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 =12;
end
% There are a total of 7 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 (hour)');
    LEGEND_STATES(:,1) = strpad('Cgen_pp in component Cgen_pp (micromolar)');
    LEGEND_CONSTANTS(:,23) = strpad('Qpp in component Cgen_pp (litre_hour)');
    LEGEND_CONSTANTS(:,1) = strpad('Ppp in component Cgen_pp (dimensionless)');
    LEGEND_ALGEBRAIC(:,1) = strpad('H_Cgen_pp in component Cgen_pp (dimensionless)');
    LEGEND_CONSTANTS(:,2) = strpad('Vpp in component Cgen_pp (litre)');
    LEGEND_ALGEBRAIC(:,9) = strpad('H_Cgen_B in component Cgen_B (dimensionless)');
    LEGEND_CONSTANTS(:,20) = strpad('Qt in component model_parameters (litre_hour)');
    LEGEND_ALGEBRAIC(:,7) = strpad('Cgen_B in component Cgen_B (micromolar)');
    LEGEND_STATES(:,2) = strpad('Cgen_rp in component Cgen_rp (micromolar)');
    LEGEND_CONSTANTS(:,3) = strpad('Prp in component Cgen_rp (dimensionless)');
    LEGEND_CONSTANTS(:,24) = strpad('Qrp in component Cgen_rp (litre_hour)');
    LEGEND_ALGEBRAIC(:,2) = strpad('H_Cgen_rp in component Cgen_rp (dimensionless)');
    LEGEND_CONSTANTS(:,4) = strpad('Vrp in component Cgen_rp (litre)');
    LEGEND_CONSTANTS(:,5) = strpad('kgen_urine in component Cgen_rp (first_order_rate_constant)');
    LEGEND_STATES(:,3) = strpad('Cgen_l in component Cgen_l (micromolar)');
    LEGEND_CONSTANTS(:,25) = strpad('Ql in component Cgen_l (litre_hour)');
    LEGEND_ALGEBRAIC(:,3) = strpad('H_Cgen_l in component Cgen_l (dimensionless)');
    LEGEND_CONSTANTS(:,6) = strpad('Vl in component Cgen_l (litre)');
    LEGEND_CONSTANTS(:,7) = strpad('Pl in component Cgen_l (dimensionless)');
    LEGEND_CONSTANTS(:,8) = strpad('Vmax in component model_parameters (micromolar_hour)');
    LEGEND_CONSTANTS(:,9) = strpad('Km in component model_parameters (micromolar)');
    LEGEND_ALGEBRAIC(:,12) = strpad('vinf in component model_parameters (micromole_hour)');
    LEGEND_ALGEBRAIC(:,4) = strpad('H_Cgen_GI in component Cgen_GI (dimensionless)');
    LEGEND_CONSTANTS(:,26) = strpad('QGI in component Cgen_GI (litre_hour)');
    LEGEND_STATES(:,4) = strpad('Cgen_GI in component Cgen_GI (micromolar)');
    LEGEND_CONSTANTS(:,10) = strpad('VGI in component Cgen_GI (litre)');
    LEGEND_STATES(:,5) = strpad('Ccon_l in component Ccon_l (micromolar)');
    LEGEND_ALGEBRAIC(:,5) = strpad('H_Ccon_l in component Ccon_l (dimensionless)');
    LEGEND_CONSTANTS(:,11) = strpad('kbile in component model_parameters (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,8) = strpad('H_Ccon_ROB in component Ccon_ROB (dimensionless)');
    LEGEND_STATES(:,6) = strpad('Ccon_ROB in component Ccon_ROB (micromolar)');
    LEGEND_CONSTANTS(:,12) = strpad('VROB in component Ccon_ROB (litre)');
    LEGEND_CONSTANTS(:,13) = strpad('kcon_urine in component Ccon_ROB (first_order_rate_constant)');
    LEGEND_STATES(:,7) = strpad('Acon_b in component Acon_b (micromole)');
    LEGEND_ALGEBRAIC(:,6) = strpad('d_t_Cgen_l in component Acon_b (hour)');
    LEGEND_CONSTANTS(:,14) = strpad('tbasal in component Acon_b (hour)');
    LEGEND_CONSTANTS(:,15) = strpad('ct in component Acon_b (hour)');
    LEGEND_CONSTANTS(:,16) = strpad('cgen in component Acon_b (litre_hour_micromole)');
    LEGEND_CONSTANTS(:,17) = strpad('cv in component model_parameters (micromole_hour)');
    LEGEND_ALGEBRAIC(:,10) = strpad('F in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,21) = strpad('G in component model_parameters (dimensionless)');
    LEGEND_ALGEBRAIC(:,11) = strpad('H in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,22) = strpad('I in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,18) = strpad('epsilon in component model_parameters (hour)');
    LEGEND_CONSTANTS(:,19) = strpad('m_rat in component model_parameters (dimensionless)');
    LEGEND_RATES(:,1) = strpad('d/dt Cgen_pp in component Cgen_pp (micromolar)');
    LEGEND_RATES(:,2) = strpad('d/dt Cgen_rp in component Cgen_rp (micromolar)');
    LEGEND_RATES(:,3) = strpad('d/dt Cgen_l in component Cgen_l (micromolar)');
    LEGEND_RATES(:,4) = strpad('d/dt Cgen_GI in component Cgen_GI (micromolar)');
    LEGEND_RATES(:,5) = strpad('d/dt Ccon_l in component Ccon_l (micromolar)');
    LEGEND_RATES(:,6) = strpad('d/dt Ccon_ROB in component Ccon_ROB (micromolar)');
    LEGEND_RATES(:,7) = strpad('d/dt Acon_b in component Acon_b (micromole)');
    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;
    CONSTANTS(:,1) = 0.59;
    CONSTANTS(:,2) = 0.188;
    STATES(:,2) = 0;
    CONSTANTS(:,3) = 1.94;
    CONSTANTS(:,4) = 0.012;
    CONSTANTS(:,5) = 9.5;
    STATES(:,3) = 0;
    CONSTANTS(:,6) = 0.0092;
    CONSTANTS(:,7) = 3.61;
    CONSTANTS(:,8) = 25.25;
    CONSTANTS(:,9) = 0.6231;
    STATES(:,4) = 0;
    CONSTANTS(:,10) = 0.011;
    STATES(:,5) = 0;
    CONSTANTS(:,11) = 111.72;
    STATES(:,6) = 0;
    CONSTANTS(:,12) = 0.2408;
    CONSTANTS(:,13) = 0.0;
    STATES(:,7) = 0;
    CONSTANTS(:,14) = 0.0865;
    CONSTANTS(:,15) = 1.0107;
    CONSTANTS(:,16) = 0.06561;
    CONSTANTS(:,17) = 1.0;
    CONSTANTS(:,18) = 0.1;
    CONSTANTS(:,19) = 0.25;
    CONSTANTS(:,20) =  14.1000.*power(CONSTANTS(:,19), 0.750000);
    CONSTANTS(:,21) = 1.00000;
    CONSTANTS(:,22) = 0.00000;
    CONSTANTS(:,23) =  0.528000.*CONSTANTS(:,20);
    CONSTANTS(:,24) =  0.289000.*CONSTANTS(:,20);
    CONSTANTS(:,25) =  0.0300000.*CONSTANTS(:,20);
    CONSTANTS(:,26) =  0.153000.*CONSTANTS(:,20);
    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(:,5) = piecewise({STATES(:,5)<0.00000, 0.00000 }, 1.00000);
    RATES(:,7) =  CONSTANTS(:,11).*ALGEBRAIC(:,5).*STATES(:,5).*CONSTANTS(:,6);
    ALGEBRAIC(:,3) = piecewise({STATES(:,3)<0.00000, 0.00000 }, 1.00000);
    ALGEBRAIC(:,8) = piecewise({STATES(:,6)<0.00000, 0.00000 }, 1.00000);
    RATES(:,5) = ( CONSTANTS(:,8).*ALGEBRAIC(:,3).*STATES(:,3))./(CONSTANTS(:,9)+ ALGEBRAIC(:,3).*STATES(:,3)) - ( CONSTANTS(:,11).*ALGEBRAIC(:,5).*STATES(:,5)+( (CONSTANTS(:,25)+CONSTANTS(:,26)).*( ALGEBRAIC(:,5).*STATES(:,5) -  ALGEBRAIC(:,8).*STATES(:,6)))./CONSTANTS(:,6));
    RATES(:,6) = ( (CONSTANTS(:,25)+CONSTANTS(:,26)).*( ALGEBRAIC(:,5).*STATES(:,5) -  ALGEBRAIC(:,8).*STATES(:,6)))./CONSTANTS(:,12) -  CONSTANTS(:,13).*ALGEBRAIC(:,8).*STATES(:,6);
    ALGEBRAIC(:,1) = piecewise({STATES(:,1)<0.00000, 0.00000 }, 1.00000);
    ALGEBRAIC(:,2) = piecewise({STATES(:,2)<0.00000, 0.00000 }, 1.00000);
    ALGEBRAIC(:,7) = (( CONSTANTS(:,24).*ALGEBRAIC(:,2).*STATES(:,2))./CONSTANTS(:,3)+( CONSTANTS(:,23).*ALGEBRAIC(:,1).*STATES(:,1))./CONSTANTS(:,1)+( (CONSTANTS(:,25)+CONSTANTS(:,26)).*ALGEBRAIC(:,3).*STATES(:,3))./CONSTANTS(:,7))./CONSTANTS(:,20);
    ALGEBRAIC(:,9) = piecewise({ALGEBRAIC(:,7)<0.00000, 0.00000 }, 1.00000);
    RATES(:,1) = ( CONSTANTS(:,23).*ALGEBRAIC(:,9).*ALGEBRAIC(:,7) - ( CONSTANTS(:,23).*ALGEBRAIC(:,1).*STATES(:,1))./CONSTANTS(:,1))./CONSTANTS(:,2);
    RATES(:,2) = ( CONSTANTS(:,24).*ALGEBRAIC(:,9).*ALGEBRAIC(:,7) - ( CONSTANTS(:,24).*ALGEBRAIC(:,2).*STATES(:,2))./CONSTANTS(:,3))./CONSTANTS(:,4) -  CONSTANTS(:,5).*ALGEBRAIC(:,2).*STATES(:,2);
    ALGEBRAIC(:,4) = piecewise({STATES(:,4)<0.00000, 0.00000 }, 1.00000);
    RATES(:,4) = ( CONSTANTS(:,26).*ALGEBRAIC(:,9).*ALGEBRAIC(:,7) - ( CONSTANTS(:,26).*ALGEBRAIC(:,4).*STATES(:,4))./CONSTANTS(:,3))./CONSTANTS(:,10);
    ALGEBRAIC(:,10) =  (-2.00000./power(CONSTANTS(:,18), 3.00000)).*power(VOI, 3.00000)+ (3.00000./power(CONSTANTS(:,18), 2.00000)).*power(VOI, 2.00000);
    ALGEBRAIC(:,11) = ( 3.00000.*power(1.00000 - VOI, 2.00000))./power(CONSTANTS(:,18), 2.00000) - ( 2.00000.*power(1.00000 - VOI, 3.00000))./power(CONSTANTS(:,18), 3.00000);
    ALGEBRAIC(:,12) = piecewise({VOI<CONSTANTS(:,18)&VOI>=0.00000,  CONSTANTS(:,17).*ALGEBRAIC(:,10) , VOI<=1.00000 - CONSTANTS(:,18)&VOI>=CONSTANTS(:,18),  CONSTANTS(:,17).*CONSTANTS(:,21) , VOI<=1.00000&VOI>1.00000 - CONSTANTS(:,18),  CONSTANTS(:,17).*ALGEBRAIC(:,11) , VOI<=1.00000+5.00000./60.0000&VOI>1.00000,  CONSTANTS(:,17).*CONSTANTS(:,22) }, NaN);
    RATES(:,3) = (( CONSTANTS(:,25).*ALGEBRAIC(:,9).*ALGEBRAIC(:,7) - ( (CONSTANTS(:,25)+CONSTANTS(:,26)).*ALGEBRAIC(:,3).*STATES(:,3))./CONSTANTS(:,7))+ALGEBRAIC(:,12)+( CONSTANTS(:,26).*ALGEBRAIC(:,4).*STATES(:,4))./CONSTANTS(:,3))./CONSTANTS(:,6) - ( CONSTANTS(:,8).*ALGEBRAIC(:,3).*STATES(:,3))./(CONSTANTS(:,9)+ ALGEBRAIC(:,3).*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(:,5) = piecewise({STATES(:,5)<0.00000, 0.00000 }, 1.00000);
    ALGEBRAIC(:,3) = piecewise({STATES(:,3)<0.00000, 0.00000 }, 1.00000);
    ALGEBRAIC(:,8) = piecewise({STATES(:,6)<0.00000, 0.00000 }, 1.00000);
    ALGEBRAIC(:,1) = piecewise({STATES(:,1)<0.00000, 0.00000 }, 1.00000);
    ALGEBRAIC(:,2) = piecewise({STATES(:,2)<0.00000, 0.00000 }, 1.00000);
    ALGEBRAIC(:,7) = (( CONSTANTS(:,24).*ALGEBRAIC(:,2).*STATES(:,2))./CONSTANTS(:,3)+( CONSTANTS(:,23).*ALGEBRAIC(:,1).*STATES(:,1))./CONSTANTS(:,1)+( (CONSTANTS(:,25)+CONSTANTS(:,26)).*ALGEBRAIC(:,3).*STATES(:,3))./CONSTANTS(:,7))./CONSTANTS(:,20);
    ALGEBRAIC(:,9) = piecewise({ALGEBRAIC(:,7)<0.00000, 0.00000 }, 1.00000);
    ALGEBRAIC(:,4) = piecewise({STATES(:,4)<0.00000, 0.00000 }, 1.00000);
    ALGEBRAIC(:,10) =  (-2.00000./power(CONSTANTS(:,18), 3.00000)).*power(VOI, 3.00000)+ (3.00000./power(CONSTANTS(:,18), 2.00000)).*power(VOI, 2.00000);
    ALGEBRAIC(:,11) = ( 3.00000.*power(1.00000 - VOI, 2.00000))./power(CONSTANTS(:,18), 2.00000) - ( 2.00000.*power(1.00000 - VOI, 3.00000))./power(CONSTANTS(:,18), 3.00000);
    ALGEBRAIC(:,12) = piecewise({VOI<CONSTANTS(:,18)&VOI>=0.00000,  CONSTANTS(:,17).*ALGEBRAIC(:,10) , VOI<=1.00000 - CONSTANTS(:,18)&VOI>=CONSTANTS(:,18),  CONSTANTS(:,17).*CONSTANTS(:,21) , VOI<=1.00000&VOI>1.00000 - CONSTANTS(:,18),  CONSTANTS(:,17).*ALGEBRAIC(:,11) , VOI<=1.00000+5.00000./60.0000&VOI>1.00000,  CONSTANTS(:,17).*CONSTANTS(:,22) }, NaN);
    ALGEBRAIC(:,6) = CONSTANTS(:,14)+ CONSTANTS(:,16).*ALGEBRAIC(:,3).*STATES(:,3).*exp( - (VOI./CONSTANTS(:,15)));
end

% Compute result of a piecewise function
function x = piecewise(cases, default)
    set = [0];
    for i = 1:2:length(cases)
        if (length(cases{i+1}) == 1)
            x(cases{i} & ~set,:) = cases{i+1};
        else
            x(cases{i} & ~set,:) = cases{i+1}(cases{i} & ~set);
        end
        set = set | cases{i};
        if(set), break, end
    end
    if (length(default) == 1)
        x(~set,:) = default;
    else
        x(~set,:) = default(~set);
    end
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