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 =4;
end
% There are a total of 3 entries in each of the rate and state variable arrays.
% There are a total of 26 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('Pha in component Pha (dimensionless)');
    LEGEND_ALGEBRAIC(:,1) = strpad('V_1 in component V_1 (dimensionless)');
    LEGEND_STATES(:,2) = strpad('Z in component Z (dimensionless)');
    LEGEND_ALGEBRAIC(:,3) = strpad('K_1 in component K_1 (dimensionless)');
    LEGEND_CONSTANTS(:,1) = strpad('V_M2 in component Pha (per_minute)');
    LEGEND_CONSTANTS(:,2) = strpad('alpha in component Pha (dimensionless)');
    LEGEND_CONSTANTS(:,3) = strpad('Glc in component Pha (micromolar)');
    LEGEND_CONSTANTS(:,4) = strpad('K_2 in component Pha (dimensionless)');
    LEGEND_CONSTANTS(:,5) = strpad('K_a1 in component Pha (micromolar)');
    LEGEND_CONSTANTS(:,6) = strpad('K_a2 in component Pha (micromolar)');
    LEGEND_CONSTANTS(:,7) = strpad('V_M1 in component V_1 (per_minute)');
    LEGEND_CONSTANTS(:,8) = strpad('gamma in component V_1 (dimensionless)');
    LEGEND_CONSTANTS(:,9) = strpad('K_a5 in component V_1 (micromolar)');
    LEGEND_CONSTANTS(:,10) = strpad('K_11 in component K_1 (dimensionless)');
    LEGEND_CONSTANTS(:,11) = strpad('K_a6 in component K_1 (micromolar)');
    LEGEND_CONSTANTS(:,26) = strpad('V_in in component V_in (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('V_2i in component V_2i (dimensionless)');
    LEGEND_ALGEBRAIC(:,4) = strpad('V_3i in component V_3i (dimensionless)');
    LEGEND_CONSTANTS(:,12) = strpad('k_f in component Z (per_minute)');
    LEGEND_STATES(:,3) = strpad('Y in component Y (dimensionless)');
    LEGEND_CONSTANTS(:,13) = strpad('k in component Z (per_minute)');
    LEGEND_CONSTANTS(:,14) = strpad('k_f in component Y (per_minute)');
    LEGEND_CONSTANTS(:,15) = strpad('v_0 in component V_in (micromolar_per_minute)');
    LEGEND_CONSTANTS(:,16) = strpad('v_1 in component V_in (micromolar_per_minute)');
    LEGEND_CONSTANTS(:,17) = strpad('beta in component V_in (dimensionless)');
    LEGEND_CONSTANTS(:,18) = strpad('v_M2i in component V_2i (micromolar_per_minute)');
    LEGEND_CONSTANTS(:,19) = strpad('n in component V_2i (dimensionless)');
    LEGEND_CONSTANTS(:,20) = strpad('K_2i in component V_2i (micromolar)');
    LEGEND_CONSTANTS(:,21) = strpad('v_M3i in component V_3i (micromolar_per_minute)');
    LEGEND_CONSTANTS(:,22) = strpad('p in component V_3i (dimensionless)');
    LEGEND_CONSTANTS(:,23) = strpad('m in component V_3i (dimensionless)');
    LEGEND_CONSTANTS(:,24) = strpad('K_Ri in component V_3i (micromolar)');
    LEGEND_CONSTANTS(:,25) = strpad('K_Ai in component V_3i (micromolar)');
    LEGEND_RATES(:,1) = strpad('d/dt Pha in component Pha (dimensionless)');
    LEGEND_RATES(:,2) = strpad('d/dt Z in component Z (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt Y in component Y (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) = 0.098;
    STATES(:,2) = 0.000179;
    CONSTANTS(:,1) = 0.6;
    CONSTANTS(:,2) = 9;
    CONSTANTS(:,3) = 10000;
    CONSTANTS(:,4) = 0.2;
    CONSTANTS(:,5) = 10000;
    CONSTANTS(:,6) = 10000;
    CONSTANTS(:,7) = 1.5;
    CONSTANTS(:,8) = 9;
    CONSTANTS(:,9) = 0.5;
    CONSTANTS(:,10) = 0.1;
    CONSTANTS(:,11) = 0.5;
    CONSTANTS(:,12) = 0.7;
    STATES(:,3) = 0.00122;
    CONSTANTS(:,13) = 10;
    CONSTANTS(:,14) = 0.7;
    CONSTANTS(:,15) = 1;
    CONSTANTS(:,16) = 5.7;
    CONSTANTS(:,17) = 0.3;
    CONSTANTS(:,18) = 30;
    CONSTANTS(:,19) = 2;
    CONSTANTS(:,20) = 0.5;
    CONSTANTS(:,21) = 325;
    CONSTANTS(:,22) = 4;
    CONSTANTS(:,23) = 4;
    CONSTANTS(:,24) = 1.7;
    CONSTANTS(:,25) = 0.46;
    CONSTANTS(:,26) = CONSTANTS(:,15)+ CONSTANTS(:,16).*CONSTANTS(:,17);
    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(:,7).*(1.00000+ CONSTANTS(:,8).*(power(STATES(:,2), 4.00000)./power(CONSTANTS(:,9), 4.00000)+power(STATES(:,2), 4.00000)));
    ALGEBRAIC(:,3) = CONSTANTS(:,10)./(1.00000+power(STATES(:,2), 4.00000)./power(CONSTANTS(:,11), 4.00000));
    RATES(:,1) =  ALGEBRAIC(:,1).*STATES(:,2).*((1.00000 - STATES(:,1))./(( ALGEBRAIC(:,3).*STATES(:,2)+1.00000) - STATES(:,1))) - ( CONSTANTS(:,1).*(1.00000+( CONSTANTS(:,2).*CONSTANTS(:,3))./(CONSTANTS(:,5)+CONSTANTS(:,3))).*STATES(:,1))./(CONSTANTS(:,4)./(1.00000+CONSTANTS(:,3)./CONSTANTS(:,6))+STATES(:,1));
    ALGEBRAIC(:,2) =  CONSTANTS(:,18).*(power(STATES(:,2), CONSTANTS(:,19))./(power(CONSTANTS(:,20), CONSTANTS(:,19))+power(STATES(:,2), CONSTANTS(:,19))));
    ALGEBRAIC(:,4) =  CONSTANTS(:,21).*(power(STATES(:,3), CONSTANTS(:,23))./power(CONSTANTS(:,24), CONSTANTS(:,23))+power(STATES(:,3), CONSTANTS(:,19))).*(power(STATES(:,2), CONSTANTS(:,22))./(power(CONSTANTS(:,25), CONSTANTS(:,22))+power(STATES(:,2), CONSTANTS(:,22))));
    RATES(:,2) = ((CONSTANTS(:,26) - ALGEBRAIC(:,2))+ALGEBRAIC(:,4)+ CONSTANTS(:,12).*STATES(:,3)) -  CONSTANTS(:,13).*STATES(:,2);
    RATES(:,3) = (ALGEBRAIC(:,2) - ALGEBRAIC(:,4)) -  CONSTANTS(:,14).*STATES(:,3);
   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(:,7).*(1.00000+ CONSTANTS(:,8).*(power(STATES(:,2), 4.00000)./power(CONSTANTS(:,9), 4.00000)+power(STATES(:,2), 4.00000)));
    ALGEBRAIC(:,3) = CONSTANTS(:,10)./(1.00000+power(STATES(:,2), 4.00000)./power(CONSTANTS(:,11), 4.00000));
    ALGEBRAIC(:,2) =  CONSTANTS(:,18).*(power(STATES(:,2), CONSTANTS(:,19))./(power(CONSTANTS(:,20), CONSTANTS(:,19))+power(STATES(:,2), CONSTANTS(:,19))));
    ALGEBRAIC(:,4) =  CONSTANTS(:,21).*(power(STATES(:,3), CONSTANTS(:,23))./power(CONSTANTS(:,24), CONSTANTS(:,23))+power(STATES(:,3), CONSTANTS(:,19))).*(power(STATES(:,2), CONSTANTS(:,22))./(power(CONSTANTS(:,25), CONSTANTS(:,22))+power(STATES(:,2), CONSTANTS(:,22))));
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