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 5 entries in each of the rate and state variable arrays.
% There are a total of 20 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 (minute)');
    LEGEND_CONSTANTS(:,1) = strpad('a_D in component parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,2) = strpad('a_E in component parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,3) = strpad('a_X in component parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,4) = strpad('k in component parameters (dimensionless)');
    LEGEND_CONSTANTS(:,5) = strpad('q_D in component parameters (dimensionless)');
    LEGEND_CONSTANTS(:,6) = strpad('q_E in component parameters (dimensionless)');
    LEGEND_CONSTANTS(:,7) = strpad('q_X in component parameters (dimensionless)');
    LEGEND_CONSTANTS(:,8) = strpad('f in component parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,9) = strpad('g in component parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,10) = strpad('p_S in component parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,11) = strpad('p_D in component parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,12) = strpad('p_E in component parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,13) = strpad('p_X in component parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,14) = strpad('d_D in component parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,15) = strpad('d_E in component parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,16) = strpad('d_X in component parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,17) = strpad('a_f in component parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,18) = strpad('R_T in component parameters (dimensionless)');
    LEGEND_CONSTANTS(:,19) = strpad('theta in component parameters (dimensionless)');
    LEGEND_CONSTANTS(:,20) = strpad('GF in component parameters (dimensionless)');
    LEGEND_STATES(:,1) = strpad('D in component D (dimensionless)');
    LEGEND_STATES(:,2) = strpad('E in component E (dimensionless)');
    LEGEND_STATES(:,3) = strpad('R_S in component R_S (dimensionless)');
    LEGEND_STATES(:,4) = strpad('X in component X (dimensionless)');
    LEGEND_STATES(:,5) = strpad('R in component R (dimensionless)');
    LEGEND_ALGEBRAIC(:,1) = strpad('unpho_RB in component unpho_RB (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('free_E2F in component free_E2F (dimensionless)');
    LEGEND_RATES(:,1) = strpad('d/dt D in component D (dimensionless)');
    LEGEND_RATES(:,2) = strpad('d/dt E in component E (dimensionless)');
    LEGEND_RATES(:,5) = strpad('d/dt R in component R (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt R_S in component R_S (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt X in component X (dimensionless)');
    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 = [];
    CONSTANTS(:,1) = 0.4;
    CONSTANTS(:,2) = 0.16;
    CONSTANTS(:,3) = 0.08;
    CONSTANTS(:,4) = 0.05;
    CONSTANTS(:,5) = 0.6;
    CONSTANTS(:,6) = 0.6;
    CONSTANTS(:,7) = 0.8;
    CONSTANTS(:,8) = 0.2;
    CONSTANTS(:,9) = 0.528;
    CONSTANTS(:,10) = 0.6;
    CONSTANTS(:,11) = 0.48;
    CONSTANTS(:,12) = 0.096;
    CONSTANTS(:,13) = 0.48;
    CONSTANTS(:,14) = 0.4;
    CONSTANTS(:,15) = 0.2;
    CONSTANTS(:,16) = 1.04;
    CONSTANTS(:,17) = 0.9;
    CONSTANTS(:,18) = 2.5;
    CONSTANTS(:,19) = 1.5;
    CONSTANTS(:,20) = 6.3;
    STATES(:,1) = 0.1;
    STATES(:,2) = 0.6;
    STATES(:,3) = 1;
    STATES(:,4) = 0.7;
    STATES(:,5) = 0.5;
    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(:,1).*CONSTANTS(:,4).*CONSTANTS(:,20))./(1.00000+ CONSTANTS(:,4).*CONSTANTS(:,20)) -  CONSTANTS(:,14).*STATES(:,2).*STATES(:,1);
    RATES(:,2) =  CONSTANTS(:,2).*(1.00000+ CONSTANTS(:,17).*(CONSTANTS(:,19) - STATES(:,3))).*1.00000 -  CONSTANTS(:,15).*STATES(:,4).*STATES(:,2);
    RATES(:,5) = ( CONSTANTS(:,13).*STATES(:,4).*((CONSTANTS(:,18) - STATES(:,3)) - STATES(:,5)))./(CONSTANTS(:,7)+((CONSTANTS(:,18) - STATES(:,3)) - STATES(:,5))+STATES(:,4)) -  CONSTANTS(:,10).*(CONSTANTS(:,19) - STATES(:,3)).*STATES(:,5);
    RATES(:,3) = ( CONSTANTS(:,10).*(CONSTANTS(:,19) - STATES(:,3)).*STATES(:,5) - ( CONSTANTS(:,11).*STATES(:,3).*STATES(:,1))./(CONSTANTS(:,5)+STATES(:,3)+STATES(:,1))) - ( CONSTANTS(:,12).*STATES(:,3).*STATES(:,2))./(CONSTANTS(:,6)+STATES(:,3)+STATES(:,2));
    RATES(:,4) = ( CONSTANTS(:,3).*STATES(:,2)+ CONSTANTS(:,8).*(CONSTANTS(:,19) - STATES(:,3))+ CONSTANTS(:,9).*power(STATES(:,4), 2.00000).*STATES(:,2)) -  CONSTANTS(:,16).*STATES(:,4);
   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(:,5)+STATES(:,3);
    ALGEBRAIC(:,2) = CONSTANTS(:,19) - STATES(:,3);
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