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 =19;
end
% There are a total of 17 entries in each of the rate and state variable arrays.
% There are a total of 18 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 (second)');
    LEGEND_STATES(:,1) = strpad('A in component differentials (molar)');
    LEGEND_STATES(:,2) = strpad('G in component differentials (molar)');
    LEGEND_STATES(:,3) = strpad('GA in component differentials (molar)');
    LEGEND_STATES(:,4) = strpad('T in component differentials (molar)');
    LEGEND_STATES(:,5) = strpad('R in component differentials (molar)');
    LEGEND_STATES(:,6) = strpad('GT in component differentials (molar)');
    LEGEND_STATES(:,7) = strpad('GD in component differentials (molar)');
    LEGEND_STATES(:,8) = strpad('Pi_ in component differentials (molar)');
    LEGEND_STATES(:,9) = strpad('D in component differentials (molar)');
    LEGEND_STATES(:,10) = strpad('RG in component differentials (molar)');
    LEGEND_STATES(:,11) = strpad('RGT in component differentials (molar)');
    LEGEND_STATES(:,12) = strpad('GAT in component differentials (molar)');
    LEGEND_STATES(:,13) = strpad('GAD in component differentials (molar)');
    LEGEND_STATES(:,14) = strpad('RGD in component differentials (molar)');
    LEGEND_STATES(:,15) = strpad('RGA in component differentials (molar)');
    LEGEND_STATES(:,16) = strpad('RGAT in component differentials (molar)');
    LEGEND_STATES(:,17) = strpad('RGAD in component differentials (molar)');
    LEGEND_ALGEBRAIC(:,8) = strpad('A2 in component A2 (molar_per_second)');
    LEGEND_ALGEBRAIC(:,9) = strpad('A3 in component A3 (molar_per_second)');
    LEGEND_ALGEBRAIC(:,17) = strpad('A5 in component A5 (molar_per_second)');
    LEGEND_ALGEBRAIC(:,7) = strpad('R2 in component R2 (molar_per_second)');
    LEGEND_ALGEBRAIC(:,10) = strpad('R3 in component R3 (molar_per_second)');
    LEGEND_ALGEBRAIC(:,15) = strpad('R4 in component R4 (molar_per_second)');
    LEGEND_ALGEBRAIC(:,1) = strpad('T1 in component T1 (molar_per_second)');
    LEGEND_ALGEBRAIC(:,6) = strpad('T3 in component T3 (molar_per_second)');
    LEGEND_ALGEBRAIC(:,16) = strpad('T4 in component T4 (molar_per_second)');
    LEGEND_ALGEBRAIC(:,4) = strpad('P1 in component P1 (molar_per_second)');
    LEGEND_ALGEBRAIC(:,13) = strpad('P2 in component P2 (molar_per_second)');
    LEGEND_ALGEBRAIC(:,11) = strpad('P3 in component P3 (molar_per_second)');
    LEGEND_ALGEBRAIC(:,18) = strpad('P4 in component P4 (molar_per_second)');
    LEGEND_ALGEBRAIC(:,5) = strpad('D1 in component D1 (molar_per_second)');
    LEGEND_ALGEBRAIC(:,14) = strpad('D2 in component D2 (molar_per_second)');
    LEGEND_ALGEBRAIC(:,12) = strpad('D3 in component D3 (molar_per_second)');
    LEGEND_ALGEBRAIC(:,19) = strpad('D4 in component D4 (molar_per_second)');
    LEGEND_ALGEBRAIC(:,2) = strpad('Z in component output (dimensionless)');
    LEGEND_ALGEBRAIC(:,3) = strpad('v in component output (per_second)');
    LEGEND_CONSTANTS(:,1) = strpad('G_tot in component output (molar)');
    LEGEND_CONSTANTS(:,2) = strpad('k1 in component P1 (per_second)');
    LEGEND_CONSTANTS(:,3) = strpad('k1 in component P2 (per_second)');
    LEGEND_CONSTANTS(:,4) = strpad('k1 in component P3 (per_second)');
    LEGEND_CONSTANTS(:,5) = strpad('k1 in component P4 (per_second)');
    LEGEND_CONSTANTS(:,6) = strpad('k1 in component T1 (per_molar_per_second)');
    LEGEND_CONSTANTS(:,7) = strpad('k1 in component D1 (per_second)');
    LEGEND_CONSTANTS(:,8) = strpad('k1 in component T3 (per_molar_per_second)');
    LEGEND_CONSTANTS(:,9) = strpad('k2 in component R2 (per_second)');
    LEGEND_CONSTANTS(:,10) = strpad('k1 in component A2 (per_molar_per_second)');
    LEGEND_CONSTANTS(:,11) = strpad('k2 in component A3 (per_second)');
    LEGEND_CONSTANTS(:,12) = strpad('k1 in component R3 (per_molar_per_second)');
    LEGEND_CONSTANTS(:,13) = strpad('k1 in component D3 (per_second)');
    LEGEND_CONSTANTS(:,14) = strpad('k1 in component D2 (per_second)');
    LEGEND_CONSTANTS(:,15) = strpad('k1 in component R4 (per_molar_per_second)');
    LEGEND_CONSTANTS(:,16) = strpad('k1 in component T4 (per_molar_per_second)');
    LEGEND_CONSTANTS(:,17) = strpad('k1 in component A5 (per_molar_per_second)');
    LEGEND_CONSTANTS(:,18) = strpad('k1 in component D4 (per_second)');
    LEGEND_RATES(:,1) = strpad('d/dt A in component differentials (molar)');
    LEGEND_RATES(:,2) = strpad('d/dt G in component differentials (molar)');
    LEGEND_RATES(:,3) = strpad('d/dt GA in component differentials (molar)');
    LEGEND_RATES(:,4) = strpad('d/dt T in component differentials (molar)');
    LEGEND_RATES(:,5) = strpad('d/dt R in component differentials (molar)');
    LEGEND_RATES(:,6) = strpad('d/dt GT in component differentials (molar)');
    LEGEND_RATES(:,7) = strpad('d/dt GD in component differentials (molar)');
    LEGEND_RATES(:,8) = strpad('d/dt Pi_ in component differentials (molar)');
    LEGEND_RATES(:,9) = strpad('d/dt D in component differentials (molar)');
    LEGEND_RATES(:,10) = strpad('d/dt RG in component differentials (molar)');
    LEGEND_RATES(:,11) = strpad('d/dt RGT in component differentials (molar)');
    LEGEND_RATES(:,12) = strpad('d/dt GAT in component differentials (molar)');
    LEGEND_RATES(:,13) = strpad('d/dt GAD in component differentials (molar)');
    LEGEND_RATES(:,14) = strpad('d/dt RGD in component differentials (molar)');
    LEGEND_RATES(:,15) = strpad('d/dt RGA in component differentials (molar)');
    LEGEND_RATES(:,16) = strpad('d/dt RGAT in component differentials (molar)');
    LEGEND_RATES(:,17) = strpad('d/dt RGAD in component differentials (molar)');
    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) = 0;
    STATES(:,2) = 0;
    STATES(:,3) = 0;
    STATES(:,4) = 0.000468;
    STATES(:,5) = 0;
    STATES(:,6) = 0;
    STATES(:,7) = 1e-8;
    STATES(:,8) = 0.0044;
    STATES(:,9) = 0.000149;
    STATES(:,10) = 0;
    STATES(:,11) = 0;
    STATES(:,12) = 0;
    STATES(:,13) = 0;
    STATES(:,14) = 0;
    STATES(:,15) = 0;
    STATES(:,16) = 0;
    STATES(:,17) = 0;
    CONSTANTS(:,1) = 1e-8;
    CONSTANTS(:,2) = 0.013;
    CONSTANTS(:,3) = 25;
    CONSTANTS(:,4) = 0.013;
    CONSTANTS(:,5) = 25;
    CONSTANTS(:,6) = 529000;
    CONSTANTS(:,7) = 0.0001;
    CONSTANTS(:,8) = 853000;
    CONSTANTS(:,9) = 1.28;
    CONSTANTS(:,10) = 386000;
    CONSTANTS(:,11) = 0.95;
    CONSTANTS(:,12) = 94700000;
    CONSTANTS(:,13) = 2;
    CONSTANTS(:,14) = 0.0001;
    CONSTANTS(:,15) = 22800000;
    CONSTANTS(:,16) = 1620000;
    CONSTANTS(:,17) = 6300000;
    CONSTANTS(:,18) = 2.75;
    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(:,1) =  CONSTANTS(:,6).*STATES(:,2).*STATES(:,4);
    ALGEBRAIC(:,5) =  CONSTANTS(:,7).*STATES(:,7);
    RATES(:,2) = ALGEBRAIC(:,5) - ALGEBRAIC(:,1);
    ALGEBRAIC(:,8) =  CONSTANTS(:,10).*STATES(:,6).*STATES(:,1);
    ALGEBRAIC(:,7) =   - CONSTANTS(:,9).*STATES(:,11);
    ALGEBRAIC(:,4) =  CONSTANTS(:,2).*STATES(:,6);
    RATES(:,6) = ((ALGEBRAIC(:,1) - ALGEBRAIC(:,4)) - ALGEBRAIC(:,7)) - ALGEBRAIC(:,8);
    ALGEBRAIC(:,9) =   - CONSTANTS(:,11).*STATES(:,13);
    ALGEBRAIC(:,10) =  CONSTANTS(:,12).*STATES(:,7).*STATES(:,5);
    RATES(:,7) = ((ALGEBRAIC(:,4) - ALGEBRAIC(:,5)) - ALGEBRAIC(:,9)) - ALGEBRAIC(:,10);
    ALGEBRAIC(:,6) =  CONSTANTS(:,8).*STATES(:,10).*STATES(:,4);
    ALGEBRAIC(:,12) =  CONSTANTS(:,13).*STATES(:,14);
    RATES(:,10) =  - ALGEBRAIC(:,6)+ALGEBRAIC(:,12);
    ALGEBRAIC(:,11) =  CONSTANTS(:,4).*STATES(:,11);
    RATES(:,14) = (ALGEBRAIC(:,10)+ALGEBRAIC(:,11)) - ALGEBRAIC(:,12);
    ALGEBRAIC(:,13) =  CONSTANTS(:,3).*STATES(:,12);
    RATES(:,12) = ALGEBRAIC(:,8) - ALGEBRAIC(:,13);
    ALGEBRAIC(:,14) =  CONSTANTS(:,14).*STATES(:,13);
    RATES(:,13) = (ALGEBRAIC(:,9)+ALGEBRAIC(:,13)) - ALGEBRAIC(:,14);
    ALGEBRAIC(:,15) =  CONSTANTS(:,15).*STATES(:,3).*STATES(:,5);
    RATES(:,3) = ALGEBRAIC(:,14) - ALGEBRAIC(:,15);
    RATES(:,5) =  - (ALGEBRAIC(:,7)+ALGEBRAIC(:,10)+ALGEBRAIC(:,15));
    ALGEBRAIC(:,16) =  CONSTANTS(:,16).*STATES(:,15).*STATES(:,4);
    RATES(:,4) =  - (ALGEBRAIC(:,1)+ALGEBRAIC(:,6)+ALGEBRAIC(:,16));
    ALGEBRAIC(:,17) =  CONSTANTS(:,17).*STATES(:,11).*STATES(:,1);
    RATES(:,1) =  - (ALGEBRAIC(:,8)+ALGEBRAIC(:,9)+ALGEBRAIC(:,17));
    RATES(:,11) = ((ALGEBRAIC(:,6)+ALGEBRAIC(:,7)) - ALGEBRAIC(:,11)) - ALGEBRAIC(:,17);
    ALGEBRAIC(:,18) =  CONSTANTS(:,5).*STATES(:,16);
    RATES(:,8) = ALGEBRAIC(:,4)+ALGEBRAIC(:,11)+ALGEBRAIC(:,13)+ALGEBRAIC(:,18);
    RATES(:,16) = (ALGEBRAIC(:,16)+ALGEBRAIC(:,17)) - ALGEBRAIC(:,18);
    ALGEBRAIC(:,19) =  CONSTANTS(:,18).*STATES(:,17);
    RATES(:,9) = ALGEBRAIC(:,5)+ALGEBRAIC(:,12)+ALGEBRAIC(:,14)+ALGEBRAIC(:,19);
    RATES(:,15) = (ALGEBRAIC(:,15) - ALGEBRAIC(:,16))+ALGEBRAIC(:,19);
    RATES(:,17) = ALGEBRAIC(:,18) - ALGEBRAIC(:,19);
   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) =  CONSTANTS(:,6).*STATES(:,2).*STATES(:,4);
    ALGEBRAIC(:,5) =  CONSTANTS(:,7).*STATES(:,7);
    ALGEBRAIC(:,8) =  CONSTANTS(:,10).*STATES(:,6).*STATES(:,1);
    ALGEBRAIC(:,7) =   - CONSTANTS(:,9).*STATES(:,11);
    ALGEBRAIC(:,4) =  CONSTANTS(:,2).*STATES(:,6);
    ALGEBRAIC(:,9) =   - CONSTANTS(:,11).*STATES(:,13);
    ALGEBRAIC(:,10) =  CONSTANTS(:,12).*STATES(:,7).*STATES(:,5);
    ALGEBRAIC(:,6) =  CONSTANTS(:,8).*STATES(:,10).*STATES(:,4);
    ALGEBRAIC(:,12) =  CONSTANTS(:,13).*STATES(:,14);
    ALGEBRAIC(:,11) =  CONSTANTS(:,4).*STATES(:,11);
    ALGEBRAIC(:,13) =  CONSTANTS(:,3).*STATES(:,12);
    ALGEBRAIC(:,14) =  CONSTANTS(:,14).*STATES(:,13);
    ALGEBRAIC(:,15) =  CONSTANTS(:,15).*STATES(:,3).*STATES(:,5);
    ALGEBRAIC(:,16) =  CONSTANTS(:,16).*STATES(:,15).*STATES(:,4);
    ALGEBRAIC(:,17) =  CONSTANTS(:,17).*STATES(:,11).*STATES(:,1);
    ALGEBRAIC(:,18) =  CONSTANTS(:,5).*STATES(:,16);
    ALGEBRAIC(:,19) =  CONSTANTS(:,18).*STATES(:,17);
    ALGEBRAIC(:,2) = (STATES(:,6)+STATES(:,11)+STATES(:,16)+STATES(:,12))./CONSTANTS(:,1);
    ALGEBRAIC(:,3) = ( CONSTANTS(:,5).*STATES(:,16)+ CONSTANTS(:,3).*STATES(:,12)+ CONSTANTS(:,4).*STATES(:,11)+ CONSTANTS(:,2).*STATES(:,6))./CONSTANTS(:,1);
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