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 =1;
end
% There are a total of 9 entries in each of the rate and state variable arrays.
% There are a total of 10 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('x1 in component x1 (nanomolar)');
    LEGEND_STATES(:,2) = strpad('x2 in component x2 (nanomolar)');
    LEGEND_STATES(:,3) = strpad('x3 in component x3 (nanomolar)');
    LEGEND_STATES(:,4) = strpad('x4 in component x4 (nanomolar)');
    LEGEND_STATES(:,5) = strpad('x5 in component x5 (nanomolar)');
    LEGEND_STATES(:,6) = strpad('x6 in component x6 (nanomolar)');
    LEGEND_STATES(:,7) = strpad('x7 in component x7 (nanomolar)');
    LEGEND_STATES(:,8) = strpad('x8 in component x8 (nanomolar)');
    LEGEND_STATES(:,9) = strpad('x9 in component x9 (nanomolar)');
    LEGEND_CONSTANTS(:,1) = strpad('k1 in component rate_variables (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,2) = strpad('k1_ in component rate_variables (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,3) = strpad('k2 in component rate_variables (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,4) = strpad('k2_ in component rate_variables (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,5) = strpad('k4 in component rate_variables (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,6) = strpad('k4_ in component rate_variables (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,7) = strpad('k5 in component rate_variables (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,8) = strpad('k5_ in component rate_variables (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,1) = strpad('scatchard in component x1 (dimensionless)');
    LEGEND_CONSTANTS(:,9) = strpad('k3 in component rate_variables (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,10) = strpad('k3_ in component rate_variables (first_order_rate_constant)');
    LEGEND_RATES(:,1) = strpad('d/dt x1 in component x1 (nanomolar)');
    LEGEND_RATES(:,2) = strpad('d/dt x2 in component x2 (nanomolar)');
    LEGEND_RATES(:,3) = strpad('d/dt x3 in component x3 (nanomolar)');
    LEGEND_RATES(:,4) = strpad('d/dt x4 in component x4 (nanomolar)');
    LEGEND_RATES(:,5) = strpad('d/dt x5 in component x5 (nanomolar)');
    LEGEND_RATES(:,6) = strpad('d/dt x6 in component x6 (nanomolar)');
    LEGEND_RATES(:,7) = strpad('d/dt x7 in component x7 (nanomolar)');
    LEGEND_RATES(:,8) = strpad('d/dt x8 in component x8 (nanomolar)');
    LEGEND_RATES(:,9) = strpad('d/dt x9 in component x9 (nanomolar)');
    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) = 10;
    STATES(:,2) = 0.1;
    STATES(:,3) = 1.0;
    STATES(:,4) = 1.0;
    STATES(:,5) = 1.0;
    STATES(:,6) = 1.0;
    STATES(:,7) = 1.0;
    STATES(:,8) = 1.0;
    STATES(:,9) = 1.0;
    CONSTANTS(:,1) = 1000000;
    CONSTANTS(:,2) = 0.0004;
    CONSTANTS(:,3) = 1000000;
    CONSTANTS(:,4) = 0.04;
    CONSTANTS(:,5) = 1000000;
    CONSTANTS(:,6) = 0.0004;
    CONSTANTS(:,7) = 10000000;
    CONSTANTS(:,8) = 0.004;
    CONSTANTS(:,9) = 1000000;
    CONSTANTS(:,10) = 0.0004;
    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(:,1) = (((((( CONSTANTS(:,2).*STATES(:,3) -  CONSTANTS(:,1).*STATES(:,1).*STATES(:,2))+ CONSTANTS(:,4).*STATES(:,4)) -  CONSTANTS(:,3).*STATES(:,1).*STATES(:,3))+ CONSTANTS(:,6).*(STATES(:,6)+STATES(:,7))) -  CONSTANTS(:,5).*STATES(:,1).*(STATES(:,5)+STATES(:,9)))+ CONSTANTS(:,8).*(STATES(:,7)+STATES(:,8)+STATES(:,9))) -  CONSTANTS(:,7).*STATES(:,1).*(STATES(:,5)+STATES(:,6)+STATES(:,7));
    RATES(:,2) = (( CONSTANTS(:,2).*STATES(:,3) -  CONSTANTS(:,1).*STATES(:,1).*STATES(:,2))+ CONSTANTS(:,10).*(STATES(:,5)+STATES(:,9))) -  CONSTANTS(:,9).*STATES(:,2).*(STATES(:,3)+STATES(:,4));
    RATES(:,3) = ((((( CONSTANTS(:,1).*STATES(:,1).*STATES(:,2) -  CONSTANTS(:,2).*STATES(:,3))+ CONSTANTS(:,4).*STATES(:,4)) -  CONSTANTS(:,3).*STATES(:,1).*STATES(:,3))+ CONSTANTS(:,10).*STATES(:,5)) -  CONSTANTS(:,9).*STATES(:,2).*STATES(:,3));
    RATES(:,4) = (( CONSTANTS(:,3).*STATES(:,1).*STATES(:,3) -  CONSTANTS(:,4).*STATES(:,4))+ CONSTANTS(:,10).*STATES(:,9)) -  CONSTANTS(:,3).*STATES(:,2).*STATES(:,4);
    RATES(:,5) = (((( CONSTANTS(:,9).*STATES(:,2).*STATES(:,3) -  CONSTANTS(:,10).*STATES(:,5))+ CONSTANTS(:,6).*STATES(:,6)) -  CONSTANTS(:,5).*STATES(:,1).*STATES(:,5))+ CONSTANTS(:,8).*STATES(:,9)) -  CONSTANTS(:,7).*STATES(:,1).*STATES(:,5);
    RATES(:,6) = (( CONSTANTS(:,5).*STATES(:,1).*STATES(:,5) -  CONSTANTS(:,6).*STATES(:,6))+ CONSTANTS(:,8).*STATES(:,7)) -  CONSTANTS(:,7).*STATES(:,1).*STATES(:,6);
    RATES(:,7) = ( CONSTANTS(:,5).*STATES(:,1).*STATES(:,9) -  CONSTANTS(:,6).*STATES(:,7))+ CONSTANTS(:,8).*(STATES(:,8) - STATES(:,7))+ CONSTANTS(:,7).*STATES(:,1).*(STATES(:,6) - STATES(:,7));
    RATES(:,8) =  CONSTANTS(:,7).*STATES(:,1).*STATES(:,7) -  CONSTANTS(:,8).*STATES(:,8);
    RATES(:,9) = (((( CONSTANTS(:,9).*STATES(:,2).*STATES(:,4) -  CONSTANTS(:,10).*STATES(:,9))+ CONSTANTS(:,6).*STATES(:,7)) -  CONSTANTS(:,5).*STATES(:,1).*STATES(:,9))+ CONSTANTS(:,7).*STATES(:,1).*STATES(:,5)) -  CONSTANTS(:,8).*STATES(:,9);
   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) = (STATES(:,3)+STATES(:,4)+STATES(:,7)+STATES(:,8)+STATES(:,9))./STATES(:,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