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 =6;
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_STATES(:,1) = strpad('C in component C (dimensionless)');
    LEGEND_ALGEBRAIC(:,1) = strpad('Ctot in component C (dimensionless)');
    LEGEND_CONSTANTS(:,1) = strpad('vi in component model_parameters (per_minute)');
    LEGEND_CONSTANTS(:,2) = strpad('k1 in component model_parameters (per_minute)');
    LEGEND_STATES(:,2) = strpad('X in component X (dimensionless)');
    LEGEND_CONSTANTS(:,3) = strpad('K5 in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,4) = strpad('kd in component model_parameters (per_minute)');
    LEGEND_STATES(:,3) = strpad('Z in component Z (dimensionless)');
    LEGEND_STATES(:,4) = strpad('M in component M (dimensionless)');
    LEGEND_CONSTANTS(:,20) = strpad('M_ in component M (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('V1 in component model_parameters (per_minute)');
    LEGEND_CONSTANTS(:,5) = strpad('K1 in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,6) = strpad('V2 in component model_parameters (per_minute)');
    LEGEND_CONSTANTS(:,7) = strpad('K2 in component model_parameters (dimensionless)');
    LEGEND_ALGEBRAIC(:,3) = strpad('X_ in component X (dimensionless)');
    LEGEND_ALGEBRAIC(:,5) = strpad('V3 in component model_parameters (per_minute)');
    LEGEND_CONSTANTS(:,8) = strpad('K3 in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,9) = strpad('V4 in component model_parameters (per_minute)');
    LEGEND_CONSTANTS(:,10) = strpad('K4 in component model_parameters (dimensionless)');
    LEGEND_STATES(:,5) = strpad('Y in component Y (dimensionless)');
    LEGEND_ALGEBRAIC(:,4) = strpad('Ytot in component Y (dimensionless)');
    LEGEND_CONSTANTS(:,11) = strpad('vs in component model_parameters (per_minute)');
    LEGEND_CONSTANTS(:,12) = strpad('d1 in component model_parameters (per_minute)');
    LEGEND_CONSTANTS(:,13) = strpad('a1 in component model_parameters (per_minute)');
    LEGEND_CONSTANTS(:,14) = strpad('a2 in component model_parameters (per_minute)');
    LEGEND_CONSTANTS(:,15) = strpad('alpha in component model_parameters (dimensionless)');
    LEGEND_ALGEBRAIC(:,6) = strpad('BP in component BP (dimensionless)');
    LEGEND_CONSTANTS(:,16) = strpad('Kd in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,17) = strpad('K6 in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,18) = strpad('V1_dash in component model_parameters (per_minute)');
    LEGEND_CONSTANTS(:,19) = strpad('V3_dash in component model_parameters (per_minute)');
    LEGEND_RATES(:,1) = strpad('d/dt C in component C (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt M in component M (dimensionless)');
    LEGEND_RATES(:,2) = strpad('d/dt X in component X (dimensionless)');
    LEGEND_RATES(:,5) = strpad('d/dt Y in component Y (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt Z in component Z (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 = [];
    STATES(:,1) = 0.01;
    CONSTANTS(:,1) = 0.1;
    CONSTANTS(:,2) = 0.5;
    STATES(:,2) = 0.01;
    CONSTANTS(:,3) = 0.02;
    CONSTANTS(:,4) = 0.02;
    STATES(:,3) = 0.28;
    STATES(:,4) = 0.01;
    CONSTANTS(:,5) = 0.02;
    CONSTANTS(:,6) = 0.25;
    CONSTANTS(:,7) = 0.02;
    CONSTANTS(:,8) = 0.1;
    CONSTANTS(:,9) = 0.1;
    CONSTANTS(:,10) = 0.1;
    STATES(:,5) = 0.01;
    CONSTANTS(:,11) = 0.1;
    CONSTANTS(:,12) = 0.05;
    CONSTANTS(:,13) = 1.5;
    CONSTANTS(:,14) = 1.5;
    CONSTANTS(:,15) = 0.1;
    CONSTANTS(:,16) = 1;
    CONSTANTS(:,17) = 0.3;
    CONSTANTS(:,18) = 0.75;
    CONSTANTS(:,19) = 0.3;
    CONSTANTS(:,20) =  - 1.00000;
    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(:,2).*STATES(:,2).*STATES(:,1))./(STATES(:,1)+CONSTANTS(:,3))) -  CONSTANTS(:,4).*STATES(:,1);
    RATES(:,5) = ((CONSTANTS(:,11) -  CONSTANTS(:,12).*STATES(:,5)) -  CONSTANTS(:,13).*STATES(:,1).*STATES(:,5))+ (CONSTANTS(:,14)+ CONSTANTS(:,15).*CONSTANTS(:,4)).*STATES(:,3);
    RATES(:,3) =  CONSTANTS(:,13).*STATES(:,1).*STATES(:,5) -  (CONSTANTS(:,14)+ CONSTANTS(:,15).*CONSTANTS(:,4)+ CONSTANTS(:,15).*CONSTANTS(:,12)).*STATES(:,3);
    ALGEBRAIC(:,2) = ( STATES(:,1).*CONSTANTS(:,18))./(STATES(:,1)+CONSTANTS(:,17));
    RATES(:,4) = ( ALGEBRAIC(:,2).*CONSTANTS(:,20))./(CONSTANTS(:,20)+CONSTANTS(:,5)) - ( CONSTANTS(:,6).*STATES(:,4))./(STATES(:,4)+CONSTANTS(:,7));
    ALGEBRAIC(:,3) = 1.00000 - STATES(:,2);
    ALGEBRAIC(:,5) =  STATES(:,4).*CONSTANTS(:,19);
    RATES(:,2) = ( ALGEBRAIC(:,5).*ALGEBRAIC(:,3))./(ALGEBRAIC(:,3)+CONSTANTS(:,8)) - ( CONSTANTS(:,9).*STATES(:,2))./(STATES(:,2)+CONSTANTS(:,10));
   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) = ( STATES(:,1).*CONSTANTS(:,18))./(STATES(:,1)+CONSTANTS(:,17));
    ALGEBRAIC(:,3) = 1.00000 - STATES(:,2);
    ALGEBRAIC(:,5) =  STATES(:,4).*CONSTANTS(:,19);
    ALGEBRAIC(:,1) = STATES(:,1)+STATES(:,3);
    ALGEBRAIC(:,4) = STATES(:,5)+STATES(:,3);
    ALGEBRAIC(:,6) = 1.00000+( CONSTANTS(:,16).*ALGEBRAIC(:,4))./power(STATES(:,1)+CONSTANTS(:,16), 2.00000);
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