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 5 entries in each of the rate and state variable arrays.
% There are a total of 18 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 (hour)');
    LEGEND_STATES(:,1) = strpad('M in component M (micromolar)');
    LEGEND_CONSTANTS(:,1) = strpad('Km in component M (micromolar)');
    LEGEND_CONSTANTS(:,2) = strpad('vs in component M (flux)');
    LEGEND_CONSTANTS(:,3) = strpad('vm in component M (flux)');
    LEGEND_CONSTANTS(:,4) = strpad('n in component M (dimensionless)');
    LEGEND_CONSTANTS(:,5) = strpad('KI in component M (micromolar)');
    LEGEND_STATES(:,2) = strpad('PN in component PN (micromolar)');
    LEGEND_STATES(:,3) = strpad('P0 in component P0 (micromolar)');
    LEGEND_CONSTANTS(:,6) = strpad('ks in component P0 (first_order_rate_constant)');
    LEGEND_STATES(:,4) = strpad('P1 in component P1 (micromolar)');
    LEGEND_CONSTANTS(:,7) = strpad('K1 in component parameters (micromolar)');
    LEGEND_CONSTANTS(:,8) = strpad('V1 in component parameters (flux)');
    LEGEND_CONSTANTS(:,9) = strpad('K2 in component parameters (micromolar)');
    LEGEND_CONSTANTS(:,10) = strpad('V2 in component parameters (flux)');
    LEGEND_STATES(:,5) = strpad('P2 in component P2 (micromolar)');
    LEGEND_CONSTANTS(:,11) = strpad('K3 in component parameters (micromolar)');
    LEGEND_CONSTANTS(:,12) = strpad('V3 in component parameters (flux)');
    LEGEND_CONSTANTS(:,13) = strpad('K4 in component parameters (micromolar)');
    LEGEND_CONSTANTS(:,14) = strpad('V4 in component parameters (flux)');
    LEGEND_CONSTANTS(:,15) = strpad('Kd in component P2 (micromolar)');
    LEGEND_CONSTANTS(:,16) = strpad('vd in component P2 (flux)');
    LEGEND_CONSTANTS(:,17) = strpad('k1 in component parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,18) = strpad('k2 in component parameters (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,1) = strpad('Pt in component Pt (micromolar)');
    LEGEND_RATES(:,1) = strpad('d/dt M in component M (micromolar)');
    LEGEND_RATES(:,3) = strpad('d/dt P0 in component P0 (micromolar)');
    LEGEND_RATES(:,4) = strpad('d/dt P1 in component P1 (micromolar)');
    LEGEND_RATES(:,5) = strpad('d/dt P2 in component P2 (micromolar)');
    LEGEND_RATES(:,2) = strpad('d/dt PN in component PN (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) = 0.6;
    CONSTANTS(:,1) = 0.5;
    CONSTANTS(:,2) = 0.76;
    CONSTANTS(:,3) = 0.65;
    CONSTANTS(:,4) = 4.0;
    CONSTANTS(:,5) = 1.0;
    STATES(:,2) = 1.1;
    STATES(:,3) = 0.5;
    CONSTANTS(:,6) = 0.38;
    STATES(:,4) = 0.6;
    CONSTANTS(:,7) = 2.0;
    CONSTANTS(:,8) = 3.2;
    CONSTANTS(:,9) = 2.0;
    CONSTANTS(:,10) = 1.58;
    STATES(:,5) = 0.6;
    CONSTANTS(:,11) = 2.0;
    CONSTANTS(:,12) = 5.0;
    CONSTANTS(:,13) = 2.0;
    CONSTANTS(:,14) = 2.5;
    CONSTANTS(:,15) = 0.2;
    CONSTANTS(:,16) = 0.95;
    CONSTANTS(:,17) = 1.9;
    CONSTANTS(:,18) = 1.3;
    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).*(power(CONSTANTS(:,5), CONSTANTS(:,4))./(power(CONSTANTS(:,5), CONSTANTS(:,4))+power(STATES(:,2), CONSTANTS(:,4)))) -  CONSTANTS(:,3).*(STATES(:,1)./(CONSTANTS(:,1)+STATES(:,1)));
    RATES(:,3) = ( CONSTANTS(:,6).*STATES(:,1) -  CONSTANTS(:,8).*(STATES(:,3)./(CONSTANTS(:,7)+STATES(:,3))))+ CONSTANTS(:,10).*(STATES(:,4)./(CONSTANTS(:,9)+STATES(:,4)));
    RATES(:,4) = ( CONSTANTS(:,8).*(STATES(:,3)./(CONSTANTS(:,7)+STATES(:,3))) - ( CONSTANTS(:,10).*(STATES(:,4)./(CONSTANTS(:,9)+STATES(:,4)))+ CONSTANTS(:,12).*(STATES(:,4)./(CONSTANTS(:,11)+STATES(:,4)))))+ CONSTANTS(:,14).*(STATES(:,5)./(CONSTANTS(:,13)+STATES(:,5)));
    RATES(:,5) = (( CONSTANTS(:,12).*(STATES(:,4)./(CONSTANTS(:,11)+STATES(:,4))) - ( CONSTANTS(:,14).*(STATES(:,5)./(CONSTANTS(:,13)+STATES(:,5)))+ CONSTANTS(:,17).*STATES(:,5)))+ CONSTANTS(:,18).*STATES(:,2)) -  CONSTANTS(:,16).*(STATES(:,5)./(CONSTANTS(:,15)+STATES(:,5)));
    RATES(:,2) =  CONSTANTS(:,17).*STATES(:,5) -  CONSTANTS(:,18).*STATES(:,2);
   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(:,5)+STATES(:,2);
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