS(:,4) = 22870;
    CONSTANTS(:,5) = 21.1;
    CONSTANTS(:,6) = 10600;
    CONSTANTS(:,7) = 4500;
    CONSTANTS(:,8) = 20;
    CONSTANTS(:,9) = 4521;
    CONSTANTS(:,10) = 10;
    CONSTANTS(:,11) = 5.2;
    CONSTANTS(:,12) = 500;
    CONSTANTS(:,13) = 1;
    CONSTANTS(:,14) = 0.1;
    CONSTANTS(:,15) = 25;
    CONSTANTS(:,16) = 100;
    CONSTANTS(:,17) = 10;
    CONSTANTS(:,18) = 1.7;
    CONSTANTS(:,19) = 30;
    CONSTANTS(:,20) = 2500;
    CONSTANTS(:,21) = 12;
    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) = CONSTANTS(:,1)./(1.00000+ (CONSTANTS(:,2)./STATES(:,1)).*(1.00000+STATES(:,2)./CONSTANTS(:,3)));
    ALGEBRAIC(:,3) = 20000.0./(1.00000+ 5.70000.*power(STATES(:,2)./(STATES(:,2)+600.000), 2.00000));
    ALGEBRAIC(:,4) = CONSTANTS(:,4)./(1.00000+( ALGEBRAIC(:,3).*CONSTANTS(:,5))./(power(STATES(:,1), 2.00000)+ STATES(:,1).*CONSTANTS(:,5)));
    ALGEBRAIC(:,6) =  1.00000.*(1.00000+STATES(:,3)./4.00000);
    ALGEBRAIC(:,7) = CONSTANTS(:,9)./(1.00000+ALGEBRAIC(:,6)./STATES(:,2)+CONSTANTS(:,10)+( CONSTANTS(:,10).*ALGEBRAIC(:,6))./STATES(:,2));
    ALGEBRAIC(:,5) = ( (CONSTANTS(:,6)./(1.00000+power(CONSTANTS(:,7)./STATES(:,2), 2.30000))).*1.00000)./(1.00000+STATES(:,3)./CONSTANTS(:,8));
    RATES(:,2) = (ALGEBRAIC(:,2)+ALGEBRAIC(:,4)) - (ALGEBRAIC(:,7)+ALGEBRAIC(:,5));
    ALGEBRAIC(:,9) =  CONSTANTS(:,16).*(STATES(:,3) -  CONSTANTS(:,17).*STATES(:,4));
    RATES(:,3) = (ALGEBRAIC(:,7)+ALGEBRAIC(:,5)) - ALGEBRAIC(:,9);
    ALGEBRAIC(:,1) = piecewise({VOI<2.00000||VOI>=8.00000, 200.000 , VOI>=2.00000&VOI<5.00000, 300.000 , VOI>=5.00000&VOI<8.00000, 100.000 }, 200.000);
    ALGEBRAIC(:,8) = ( CONSTANTS(:,12).*CONSTANTS(:,11).*STATES(:,4))./( CONSTANTS(:,13).*CONSTANTS(:,14)+ CONSTANTS(:,14).*CONSTANTS(:,11)+ CONSTANTS(:,15).*STATES(:,4)+ CONSTANTS(:,11).*STATES(:,4));
    ALGEBRAIC(:,11) = ( (0.700000 -  0.0250000.*((STATES(:,2)+STATES(:,3)) - 150.000)).*CONSTANTS(:,20).*STATES(:,4))./(CONSTANTS(:,21)+STATES(:,4));
    RATES(:,1) = (ALGEBRAIC(:,8)+ALGEBRAIC(:,11)+ALGEBRAIC(:,1)) - (ALGEBRAIC(:,2)+ALGEBRAIC(:,4));
    ALGEBRAIC(:,10) =  ( CONSTANTS(:,18).*(STATES(:,2)+STATES(:,3)) - CONSTANTS(:,19)).*STATES(:,4);
    RATES(:,4) = ALGEBRAIC(:,9) - (ALGEBRAIC(:,10)+ALGEBRAIC(:,8)+ALGEBRAIC(:,11));
   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) = CONSTANTS(:,1)./(1.00000+ (CONSTANTS(:,2)./STATES(:,1)).*(1.00000+STATES(:,2)./CONSTANTS(:,3)));
    ALGEBRAIC(:,3) = 20000.0./(1.00000+ 5.70000.*power(STATES(:,2)./(STATES(:,2)+600.000), 2.00000));
    ALGEBRAIC(:,4) = CONSTANTS(:,4)./(1.00000+( ALGEBRAIC(:,3).*CONSTANTS(:,5))./(power(STATES(:,1), 2.00000)+ STATES(:,1).*CONSTANTS(:,5)));
    ALGEBRAIC(:,6) =  1.00000.*(1.00000+STATES(:,3)./4.00000);
    ALGEBRAIC(:,7) = CONSTANTS(:,9)./(1.00000+ALGEBRAIC(:,6)./STATES(:,2)+CONSTANTS(:,10)+( CONSTANTS(:,10).*ALGEBRAIC(:,6))./STATES(:,2));
    ALGEBRAIC(:,5) = ( (CONSTANTS(:,6)./(1.00000+power(CONSTANTS(:,7)./STATES(:,2), 2.30000))).*1.00000)./(1.00000+STATES(:,3)./CONSTANTS(:,8));
    ALGEBRAIC(:,9) =  CONSTANTS(:,16).*(STATES(:,3) -  CONSTANTS(:,17).*STATES(:,4));
    ALGEBRAIC(:,1) = piecewise({VOI<2.00000||VOI>=8.00000, 200.000 , VOI>=2.00000&VOI<5.00000, 300.000 , VOI>=5.00000&VOI<8.00000, 100.000 }, 200.000);
    ALGEBRAIC(:,8) = ( CONSTANTS(:,12).*CONSTANTS(:,11).*STATES(:,4))./( CONSTANTS(:,13).*CONSTANTS(:,14)+ CONSTANTS(:,14).*CONSTANTS(:,11)+ CONSTANTS(:,15).*STATES(:,4)+ CONSTANTS(:,11).*STATES(:,4));
    ALGEBRAIC(:,11) = ( (0.700000 -  0.0250000.*((STATES(:,2)+STATES(:,3)) - 150.000)).*CONSTANTS(:,20).*STATES(:,4))./(CONSTANTS(:,21)+STATES(:,4));
    ALGEBRAIC(:,10) =  ( CONSTANTS(:,18).*(STATES(:,2)+STATES(:,3)) - CONSTANTS(:,19)).*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