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 =2;
end
% There are a total of 15 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 (second)');
    LEGEND_STATES(:,1) = strpad('Arg in component Arg (micromolar)');
    LEGEND_ALGEBRAIC(:,1) = strpad('S in component Arg (flux)');
    LEGEND_STATES(:,2) = strpad('Fe3 in component Fe3 (micromolar)');
    LEGEND_STATES(:,3) = strpad('Fe3_Arg in component Fe3_Arg (micromolar)');
    LEGEND_STATES(:,4) = strpad('Fe2_Arg in component Fe2_Arg (micromolar)');
    LEGEND_STATES(:,5) = strpad('Fe2 in component Fe2 (micromolar)');
    LEGEND_CONSTANTS(:,1) = strpad('k1 in component model_constants (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,2) = strpad('k_1 in component model_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,3) = strpad('k4 in component model_constants (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,4) = strpad('k_4 in component model_constants (first_order_rate_constant)');
    LEGEND_STATES(:,6) = strpad('Fe3_NO in component Fe3_NO (micromolar)');
    LEGEND_STATES(:,7) = strpad('Fe2_NO in component Fe2_NO (micromolar)');
    LEGEND_CONSTANTS(:,5) = strpad('O2 in component model_constants (micromolar)');
    LEGEND_STATES(:,8) = strpad('Fe3_NOHA in component Fe3_NOHA (micromolar)');
    LEGEND_STATES(:,9) = strpad('NOHA in component NOHA (micromolar)');
    LEGEND_CONSTANTS(:,6) = strpad('k2 in component model_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,7) = strpad('k13 in component model_constants (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,8) = strpad('k14 in component model_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,9) = strpad('k8 in component model_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,10) = strpad('k_8 in component model_constants (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,11) = strpad('k3 in component model_constants (first_order_rate_constant)');
    LEGEND_STATES(:,10) = strpad('Fe2_NOHA in component Fe2_NOHA (micromolar)');
    LEGEND_CONSTANTS(:,12) = strpad('k9 in component model_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,13) = strpad('k_9 in component model_constants (second_order_rate_constant)');
    LEGEND_STATES(:,11) = strpad('Fe3_O2_Arg in component Fe3_O2_Arg (micromolar)');
    LEGEND_CONSTANTS(:,14) = strpad('k5 in component model_constants (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,15) = strpad('k_5 in component model_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,16) = strpad('k6 in component model_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,17) = strpad('k7 in component model_constants (first_order_rate_constant)');
    LEGEND_STATES(:,12) = strpad('Fe3_O2_NOHA in component Fe3_O2_NOHA (micromolar)');
    LEGEND_CONSTANTS(:,18) = strpad('k_10 in component model_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,19) = strpad('k10 in component model_constants (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,20) = strpad('k11 in component model_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,21) = strpad('k12 in component model_constants (first_order_rate_constant)');
    LEGEND_STATES(:,13) = strpad('NO in component NO (micromolar)');
    LEGEND_ALGEBRAIC(:,2) = strpad('dNOdt in component NO (flux)');
    LEGEND_STATES(:,14) = strpad('citrulline in component citrulline (micromolar)');
    LEGEND_STATES(:,15) = strpad('NO3 in component NO3 (micromolar)');
    LEGEND_RATES(:,1) = strpad('d/dt Arg in component Arg (micromolar)');
    LEGEND_RATES(:,2) = strpad('d/dt Fe3 in component Fe3 (micromolar)');
    LEGEND_RATES(:,3) = strpad('d/dt Fe3_Arg in component Fe3_Arg (micromolar)');
    LEGEND_RATES(:,5) = strpad('d/dt Fe2 in component Fe2 (micromolar)');
    LEGEND_RATES(:,4) = strpad('d/dt Fe2_Arg in component Fe2_Arg (micromolar)');
    LEGEND_RATES(:,11) = strpad('d/dt Fe3_O2_Arg in component Fe3_O2_Arg (micromolar)');
    LEGEND_RATES(:,8) = strpad('d/dt Fe3_NOHA in component Fe3_NOHA (micromolar)');
    LEGEND_RATES(:,10) = strpad('d/dt Fe2_NOHA in component Fe2_NOHA (micromolar)');
    LEGEND_RATES(:,12) = strpad('d/dt Fe3_O2_NOHA in component Fe3_O2_NOHA (micromolar)');
    LEGEND_RATES(:,6) = strpad('d/dt Fe3_NO in component Fe3_NO (micromolar)');
    LEGEND_RATES(:,7) = strpad('d/dt Fe2_NO in component Fe2_NO (micromolar)');
    LEGEND_RATES(:,13) = strpad('d/dt NO in component NO (micromolar)');
    LEGEND_RATES(:,14) = strpad('d/dt citrulline in component citrulline (micromolar)');
    LEGEND_RATES(:,15) = strpad('d/dt NO3 in component NO3 (micromolar)');
    LEGEND_RATES(:,9) = strpad('d/dt NOHA in component NOHA (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) = 100.0;
    STATES(:,2) = 0.045;
    STATES(:,3) = 0.0;
    STATES(:,4) = 0.0;
    STATES(:,5) = 0.0;
    CONSTANTS(:,1) = 0.1;
    CONSTANTS(:,2) = 0.1;
    CONSTANTS(:,3) = 1.89;
    CONSTANTS(:,4) = 11.4;
    STATES(:,6) = 0.0;
    STATES(:,7) = 0.0;
    CONSTANTS(:,5) = 172.0;
    STATES(:,8) = 0.0;
    STATES(:,9) = 0.0;
    CONSTANTS(:,6) = 0.91;
    CONSTANTS(:,7) = 0.033;
    CONSTANTS(:,8) = 53.9;
    CONSTANTS(:,9) = 0.1;
    CONSTANTS(:,10) = 0.1;
    CONSTANTS(:,11) = 0.91;
    STATES(:,10) = 0.0;
    CONSTANTS(:,12) = 11.4;
    CONSTANTS(:,13) = 1.89;
    STATES(:,11) = 0.0;
    CONSTANTS(:,14) = 2.58;
    CONSTANTS(:,15) = 98.0;
    CONSTANTS(:,16) = 12.6;
    CONSTANTS(:,17) = 0.91;
    STATES(:,12) = 0.0;
    CONSTANTS(:,18) = 89.9;
    CONSTANTS(:,19) = 3.33;
    CONSTANTS(:,20) = 29.4;
    CONSTANTS(:,21) = 0.91;
    STATES(:,13) = 0.0;
    STATES(:,14) = 0.0;
    STATES(:,15) = 0.0;
    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(:,2) = ( CONSTANTS(:,2).*STATES(:,3)+ CONSTANTS(:,8).*STATES(:,6)+ CONSTANTS(:,7).*STATES(:,7).*CONSTANTS(:,5)+ CONSTANTS(:,9).*STATES(:,8)) - ( CONSTANTS(:,1).*STATES(:,1).*STATES(:,2)+ CONSTANTS(:,6).*STATES(:,2)+ CONSTANTS(:,10).*STATES(:,9).*STATES(:,2));
    RATES(:,3) =  CONSTANTS(:,1).*STATES(:,2).*STATES(:,1) - ( CONSTANTS(:,2).*STATES(:,3)+ CONSTANTS(:,11).*STATES(:,3));
    RATES(:,5) = ( CONSTANTS(:,6).*STATES(:,2)+ CONSTANTS(:,4).*STATES(:,4)+ CONSTANTS(:,12).*STATES(:,10)) - ( CONSTANTS(:,3).*STATES(:,5).*STATES(:,1)+ CONSTANTS(:,13).*STATES(:,5).*STATES(:,9));
    RATES(:,4) = ( CONSTANTS(:,11).*STATES(:,3)+ CONSTANTS(:,15).*STATES(:,11)+ CONSTANTS(:,3).*STATES(:,5).*STATES(:,1)) - ( CONSTANTS(:,14).*STATES(:,4).*CONSTANTS(:,5)+ CONSTANTS(:,4).*STATES(:,4));
    RATES(:,11) =  CONSTANTS(:,14).*STATES(:,4).*CONSTANTS(:,5) - ( CONSTANTS(:,16).*STATES(:,11)+ CONSTANTS(:,15).*STATES(:,11));
    RATES(:,8) = ( CONSTANTS(:,16).*STATES(:,11)+ CONSTANTS(:,10).*STATES(:,2).*STATES(:,9)) - ( CONSTANTS(:,17).*STATES(:,8)+ CONSTANTS(:,9).*STATES(:,8));
    RATES(:,10) = ( CONSTANTS(:,17).*STATES(:,8)+ CONSTANTS(:,18).*STATES(:,12)+ CONSTANTS(:,13).*STATES(:,5).*STATES(:,9)) - ( CONSTANTS(:,12).*STATES(:,10)+ CONSTANTS(:,19).*STATES(:,10).*CONSTANTS(:,5));
    RATES(:,12) =  CONSTANTS(:,19).*STATES(:,10).*CONSTANTS(:,5) - ( CONSTANTS(:,20).*STATES(:,12)+ CONSTANTS(:,18).*STATES(:,12));
    RATES(:,6) =  CONSTANTS(:,20).*STATES(:,12) - ( CONSTANTS(:,8).*STATES(:,6)+ CONSTANTS(:,21).*STATES(:,6));
    RATES(:,7) =  CONSTANTS(:,21).*STATES(:,6) -  CONSTANTS(:,7).*STATES(:,7).*CONSTANTS(:,5);
    RATES(:,13) =  CONSTANTS(:,8).*STATES(:,6);
    RATES(:,14) =  CONSTANTS(:,20).*STATES(:,12);
    RATES(:,15) =  CONSTANTS(:,7).*STATES(:,7).*CONSTANTS(:,5);
    RATES(:,9) = ( CONSTANTS(:,9).*STATES(:,8)+ CONSTANTS(:,12).*STATES(:,10)) - ( CONSTANTS(:,10).*STATES(:,2).*STATES(:,9)+ CONSTANTS(:,13).*STATES(:,5).*STATES(:,9));
    ALGEBRAIC(:,1) = ( CONSTANTS(:,1).*STATES(:,1).*STATES(:,2)+ CONSTANTS(:,3).*STATES(:,1).*STATES(:,5)) - ( CONSTANTS(:,2).*STATES(:,3)+ CONSTANTS(:,4).*STATES(:,4));
    RATES(:,1) = ( CONSTANTS(:,2).*STATES(:,3)+ CONSTANTS(:,4).*STATES(:,4)+ALGEBRAIC(:,1)) - ( CONSTANTS(:,1).*STATES(:,1).*STATES(:,2)+ CONSTANTS(:,3).*STATES(:,1).*STATES(:,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(:,1) = ( CONSTANTS(:,1).*STATES(:,1).*STATES(:,2)+ CONSTANTS(:,3).*STATES(:,1).*STATES(:,5)) - ( CONSTANTS(:,2).*STATES(:,3)+ CONSTANTS(:,4).*STATES(:,4));
    ALGEBRAIC(:,2) =  CONSTANTS(:,8).*STATES(:,6);
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