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 =17;
end
% There are a total of 11 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 (second)');
    LEGEND_STATES(:,1) = strpad('q_L in component environment (fmol)');
    LEGEND_STATES(:,2) = strpad('q_K1 in component environment (fmol)');
    LEGEND_STATES(:,3) = strpad('q_K2 in component environment (fmol)');
    LEGEND_STATES(:,4) = strpad('q_LK1 in component environment (fmol)');
    LEGEND_STATES(:,5) = strpad('q_P in component environment (fmol)');
    LEGEND_STATES(:,6) = strpad('q_LK1K2 in component environment (fmol)');
    LEGEND_STATES(:,7) = strpad('q_LK1K2P in component environment (fmol)');
    LEGEND_STATES(:,8) = strpad('q_Ubiq in component environment (fmol)');
    LEGEND_STATES(:,9) = strpad('q_LKKPU in component environment (fmol)');
    LEGEND_STATES(:,10) = strpad('q_LKKPUtag in component environment (fmol)');
    LEGEND_STATES(:,11) = strpad('q_LPUtag in component environment (fmol)');
    LEGEND_ALGEBRAIC(:,12) = strpad('v_Re1 in component RTK (fmol_per_sec)');
    LEGEND_ALGEBRAIC(:,13) = strpad('v_Re2 in component RTK (fmol_per_sec)');
    LEGEND_ALGEBRAIC(:,14) = strpad('v_Re3 in component RTK (fmol_per_sec)');
    LEGEND_ALGEBRAIC(:,15) = strpad('v_Re4 in component RTK (fmol_per_sec)');
    LEGEND_ALGEBRAIC(:,16) = strpad('v_Re5 in component RTK (fmol_per_sec)');
    LEGEND_ALGEBRAIC(:,17) = strpad('v_Re6 in component RTK (fmol_per_sec)');
    LEGEND_CONSTANTS(:,1) = strpad('kappa_Re1 in component RTK_parameters (fmol_per_sec)');
    LEGEND_CONSTANTS(:,2) = strpad('kappa_Re2 in component RTK_parameters (fmol_per_sec)');
    LEGEND_CONSTANTS(:,3) = strpad('kappa_Re3 in component RTK_parameters (fmol_per_sec)');
    LEGEND_CONSTANTS(:,4) = strpad('kappa_Re4 in component RTK_parameters (fmol_per_sec)');
    LEGEND_CONSTANTS(:,5) = strpad('kappa_Re5 in component RTK_parameters (fmol_per_sec)');
    LEGEND_CONSTANTS(:,6) = strpad('kappa_Re6 in component RTK_parameters (fmol_per_sec)');
    LEGEND_CONSTANTS(:,7) = strpad('K_L in component RTK_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,8) = strpad('K_K1 in component RTK_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,9) = strpad('K_K2 in component RTK_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,10) = strpad('K_LK1 in component RTK_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,11) = strpad('K_P in component RTK_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,12) = strpad('K_LK1K2 in component RTK_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,13) = strpad('K_LK1K2P in component RTK_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,14) = strpad('K_Ubiq in component RTK_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,15) = strpad('K_LKKPU in component RTK_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,16) = strpad('K_LKKPUtag in component RTK_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,17) = strpad('K_LPUtag in component RTK_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,18) = strpad('R in component constants (J_per_K_per_mol)');
    LEGEND_CONSTANTS(:,19) = strpad('T in component constants (kelvin)');
    LEGEND_ALGEBRAIC(:,1) = strpad('mu_L in component RTK (J_per_mol)');
    LEGEND_ALGEBRAIC(:,2) = strpad('mu_K1 in component RTK (J_per_mol)');
    LEGEND_ALGEBRAIC(:,3) = strpad('mu_K2 in component RTK (J_per_mol)');
    LEGEND_ALGEBRAIC(:,4) = strpad('mu_LK1 in component RTK (J_per_mol)');
    LEGEND_ALGEBRAIC(:,5) = strpad('mu_P in component RTK (J_per_mol)');
    LEGEND_ALGEBRAIC(:,6) = strpad('mu_LK1K2 in component RTK (J_per_mol)');
    LEGEND_ALGEBRAIC(:,7) = strpad('mu_LK1K2P in component RTK (J_per_mol)');
    LEGEND_ALGEBRAIC(:,8) = strpad('mu_Ubiq in component RTK (J_per_mol)');
    LEGEND_ALGEBRAIC(:,9) = strpad('mu_LKKPU in component RTK (J_per_mol)');
    LEGEND_ALGEBRAIC(:,10) = strpad('mu_LKKPUtag in component RTK (J_per_mol)');
    LEGEND_ALGEBRAIC(:,11) = strpad('mu_LPUtag in component RTK (J_per_mol)');
    LEGEND_CONSTANTS(:,20) = strpad('F in component constants (C_per_mol)');
    LEGEND_RATES(:,1) = strpad('d/dt q_L in component environment (fmol)');
    LEGEND_RATES(:,2) = strpad('d/dt q_K1 in component environment (fmol)');
    LEGEND_RATES(:,3) = strpad('d/dt q_K2 in component environment (fmol)');
    LEGEND_RATES(:,4) = strpad('d/dt q_LK1 in component environment (fmol)');
    LEGEND_RATES(:,5) = strpad('d/dt q_P in component environment (fmol)');
    LEGEND_RATES(:,6) = strpad('d/dt q_LK1K2 in component environment (fmol)');
    LEGEND_RATES(:,7) = strpad('d/dt q_LK1K2P in component environment (fmol)');
    LEGEND_RATES(:,8) = strpad('d/dt q_Ubiq in component environment (fmol)');
    LEGEND_RATES(:,9) = strpad('d/dt q_LKKPU in component environment (fmol)');
    LEGEND_RATES(:,10) = strpad('d/dt q_LKKPUtag in component environment (fmol)');
    LEGEND_RATES(:,11) = strpad('d/dt q_LPUtag in component environment (fmol)');
    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) = 1;
    STATES(:,2) = 1e-3;
    STATES(:,3) = 1e-3;
    STATES(:,4) = 1e-6;
    STATES(:,5) = 1;
    STATES(:,6) = 1e-9;
    STATES(:,7) = 1e-9;
    STATES(:,8) = 1;
    STATES(:,9) = 1e-88;
    STATES(:,10) = 1e-88;
    STATES(:,11) = 1e-88;
    CONSTANTS(:,1) = 1.31758e-07;
    CONSTANTS(:,2) = 0.0862846;
    CONSTANTS(:,3) = 0.00038952;
    CONSTANTS(:,4) = 2.66799e-09;
    CONSTANTS(:,5) = 26.6799;
    CONSTANTS(:,6) = 2667.99;
    CONSTANTS(:,7) = 8.32274e+08;
    CONSTANTS(:,8) = 0.000770619;
    CONSTANTS(:,9) = 44390;
    CONSTANTS(:,10) = 0.22063;
    CONSTANTS(:,11) = 6.4394e+12;
    CONSTANTS(:,12) = 3.36906e-07;
    CONSTANTS(:,13) = 7.46298e-05;
    CONSTANTS(:,14) = 4.24411e+13;
    CONSTANTS(:,15) = 10.8958;
    CONSTANTS(:,16) = 1.08958e-11;
    CONSTANTS(:,17) = 2.69163e-14;
    CONSTANTS(:,18) = 8.31;
    CONSTANTS(:,19) = 310;
    CONSTANTS(:,20) = 96485;
    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
    ALGEBRAIC(:,1) =  CONSTANTS(:,18).*CONSTANTS(:,19).*log( CONSTANTS(:,7).*STATES(:,1));
    ALGEBRAIC(:,2) =  CONSTANTS(:,18).*CONSTANTS(:,19).*log( CONSTANTS(:,8).*STATES(:,2));
    ALGEBRAIC(:,4) =  CONSTANTS(:,18).*CONSTANTS(:,19).*log( CONSTANTS(:,10).*STATES(:,4));
    ALGEBRAIC(:,12) =  CONSTANTS(:,1).*(exp((ALGEBRAIC(:,1)+ALGEBRAIC(:,2))./( CONSTANTS(:,18).*CONSTANTS(:,19))) - exp(ALGEBRAIC(:,4)./( CONSTANTS(:,18).*CONSTANTS(:,19))));
    RATES(:,1) =  - ALGEBRAIC(:,12);
    ALGEBRAIC(:,3) =  CONSTANTS(:,18).*CONSTANTS(:,19).*log( CONSTANTS(:,9).*STATES(:,3));
    ALGEBRAIC(:,6) =  CONSTANTS(:,18).*CONSTANTS(:,19).*log( CONSTANTS(:,12).*STATES(:,6));
    ALGEBRAIC(:,13) =  CONSTANTS(:,2).*(exp((ALGEBRAIC(:,4)+ALGEBRAIC(:,3))./( CONSTANTS(:,18).*CONSTANTS(:,19))) - exp(ALGEBRAIC(:,6)./( CONSTANTS(:,18).*CONSTANTS(:,19))));
    RATES(:,4) = ALGEBRAIC(:,12) - ALGEBRAIC(:,13);
    ALGEBRAIC(:,5) =  CONSTANTS(:,18).*CONSTANTS(:,19).*log( CONSTANTS(:,11).*STATES(:,5));
    ALGEBRAIC(:,7) =  CONSTANTS(:,18).*CONSTANTS(:,19).*log( CONSTANTS(:,13).*STATES(:,7));
    ALGEBRAIC(:,14) =  CONSTANTS(:,3).*(exp((ALGEBRAIC(:,5)+ALGEBRAIC(:,6))./( CONSTANTS(:,18).*CONSTANTS(:,19))) - exp(ALGEBRAIC(:,7)./( CONSTANTS(:,18).*CONSTANTS(:,19))));
    RATES(:,5) =  - ALGEBRAIC(:,14);
    RATES(:,6) = ALGEBRAIC(:,13) - ALGEBRAIC(:,14);
    ALGEBRAIC(:,8) =  CONSTANTS(:,18).*CONSTANTS(:,19).*log( CONSTANTS(:,14).*STATES(:,8));
    ALGEBRAIC(:,9) =  CONSTANTS(:,18).*CONSTANTS(:,19).*log( CONSTANTS(:,15).*STATES(:,9));
    ALGEBRAIC(:,15) =  CONSTANTS(:,4).*(exp((ALGEBRAIC(:,8)+ALGEBRAIC(:,7))./( CONSTANTS(:,18).*CONSTANTS(:,19))) - exp(ALGEBRAIC(:,9)./( CONSTANTS(:,18).*CONSTANTS(:,19))));
    RATES(:,7) = ALGEBRAIC(:,14) - ALGEBRAIC(:,15);
    RATES(:,8) =  - ALGEBRAIC(:,15);
    ALGEBRAIC(:,11) =  CONSTANTS(:,18).*CONSTANTS(:,19).*log( CONSTANTS(:,17).*STATES(:,11));
    ALGEBRAIC(:,16) =  CONSTANTS(:,5).*(exp(ALGEBRAIC(:,9)./( CONSTANTS(:,18).*CONSTANTS(:,19))) - exp((ALGEBRAIC(:,2)+ALGEBRAIC(:,3)+ALGEBRAIC(:,11))./( CONSTANTS(:,18).*CONSTANTS(:,19))));
    RATES(:,2) =  - ALGEBRAIC(:,12)+ALGEBRAIC(:,16);
    RATES(:,3) =  - ALGEBRAIC(:,13)+ALGEBRAIC(:,16);
    RATES(:,11) = ALGEBRAIC(:,16);
    ALGEBRAIC(:,10) =  CONSTANTS(:,18).*CONSTANTS(:,19).*log( CONSTANTS(:,16).*STATES(:,10));
    ALGEBRAIC(:,17) =  CONSTANTS(:,6).*(exp(ALGEBRAIC(:,9)./( CONSTANTS(:,18).*CONSTANTS(:,19))) - exp(ALGEBRAIC(:,10)./( CONSTANTS(:,18).*CONSTANTS(:,19))));
    RATES(:,9) = (ALGEBRAIC(:,15) - ALGEBRAIC(:,16)) - ALGEBRAIC(:,17);
    RATES(:,10) = ALGEBRAIC(:,17);
   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) =  CONSTANTS(:,18).*CONSTANTS(:,19).*log( CONSTANTS(:,7).*STATES(:,1));
    ALGEBRAIC(:,2) =  CONSTANTS(:,18).*CONSTANTS(:,19).*log( CONSTANTS(:,8).*STATES(:,2));
    ALGEBRAIC(:,4) =  CONSTANTS(:,18).*CONSTANTS(:,19).*log( CONSTANTS(:,10).*STATES(:,4));
    ALGEBRAIC(:,12) =  CONSTANTS(:,1).*(exp((ALGEBRAIC(:,1)+ALGEBRAIC(:,2))./( CONSTANTS(:,18).*CONSTANTS(:,19))) - exp(ALGEBRAIC(:,4)./( CONSTANTS(:,18).*CONSTANTS(:,19))));
    ALGEBRAIC(:,3) =  CONSTANTS(:,18).*CONSTANTS(:,19).*log( CONSTANTS(:,9).*STATES(:,3));
    ALGEBRAIC(:,6) =  CONSTANTS(:,18).*CONSTANTS(:,19).*log( CONSTANTS(:,12).*STATES(:,6));
    ALGEBRAIC(:,13) =  CONSTANTS(:,2).*(exp((ALGEBRAIC(:,4)+ALGEBRAIC(:,3))./( CONSTANTS(:,18).*CONSTANTS(:,19))) - exp(ALGEBRAIC(:,6)./( CONSTANTS(:,18).*CONSTANTS(:,19))));
    ALGEBRAIC(:,5) =  CONSTANTS(:,18).*CONSTANTS(:,19).*log( CONSTANTS(:,11).*STATES(:,5));
    ALGEBRAIC(:,7) =  CONSTANTS(:,18).*CONSTANTS(:,19).*log( CONSTANTS(:,13).*STATES(:,7));
    ALGEBRAIC(:,14) =  CONSTANTS(:,3).*(exp((ALGEBRAIC(:,5)+ALGEBRAIC(:,6))./( CONSTANTS(:,18).*CONSTANTS(:,19))) - exp(ALGEBRAIC(:,7)./( CONSTANTS(:,18).*CONSTANTS(:,19))));
    ALGEBRAIC(:,8) =  CONSTANTS(:,18).*CONSTANTS(:,19).*log( CONSTANTS(:,14).*STATES(:,8));
    ALGEBRAIC(:,9) =  CONSTANTS(:,18).*CONSTANTS(:,19).*log( CONSTANTS(:,15).*STATES(:,9));
    ALGEBRAIC(:,15) =  CONSTANTS(:,4).*(exp((ALGEBRAIC(:,8)+ALGEBRAIC(:,7))./( CONSTANTS(:,18).*CONSTANTS(:,19))) - exp(ALGEBRAIC(:,9)./( CONSTANTS(:,18).*CONSTANTS(:,19))));
    ALGEBRAIC(:,11) =  CONSTANTS(:,18).*CONSTANTS(:,19).*log( CONSTANTS(:,17).*STATES(:,11));
    ALGEBRAIC(:,16) =  CONSTANTS(:,5).*(exp(ALGEBRAIC(:,9)./( CONSTANTS(:,18).*CONSTANTS(:,19))) - exp((ALGEBRAIC(:,2)+ALGEBRAIC(:,3)+ALGEBRAIC(:,11))./( CONSTANTS(:,18).*CONSTANTS(:,19))));
    ALGEBRAIC(:,10) =  CONSTANTS(:,18).*CONSTANTS(:,19).*log( CONSTANTS(:,16).*STATES(:,10));
    ALGEBRAIC(:,17) =  CONSTANTS(:,6).*(exp(ALGEBRAIC(:,9)./( CONSTANTS(:,18).*CONSTANTS(:,19))) - exp(ALGEBRAIC(:,10)./( CONSTANTS(:,18).*CONSTANTS(:,19))));
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