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 =3;
end
% There are a total of 1 entries in each of the rate and state variable arrays.
% There are a total of 43 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('t in component GLUT2_BG (second)');
    LEGEND_CONSTANTS(:,1) = strpad('K_Ai in component params_BG (per_fmol)');
    LEGEND_CONSTANTS(:,2) = strpad('K_Ao in component params_BG (per_fmol)');
    LEGEND_CONSTANTS(:,3) = strpad('K_1 in component params_BG (per_fmol)');
    LEGEND_CONSTANTS(:,4) = strpad('K_2 in component params_BG (per_fmol)');
    LEGEND_CONSTANTS(:,5) = strpad('K_3 in component params_BG (per_fmol)');
    LEGEND_CONSTANTS(:,6) = strpad('K_4 in component params_BG (per_fmol)');
    LEGEND_CONSTANTS(:,7) = strpad('kappa_r1 in component params_BG (fmol_per_s)');
    LEGEND_CONSTANTS(:,8) = strpad('kappa_r2 in component params_BG (fmol_per_s)');
    LEGEND_CONSTANTS(:,9) = strpad('kappa_r3 in component params_BG (fmol_per_s)');
    LEGEND_CONSTANTS(:,10) = strpad('kappa_r4 in component params_BG (fmol_per_s)');
    LEGEND_CONSTANTS(:,31) = strpad('q_Ai in component GLUT2_BG (fmol)');
    LEGEND_ALGEBRAIC(:,1) = strpad('q_Ao in component GLUT2_BG (fmol)');
    LEGEND_CONSTANTS(:,38) = strpad('lambda in component GLUT2_BG (dimensionless)');
    LEGEND_CONSTANTS(:,34) = strpad('q_tot in component GLUT2_BG (fmol)');
    LEGEND_CONSTANTS(:,39) = strpad('v_max in component GLUT2_BG (fmol_per_s)');
    LEGEND_CONSTANTS(:,40) = strpad('k_m_1 in component GLUT2_BG (dimensionless)');
    LEGEND_CONSTANTS(:,41) = strpad('k_m_2 in component GLUT2_BG (dimensionless)');
    LEGEND_CONSTANTS(:,42) = strpad('k_m_3 in component GLUT2_BG (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('v in component GLUT2_BG (fmol_per_s)');
    LEGEND_CONSTANTS(:,36) = strpad('v_max_free in component GLUT2_BG (fmol_per_s)');
    LEGEND_ALGEBRAIC(:,3) = strpad('v_free in component GLUT2_BG (fmol_per_s)');
    LEGEND_CONSTANTS(:,35) = strpad('k_m_1_free in component GLUT2_BG (dimensionless)');
    LEGEND_CONSTANTS(:,37) = strpad('k_m_2_free in component GLUT2_BG (dimensionless)');
    LEGEND_CONSTANTS(:,11) = strpad('k_m_3_free in component GLUT2_BG (dimensionless)');
    LEGEND_CONSTANTS(:,12) = strpad('k_oi_math in component GLUT2_BG (mM)');
    LEGEND_CONSTANTS(:,13) = strpad('k_io_math in component GLUT2_BG (mM)');
    LEGEND_CONSTANTS(:,14) = strpad('v_oi_max in component GLUT2_BG (mM_per_s)');
    LEGEND_CONSTANTS(:,15) = strpad('v_io_max in component GLUT2_BG (mM_per_s)');
    LEGEND_CONSTANTS(:,16) = strpad('V_E in component GLUT2_BG (pL)');
    LEGEND_CONSTANTS(:,17) = strpad('GC in component GLUT2_BG (uM)');
    LEGEND_CONSTANTS(:,18) = strpad('g_i in component GLUT2_BG (mM)');
    LEGEND_STATES(:,1) = strpad('g_o in component GLUT2_BG (mM)');
    LEGEND_CONSTANTS(:,19) = strpad('V_i in component GLUT2_BG (pL)');
    LEGEND_CONSTANTS(:,20) = strpad('V_o in component GLUT2_BG (pL)');
    LEGEND_CONSTANTS(:,21) = strpad('R in component params_BG (J_per_K_mol)');
    LEGEND_CONSTANTS(:,22) = strpad('T in component params_BG (kelvin)');
    LEGEND_CONSTANTS(:,32) = strpad('q_init_Ai in component params_BG (fmol)');
    LEGEND_CONSTANTS(:,33) = strpad('q_init_Ao in component params_BG (fmol)');
    LEGEND_CONSTANTS(:,23) = strpad('q_init_1 in component params_BG (fmol)');
    LEGEND_CONSTANTS(:,24) = strpad('q_init_2 in component params_BG (fmol)');
    LEGEND_CONSTANTS(:,25) = strpad('q_init_3 in component params_BG (fmol)');
    LEGEND_CONSTANTS(:,26) = strpad('q_init_4 in component params_BG (fmol)');
    LEGEND_CONSTANTS(:,27) = strpad('V_i in component params_BG (pL)');
    LEGEND_CONSTANTS(:,28) = strpad('g_i in component params_BG (mM)');
    LEGEND_CONSTANTS(:,29) = strpad('g_o in component params_BG (mM)');
    LEGEND_CONSTANTS(:,30) = strpad('V_o in component params_BG (pL)');
    LEGEND_RATES(:,1) = strpad('d/dt g_o in component GLUT2_BG (mM)');
    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) = 149.65;
    CONSTANTS(:,2) = 149.65;
    CONSTANTS(:,3) = 33.20;
    CONSTANTS(:,4) = 4.25e+03;
    CONSTANTS(:,5) = 344.59;
    CONSTANTS(:,6) = 1.99;
    CONSTANTS(:,7) = 0.36;
    CONSTANTS(:,8) = 0.26;
    CONSTANTS(:,9) = 1.01e+05;
    CONSTANTS(:,10) = 1.01e+04;
    CONSTANTS(:,11) = 218.96;
    CONSTANTS(:,12) = 0.1094;
    CONSTANTS(:,13) = 1.609;
    CONSTANTS(:,14) = 0.004839;
    CONSTANTS(:,15) = 0.07117;
    CONSTANTS(:,16) = 1;
    CONSTANTS(:,17) = 6.67;
    CONSTANTS(:,18) = 1e-8;
    STATES(:,1) = 1e-8;
    CONSTANTS(:,19) = 0.09;
    CONSTANTS(:,20) = 0.09;
    CONSTANTS(:,21) = 8.31;
    CONSTANTS(:,22) = 273.15;
    CONSTANTS(:,23) = 0.0017;
    CONSTANTS(:,24) = 0.0017;
    CONSTANTS(:,25) = 0.0017;
    CONSTANTS(:,26) = 0.0017;
    CONSTANTS(:,27) = 0.09;
    CONSTANTS(:,28) = 10;
    CONSTANTS(:,29) = 1e-5;
    CONSTANTS(:,30) = 0.09;
    CONSTANTS(:,31) =  CONSTANTS(:,18).*CONSTANTS(:,19);
    CONSTANTS(:,32) =  CONSTANTS(:,28).*CONSTANTS(:,27);
    CONSTANTS(:,33) =  CONSTANTS(:,29).*CONSTANTS(:,30);
    CONSTANTS(:,42) = 1.00000;
    CONSTANTS(:,34) = ( CONSTANTS(:,17).*CONSTANTS(:,16).*1.00000)./1000.00;
    CONSTANTS(:,35) =  CONSTANTS(:,12).*CONSTANTS(:,19).*CONSTANTS(:,1);
    CONSTANTS(:,36) = ( CONSTANTS(:,14).*CONSTANTS(:,16))./CONSTANTS(:,35);
    CONSTANTS(:,37) = ( CONSTANTS(:,15).*CONSTANTS(:,16))./CONSTANTS(:,36);
    CONSTANTS(:,38) = CONSTANTS(:,8)./CONSTANTS(:,7);
    CONSTANTS(:,39) = ( CONSTANTS(:,34).*CONSTANTS(:,8).*CONSTANTS(:,5))./(CONSTANTS(:,5)./CONSTANTS(:,3)+CONSTANTS(:,5)./CONSTANTS(:,6));
    CONSTANTS(:,40) = (CONSTANTS(:,5)./CONSTANTS(:,3)+CONSTANTS(:,5)./CONSTANTS(:,6))./(CONSTANTS(:,5)./CONSTANTS(:,4)+( CONSTANTS(:,38).*CONSTANTS(:,5))./CONSTANTS(:,6));
    CONSTANTS(:,41) = (CONSTANTS(:,5)./CONSTANTS(:,3)+CONSTANTS(:,5)./CONSTANTS(:,6))./(1.00000+( CONSTANTS(:,38).*CONSTANTS(:,5))./CONSTANTS(:,3));
    CONSTANTS(:,42) = (CONSTANTS(:,5)./CONSTANTS(:,3)+CONSTANTS(:,5)./CONSTANTS(:,6))./( CONSTANTS(:,38).*(1.00000+CONSTANTS(:,5)./CONSTANTS(:,4)));
    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(:,42);
   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(:,1).*CONSTANTS(:,20);
    ALGEBRAIC(:,2) = ( CONSTANTS(:,39).*( CONSTANTS(:,2).*ALGEBRAIC(:,1) -  CONSTANTS(:,1).*CONSTANTS(:,31)))./(1.00000+( CONSTANTS(:,2).*ALGEBRAIC(:,1))./CONSTANTS(:,40)+( CONSTANTS(:,1).*CONSTANTS(:,31))./CONSTANTS(:,41)+( CONSTANTS(:,2).*ALGEBRAIC(:,1).*CONSTANTS(:,1).*CONSTANTS(:,31))./CONSTANTS(:,42));
    ALGEBRAIC(:,3) = ( CONSTANTS(:,36).*( CONSTANTS(:,2).*ALGEBRAIC(:,1) -  CONSTANTS(:,1).*CONSTANTS(:,31)))./(1.00000+( CONSTANTS(:,2).*ALGEBRAIC(:,1))./CONSTANTS(:,35)+( CONSTANTS(:,1).*CONSTANTS(:,31))./CONSTANTS(:,37)+( CONSTANTS(:,2).*ALGEBRAIC(:,1).*CONSTANTS(:,1).*CONSTANTS(:,31))./CONSTANTS(:,11));
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