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 =8;
end
% There are a total of 6 entries in each of the rate and state variable arrays.
% There are a total of 21 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 (min)');
    LEGEND_CONSTANTS(:,1) = strpad('Vp in component environment (l)');
    LEGEND_CONSTANTS(:,2) = strpad('Vi in component environment (l)');
    LEGEND_CONSTANTS(:,3) = strpad('Vg in component environment (l)');
    LEGEND_CONSTANTS(:,4) = strpad('E in component environment (l_per_min)');
    LEGEND_STATES(:,1) = strpad('Ip in component plasma_insulin (mU)');
    LEGEND_ALGEBRAIC(:,1) = strpad('Ip_conc in component plasma_insulin (mU_per_l)');
    LEGEND_CONSTANTS(:,5) = strpad('tp in component plasma_insulin (min)');
    LEGEND_ALGEBRAIC(:,2) = strpad('f1_G in component plasma_insulin (mU_per_min)');
    LEGEND_CONSTANTS(:,6) = strpad('Rm in component plasma_insulin (mU_per_min)');
    LEGEND_CONSTANTS(:,7) = strpad('C1 in component plasma_insulin (mg_per_l)');
    LEGEND_CONSTANTS(:,8) = strpad('a1 in component plasma_insulin (mg_per_l)');
    LEGEND_STATES(:,2) = strpad('Ii in component intercellular_insulin (mU)');
    LEGEND_STATES(:,3) = strpad('G in component glucose (mg)');
    LEGEND_ALGEBRAIC(:,3) = strpad('Ii_conc in component intercellular_insulin (mU_per_l)');
    LEGEND_CONSTANTS(:,9) = strpad('ti in component intercellular_insulin (min)');
    LEGEND_ALGEBRAIC(:,4) = strpad('G_conc in component glucose (mg_per_dl)');
    LEGEND_CONSTANTS(:,10) = strpad('Gin in component glucose (mg_per_min)');
    LEGEND_ALGEBRAIC(:,5) = strpad('f2_G in component glucose (mg_per_min)');
    LEGEND_ALGEBRAIC(:,6) = strpad('f3_G in component glucose (dimensionless)');
    LEGEND_ALGEBRAIC(:,7) = strpad('f4_Ii in component glucose (mg_per_min)');
    LEGEND_ALGEBRAIC(:,8) = strpad('f5_x3 in component glucose (mg_per_min)');
    LEGEND_CONSTANTS(:,11) = strpad('C2 in component glucose (mg_per_l)');
    LEGEND_CONSTANTS(:,12) = strpad('C3 in component glucose (mg_per_l)');
    LEGEND_CONSTANTS(:,13) = strpad('C4 in component glucose (mU_per_l)');
    LEGEND_CONSTANTS(:,14) = strpad('C5 in component glucose (mU_per_l)');
    LEGEND_CONSTANTS(:,15) = strpad('U0 in component glucose (mg_per_min)');
    LEGEND_CONSTANTS(:,16) = strpad('Um in component glucose (mg_per_min)');
    LEGEND_CONSTANTS(:,17) = strpad('Ub in component glucose (mg_per_min)');
    LEGEND_CONSTANTS(:,18) = strpad('beta in component glucose (dimensionless)');
    LEGEND_CONSTANTS(:,19) = strpad('Rg in component glucose (mg_per_min)');
    LEGEND_CONSTANTS(:,20) = strpad('alpha in component glucose (l_per_mU)');
    LEGEND_STATES(:,4) = strpad('x3 in component delay (min)');
    LEGEND_CONSTANTS(:,21) = strpad('td in component delay (min)');
    LEGEND_STATES(:,5) = strpad('x1 in component delay (min)');
    LEGEND_STATES(:,6) = strpad('x2 in component delay (min)');
    LEGEND_RATES(:,1) = strpad('d/dt Ip in component plasma_insulin (mU)');
    LEGEND_RATES(:,2) = strpad('d/dt Ii in component intercellular_insulin (mU)');
    LEGEND_RATES(:,3) = strpad('d/dt G in component glucose (mg)');
    LEGEND_RATES(:,5) = strpad('d/dt x1 in component delay (min)');
    LEGEND_RATES(:,6) = strpad('d/dt x2 in component delay (min)');
    LEGEND_RATES(:,4) = strpad('d/dt x3 in component delay (min)');
    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) = 3;
    CONSTANTS(:,2) = 11;
    CONSTANTS(:,3) = 10;
    CONSTANTS(:,4) = 0.2;
    STATES(:,1) = 93.36441699;
    CONSTANTS(:,5) = 6;
    CONSTANTS(:,6) = 210;
    CONSTANTS(:,7) = 2000;
    CONSTANTS(:,8) = 300;
    STATES(:,2) = 243.2865183;
    STATES(:,3) = 12342.61665;
    CONSTANTS(:,9) = 100;
    CONSTANTS(:,10) = 216;
    CONSTANTS(:,11) = 144;
    CONSTANTS(:,12) = 1000;
    CONSTANTS(:,13) = 80;
    CONSTANTS(:,14) = 26;
    CONSTANTS(:,15) = 40;
    CONSTANTS(:,16) = 940;
    CONSTANTS(:,17) = 72;
    CONSTANTS(:,18) = 1.77;
    CONSTANTS(:,19) = 180;
    CONSTANTS(:,20) = 0.29;
    STATES(:,4) = 104.5878705;
    CONSTANTS(:,21) = 36;
    STATES(:,5) = 110.420253;
    STATES(:,6) = 112.7601171;
    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(:,2) =  CONSTANTS(:,4).*(STATES(:,1)./CONSTANTS(:,1) - STATES(:,2)./CONSTANTS(:,2)) - STATES(:,2)./CONSTANTS(:,9);
    RATES(:,5) =  (3.00000./CONSTANTS(:,21)).*(STATES(:,1)./1.00000 - STATES(:,5));
    RATES(:,6) =  (3.00000./CONSTANTS(:,21)).*(STATES(:,5) - STATES(:,6));
    RATES(:,4) =  (3.00000./CONSTANTS(:,21)).*(STATES(:,6) - STATES(:,4));
    ALGEBRAIC(:,2) = CONSTANTS(:,6)./(1.00000+exp((CONSTANTS(:,7) - STATES(:,3)./CONSTANTS(:,3))./CONSTANTS(:,8)));
    RATES(:,1) = ALGEBRAIC(:,2) - ( CONSTANTS(:,4).*(STATES(:,1)./CONSTANTS(:,1) - STATES(:,2)./CONSTANTS(:,2))+STATES(:,1)./CONSTANTS(:,5));
    ALGEBRAIC(:,5) =  CONSTANTS(:,17).*(1.00000 - exp( - STATES(:,3)./( CONSTANTS(:,11).*CONSTANTS(:,3))));
    ALGEBRAIC(:,6) = STATES(:,3)./( CONSTANTS(:,12).*CONSTANTS(:,3));
    ALGEBRAIC(:,7) = CONSTANTS(:,15)+(CONSTANTS(:,16) - CONSTANTS(:,15))./(1.00000+exp(  - CONSTANTS(:,18).*log( (STATES(:,2)./CONSTANTS(:,13)).*(1.00000./CONSTANTS(:,2)+1.00000./( CONSTANTS(:,4).*CONSTANTS(:,9))))));
    ALGEBRAIC(:,8) = CONSTANTS(:,19)./(1.00000+exp( CONSTANTS(:,20).*(( STATES(:,4).*1.00000)./CONSTANTS(:,1) - CONSTANTS(:,14))));
    RATES(:,3) = CONSTANTS(:,10)+ALGEBRAIC(:,8)+ - (ALGEBRAIC(:,5)+ ALGEBRAIC(:,6).*ALGEBRAIC(:,7));
   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(:,2) = CONSTANTS(:,6)./(1.00000+exp((CONSTANTS(:,7) - STATES(:,3)./CONSTANTS(:,3))./CONSTANTS(:,8)));
    ALGEBRAIC(:,5) =  CONSTANTS(:,17).*(1.00000 - exp( - STATES(:,3)./( CONSTANTS(:,11).*CONSTANTS(:,3))));
    ALGEBRAIC(:,6) = STATES(:,3)./( CONSTANTS(:,12).*CONSTANTS(:,3));
    ALGEBRAIC(:,7) = CONSTANTS(:,15)+(CONSTANTS(:,16) - CONSTANTS(:,15))./(1.00000+exp(  - CONSTANTS(:,18).*log( (STATES(:,2)./CONSTANTS(:,13)).*(1.00000./CONSTANTS(:,2)+1.00000./( CONSTANTS(:,4).*CONSTANTS(:,9))))));
    ALGEBRAIC(:,8) = CONSTANTS(:,19)./(1.00000+exp( CONSTANTS(:,20).*(( STATES(:,4).*1.00000)./CONSTANTS(:,1) - CONSTANTS(:,14))));
    ALGEBRAIC(:,1) = STATES(:,1)./CONSTANTS(:,1);
    ALGEBRAIC(:,3) = STATES(:,2)./CONSTANTS(:,2);
    ALGEBRAIC(:,4) = STATES(:,3)./( CONSTANTS(:,3).*10.0000);
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