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 9 entries in each of the rate and state variable arrays.
% There are a total of 30 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('NO in component NO (micromolar)');
    LEGEND_STATES(:,2) = strpad('O_2m in component O_2m (micromolar)');
    LEGEND_CONSTANTS(:,1) = strpad('O_2 in component NO (micromolar)');
    LEGEND_STATES(:,3) = strpad('NO_2 in component NO (micromolar)');
    LEGEND_STATES(:,4) = strpad('N2O3 in component N2O3 (micromolar)');
    LEGEND_STATES(:,5) = strpad('GSNO in component GSNO (micromolar)');
    LEGEND_STATES(:,6) = strpad('CcOX in component NO (micromolar)');
    LEGEND_STATES(:,7) = strpad('FeLn in component FeLn (micromolar)');
    LEGEND_CONSTANTS(:,29) = strpad('r_1NO in component NO (flux)');
    LEGEND_ALGEBRAIC(:,1) = strpad('r_4NO in component NO (flux)');
    LEGEND_ALGEBRAIC(:,2) = strpad('r_12aNO in component NO (flux)');
    LEGEND_ALGEBRAIC(:,3) = strpad('r_12bNOp in component NO (flux)');
    LEGEND_ALGEBRAIC(:,4) = strpad('r_12bNOm in component NO (flux)');
    LEGEND_ALGEBRAIC(:,5) = strpad('r_14NO in component NO (flux)');
    LEGEND_ALGEBRAIC(:,6) = strpad('r_15NO in component NO (flux)');
    LEGEND_ALGEBRAIC(:,7) = strpad('r_16NO in component NO (flux)');
    LEGEND_CONSTANTS(:,2) = strpad('k_1NO in component model_constant (flux)');
    LEGEND_CONSTANTS(:,3) = strpad('k_4NO in component model_constant (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,4) = strpad('k_12aNO in component model_constant (rate2)');
    LEGEND_CONSTANTS(:,5) = strpad('k_12bNOp in component model_constant (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,6) = strpad('k_12bNOm in component model_constant (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,7) = strpad('k_14NO in component model_constant (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,8) = strpad('k_15NO in component model_constant (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,9) = strpad('k_16NO in component model_constant (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,10) = strpad('SOD in component O_2m (micromolar)');
    LEGEND_CONSTANTS(:,30) = strpad('r_2NO in component O_2m (flux)');
    LEGEND_ALGEBRAIC(:,8) = strpad('r_5NO in component O_2m (flux)');
    LEGEND_ALGEBRAIC(:,9) = strpad('r_10NO in component O_2m (flux)');
    LEGEND_CONSTANTS(:,11) = strpad('k_2NO in component model_constant (flux)');
    LEGEND_CONSTANTS(:,12) = strpad('k_5NO in component model_constant (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,13) = strpad('k_10NO in component model_constant (rate2)');
    LEGEND_STATES(:,8) = strpad('ONOO_m in component ONOO_m (micromolar)');
    LEGEND_STATES(:,9) = strpad('GSH in component GSH (micromolar)');
    LEGEND_CONSTANTS(:,14) = strpad('GPX in component ONOO_m (micromolar)');
    LEGEND_CONSTANTS(:,15) = strpad('CO_2 in component ONOO_m (micromolar)');
    LEGEND_CONSTANTS(:,16) = strpad('Cyt_c in component ONOO_m (micromolar)');
    LEGEND_ALGEBRAIC(:,10) = strpad('r_6NO in component ONOO_m (flux)');
    LEGEND_ALGEBRAIC(:,11) = strpad('r_7NO in component ONOO_m (flux)');
    LEGEND_ALGEBRAIC(:,13) = strpad('r_8NO in component ONOO_m (flux)');
    LEGEND_ALGEBRAIC(:,15) = strpad('r_9NO in component ONOO_m (flux)');
    LEGEND_CONSTANTS(:,17) = strpad('k_6NO in component model_constant (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,18) = strpad('k_7NO in component model_constant (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,19) = strpad('k_8NO in component model_constant (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,20) = strpad('k_9NO in component model_constant (second_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,14) = strpad('GSSG in component GSH (micromolar)');
    LEGEND_ALGEBRAIC(:,12) = strpad('FeLnNO in component GSH (micromolar)');
    LEGEND_CONSTANTS(:,21) = strpad('FeLn_0 in component model_constant (micromolar)');
    LEGEND_CONSTANTS(:,22) = strpad('GSH_0 in component model_constant (micromolar)');
    LEGEND_ALGEBRAIC(:,16) = strpad('r_11NO in component GSH (flux)');
    LEGEND_ALGEBRAIC(:,17) = strpad('r_m in component GSH (flux)');
    LEGEND_ALGEBRAIC(:,19) = strpad('r_17NO in component GSH (flux)');
    LEGEND_CONSTANTS(:,23) = strpad('k_11NO in component model_constant (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,24) = strpad('v_m in component model_constant (flux)');
    LEGEND_CONSTANTS(:,25) = strpad('k_m in component model_constant (micromolar)');
    LEGEND_CONSTANTS(:,26) = strpad('k_17NO in component model_constant (second_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,18) = strpad('r_13NO in component N2O3 (flux)');
    LEGEND_CONSTANTS(:,27) = strpad('k_13NO in component model_constant (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,28) = strpad('k_17bNO in component model_constant (second_order_rate_constant)');
    LEGEND_RATES(:,1) = strpad('d/dt NO in component NO (micromolar)');
    LEGEND_RATES(:,6) = strpad('d/dt CcOX in component NO (micromolar)');
    LEGEND_RATES(:,3) = strpad('d/dt NO_2 in component NO (micromolar)');
    LEGEND_RATES(:,2) = strpad('d/dt O_2m in component O_2m (micromolar)');
    LEGEND_RATES(:,8) = strpad('d/dt ONOO_m in component ONOO_m (micromolar)');
    LEGEND_RATES(:,9) = strpad('d/dt GSH in component GSH (micromolar)');
    LEGEND_RATES(:,5) = strpad('d/dt GSNO in component GSNO (micromolar)');
    LEGEND_RATES(:,4) = strpad('d/dt N2O3 in component N2O3 (micromolar)');
    LEGEND_RATES(:,7) = strpad('d/dt FeLn in component FeLn (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) = 0;
    STATES(:,2) = 0;
    CONSTANTS(:,1) = 35;
    STATES(:,3) = 0;
    STATES(:,4) = 0;
    STATES(:,5) = 0;
    STATES(:,6) = 0.1;
    STATES(:,7) = 0.05;
    CONSTANTS(:,2) = 1;
    CONSTANTS(:,3) = 6700;
    CONSTANTS(:,4) = 0.000006;
    CONSTANTS(:,5) = 1100;
    CONSTANTS(:,6) = 81000;
    CONSTANTS(:,7) = 0.0002;
    CONSTANTS(:,8) = 100;
    CONSTANTS(:,9) = 1.21;
    CONSTANTS(:,10) = 10;
    CONSTANTS(:,11) = 0.1;
    CONSTANTS(:,12) = 2400;
    CONSTANTS(:,13) = 0.0006;
    STATES(:,8) = 0;
    STATES(:,9) = 10000;
    CONSTANTS(:,14) = 5.8;
    CONSTANTS(:,15) = 1000;
    CONSTANTS(:,16) = 400;
    CONSTANTS(:,17) = 0.00135;
    CONSTANTS(:,18) = 2;
    CONSTANTS(:,19) = 0.058;
    CONSTANTS(:,20) = 0.025;
    CONSTANTS(:,21) = 0.05;
    CONSTANTS(:,22) = 10000;
    CONSTANTS(:,23) = 66;
    CONSTANTS(:,24) = 320;
    CONSTANTS(:,25) = 50;
    CONSTANTS(:,26) = 66;
    CONSTANTS(:,27) = 1600;
    CONSTANTS(:,28) = 0.0002;
    CONSTANTS(:,29) = CONSTANTS(:,2);
    CONSTANTS(:,30) = CONSTANTS(:,11);
    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(:,4).*power(STATES(:,1), 2.00000).*CONSTANTS(:,1);
    ALGEBRAIC(:,3) =  CONSTANTS(:,5).*STATES(:,3).*STATES(:,1);
    ALGEBRAIC(:,4) =  CONSTANTS(:,6).*STATES(:,4);
    RATES(:,3) = ( 2.00000.*ALGEBRAIC(:,2) - ALGEBRAIC(:,3))+ALGEBRAIC(:,4);
    ALGEBRAIC(:,6) =  CONSTANTS(:,8).*STATES(:,6).*STATES(:,1);
    RATES(:,6) =  - ALGEBRAIC(:,6);
    ALGEBRAIC(:,1) =  CONSTANTS(:,3).*STATES(:,1).*STATES(:,2);
    ALGEBRAIC(:,5) =  CONSTANTS(:,7).*STATES(:,5);
    ALGEBRAIC(:,7) =  CONSTANTS(:,9).*STATES(:,7).*STATES(:,1);
    RATES(:,1) = (((((CONSTANTS(:,29) - ALGEBRAIC(:,1)) -  2.00000.*ALGEBRAIC(:,2)) - ALGEBRAIC(:,3))+ALGEBRAIC(:,4)+ALGEBRAIC(:,5)) - ALGEBRAIC(:,6)) - ALGEBRAIC(:,7);
    ALGEBRAIC(:,8) =  CONSTANTS(:,12).*CONSTANTS(:,10).*STATES(:,2);
    ALGEBRAIC(:,9) =  CONSTANTS(:,13).*power(STATES(:,5), 2.00000).*STATES(:,2);
    RATES(:,2) = ((CONSTANTS(:,30) - ALGEBRAIC(:,1)) - ALGEBRAIC(:,8)) - ALGEBRAIC(:,9);
    ALGEBRAIC(:,10) =  CONSTANTS(:,17).*STATES(:,8).*STATES(:,9);
    ALGEBRAIC(:,11) =  CONSTANTS(:,18).*STATES(:,8).*CONSTANTS(:,14);
    ALGEBRAIC(:,13) =  CONSTANTS(:,19).*STATES(:,8).*CONSTANTS(:,15);
    ALGEBRAIC(:,15) =  CONSTANTS(:,20).*STATES(:,8).*CONSTANTS(:,16);
    RATES(:,8) = (((ALGEBRAIC(:,1) - ALGEBRAIC(:,10)) - ALGEBRAIC(:,11)) - ALGEBRAIC(:,13)) - ALGEBRAIC(:,15);
    ALGEBRAIC(:,16) =  CONSTANTS(:,23).*STATES(:,4).*STATES(:,9);
    ALGEBRAIC(:,18) =  CONSTANTS(:,27).*STATES(:,4);
    RATES(:,4) = (( - ALGEBRAIC(:,16)+ALGEBRAIC(:,3)) - ALGEBRAIC(:,4)) - ALGEBRAIC(:,18);
    ALGEBRAIC(:,14) = ((CONSTANTS(:,22) - STATES(:,9)) - STATES(:,5))./2.00000;
    ALGEBRAIC(:,17) = ( CONSTANTS(:,24).*ALGEBRAIC(:,14))./(CONSTANTS(:,25)+ALGEBRAIC(:,14));
    ALGEBRAIC(:,12) = CONSTANTS(:,21) - STATES(:,7);
    ALGEBRAIC(:,19) =  CONSTANTS(:,26).*ALGEBRAIC(:,12).*STATES(:,9);
    RATES(:,9) = (( - ALGEBRAIC(:,10) - ALGEBRAIC(:,16))+ 2.00000.*ALGEBRAIC(:,17)) - ALGEBRAIC(:,19);
    RATES(:,5) = (((ALGEBRAIC(:,10) -  2.00000.*ALGEBRAIC(:,9))+ALGEBRAIC(:,16)) - ALGEBRAIC(:,5))+ALGEBRAIC(:,19);
    RATES(:,7) =  - ALGEBRAIC(:,7)+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(:,2) =  CONSTANTS(:,4).*power(STATES(:,1), 2.00000).*CONSTANTS(:,1);
    ALGEBRAIC(:,3) =  CONSTANTS(:,5).*STATES(:,3).*STATES(:,1);
    ALGEBRAIC(:,4) =  CONSTANTS(:,6).*STATES(:,4);
    ALGEBRAIC(:,6) =  CONSTANTS(:,8).*STATES(:,6).*STATES(:,1);
    ALGEBRAIC(:,1) =  CONSTANTS(:,3).*STATES(:,1).*STATES(:,2);
    ALGEBRAIC(:,5) =  CONSTANTS(:,7).*STATES(:,5);
    ALGEBRAIC(:,7) =  CONSTANTS(:,9).*STATES(:,7).*STATES(:,1);
    ALGEBRAIC(:,8) =  CONSTANTS(:,12).*CONSTANTS(:,10).*STATES(:,2);
    ALGEBRAIC(:,9) =  CONSTANTS(:,13).*power(STATES(:,5), 2.00000).*STATES(:,2);
    ALGEBRAIC(:,10) =  CONSTANTS(:,17).*STATES(:,8).*STATES(:,9);
    ALGEBRAIC(:,11) =  CONSTANTS(:,18).*STATES(:,8).*CONSTANTS(:,14);
    ALGEBRAIC(:,13) =  CONSTANTS(:,19).*STATES(:,8).*CONSTANTS(:,15);
    ALGEBRAIC(:,15) =  CONSTANTS(:,20).*STATES(:,8).*CONSTANTS(:,16);
    ALGEBRAIC(:,16) =  CONSTANTS(:,23).*STATES(:,4).*STATES(:,9);
    ALGEBRAIC(:,18) =  CONSTANTS(:,27).*STATES(:,4);
    ALGEBRAIC(:,14) = ((CONSTANTS(:,22) - STATES(:,9)) - STATES(:,5))./2.00000;
    ALGEBRAIC(:,17) = ( CONSTANTS(:,24).*ALGEBRAIC(:,14))./(CONSTANTS(:,25)+ALGEBRAIC(:,14));
    ALGEBRAIC(:,12) = CONSTANTS(:,21) - STATES(:,7);
    ALGEBRAIC(:,19) =  CONSTANTS(:,26).*ALGEBRAIC(:,12).*STATES(:,9);
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