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 =0;
end
% There are a total of 5 entries in each of the rate and state variable arrays.
% There are a total of 36 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('x1 in component x1 (microg_l)');
    LEGEND_CONSTANTS(:,1) = strpad('lambda_1 in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,2) = strpad('x3 in component x3 (microg_l)');
    LEGEND_CONSTANTS(:,2) = strpad('a1 in component model_parameters (flux)');
    LEGEND_CONSTANTS(:,3) = strpad('a2 in component model_parameters (flux)');
    LEGEND_CONSTANTS(:,4) = strpad('a3 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,5) = strpad('a4 in component model_parameters (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,6) = strpad('a5 in component model_parameters (per_microg_l)');
    LEGEND_CONSTANTS(:,7) = strpad('a6 in component model_parameters (per_microg_l2)');
    LEGEND_CONSTANTS(:,8) = strpad('a7 in component model_parameters (per_microg_l)');
    LEGEND_CONSTANTS(:,9) = strpad('a8 in component model_parameters (per_microg_l2)');
    LEGEND_STATES(:,3) = strpad('x2 in component x2 (microg_l)');
    LEGEND_CONSTANTS(:,10) = strpad('lambda_2 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,11) = strpad('a9 in component model_parameters (flux)');
    LEGEND_CONSTANTS(:,12) = strpad('a10 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,13) = strpad('a11 in component model_parameters (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,14) = strpad('a12 in component model_parameters (per_microg_l)');
    LEGEND_CONSTANTS(:,15) = strpad('a13 in component model_parameters (per_microg_l2)');
    LEGEND_CONSTANTS(:,16) = strpad('a14 in component model_parameters (per_microg_l)');
    LEGEND_CONSTANTS(:,17) = strpad('a15 in component model_parameters (per_microg_l2)');
    LEGEND_CONSTANTS(:,34) = strpad('lambda_3_ in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,4) = strpad('x4 in component x4 (microg_l)');
    LEGEND_STATES(:,5) = strpad('x5 in component x5 (microg_l)');
    LEGEND_CONSTANTS(:,18) = strpad('a16 in component model_parameters (flux)');
    LEGEND_CONSTANTS(:,19) = strpad('a17 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,20) = strpad('a18 in component model_parameters (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,21) = strpad('a19 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,22) = strpad('a20 in component model_parameters (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,23) = strpad('a21 in component model_parameters (per_microg_l)');
    LEGEND_CONSTANTS(:,24) = strpad('a22 in component model_parameters (per_microg_l2)');
    LEGEND_CONSTANTS(:,25) = strpad('a23 in component model_parameters (per_microg_l)');
    LEGEND_CONSTANTS(:,26) = strpad('a24 in component model_parameters (per_microg_l2)');
    LEGEND_CONSTANTS(:,27) = strpad('a25 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,28) = strpad('a26 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,35) = strpad('lambda_4_ in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,29) = strpad('a27 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,36) = strpad('lambda_5_ in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,30) = strpad('a28 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,31) = strpad('lambda_3 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,32) = strpad('lambda_4 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,33) = strpad('lambda_5 in component model_parameters (first_order_rate_constant)');
    LEGEND_RATES(:,1) = strpad('d/dt x1 in component x1 (microg_l)');
    LEGEND_RATES(:,3) = strpad('d/dt x2 in component x2 (microg_l)');
    LEGEND_RATES(:,2) = strpad('d/dt x3 in component x3 (microg_l)');
    LEGEND_RATES(:,4) = strpad('d/dt x4 in component x4 (microg_l)');
    LEGEND_RATES(:,5) = strpad('d/dt x5 in component x5 (microg_l)');
    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) = 0.01067;
    CONSTANTS(:,1) = 0.059;
    STATES(:,2) = 6.51;
    CONSTANTS(:,2) = 0.000017;
    CONSTANTS(:,3) = 0.0023;
    CONSTANTS(:,4) = 0.6;
    CONSTANTS(:,5) = 45;
    CONSTANTS(:,6) = 36;
    CONSTANTS(:,7) = 216;
    CONSTANTS(:,8) = 0.28;
    CONSTANTS(:,9) = 0.36;
    STATES(:,3) = 0.04665;
    CONSTANTS(:,10) = 0.028;
    CONSTANTS(:,11) = 0.0003;
    CONSTANTS(:,12) = 0.18;
    CONSTANTS(:,13) = 150;
    CONSTANTS(:,14) = 18;
    CONSTANTS(:,15) = 460;
    CONSTANTS(:,16) = 0.46;
    CONSTANTS(:,17) = 0.1;
    STATES(:,4) = 60.61;
    STATES(:,5) = 12.61;
    CONSTANTS(:,18) = 0.04;
    CONSTANTS(:,19) = 150;
    CONSTANTS(:,20) = 3800;
    CONSTANTS(:,21) = 57;
    CONSTANTS(:,22) = 2600;
    CONSTANTS(:,23) = 200;
    CONSTANTS(:,24) = 9400;
    CONSTANTS(:,25) = 10;
    CONSTANTS(:,26) = 320;
    CONSTANTS(:,27) = 0.04;
    CONSTANTS(:,28) = 0.00097;
    CONSTANTS(:,29) = 0.57;
    CONSTANTS(:,30) = 0.0017;
    CONSTANTS(:,31) = 0.0986;
    CONSTANTS(:,32) = 0.024;
    CONSTANTS(:,33) = 3e-5;
    CONSTANTS(:,34) = CONSTANTS(:,31)+CONSTANTS(:,29)+CONSTANTS(:,30);
    CONSTANTS(:,35) = CONSTANTS(:,32)+CONSTANTS(:,27);
    CONSTANTS(:,36) = CONSTANTS(:,33)+CONSTANTS(:,28);
    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)+(CONSTANTS(:,3)+ CONSTANTS(:,4).*STATES(:,1)+ CONSTANTS(:,5).*power(STATES(:,1), 2.00000))./(1.00000+ CONSTANTS(:,6).*STATES(:,1)+ CONSTANTS(:,7).*power(STATES(:,1), 2.00000)+ CONSTANTS(:,8).*STATES(:,2)+ CONSTANTS(:,9).*power(STATES(:,2), 2.00000))) -  CONSTANTS(:,1).*STATES(:,1);
    RATES(:,3) = (CONSTANTS(:,11)+ CONSTANTS(:,12).*STATES(:,1)+ CONSTANTS(:,13).*power(STATES(:,1), 2.00000))./(1.00000+ CONSTANTS(:,14).*STATES(:,1)+ CONSTANTS(:,15).*power(STATES(:,1), 2.00000)+ CONSTANTS(:,16).*STATES(:,2)+ CONSTANTS(:,17).*power(STATES(:,2), 2.00000)) -  CONSTANTS(:,10).*STATES(:,3);
    RATES(:,2) = (CONSTANTS(:,18)+( CONSTANTS(:,19).*STATES(:,1)+ CONSTANTS(:,20).*power(STATES(:,1), 2.00000)+ CONSTANTS(:,21).*STATES(:,3)+ CONSTANTS(:,22).*power(STATES(:,3), 2.00000))./(1.00000+ CONSTANTS(:,23).*STATES(:,1)+ CONSTANTS(:,24).*power(STATES(:,1), 2.00000)+ CONSTANTS(:,25).*STATES(:,3)+ CONSTANTS(:,26).*power(STATES(:,3), 2.00000))+ CONSTANTS(:,27).*STATES(:,4)+ CONSTANTS(:,28).*STATES(:,5)) -  CONSTANTS(:,34).*STATES(:,2);
    RATES(:,4) =  CONSTANTS(:,29).*STATES(:,2) -  CONSTANTS(:,35).*STATES(:,4);
    RATES(:,5) =  CONSTANTS(:,30).*STATES(:,2) -  CONSTANTS(:,36).*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
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