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 =16;
end
% There are a total of 3 entries in each of the rate and state variable arrays.
% There are a total of 37 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_CONSTANTS(:,1) = strpad('T_a in component model_parameters (celsius)');
    LEGEND_CONSTANTS(:,2) = strpad('T_b in component model_parameters (celsius)');
    LEGEND_CONSTANTS(:,3) = strpad('delta_T in component model_parameters (celsius)');
    LEGEND_CONSTANTS(:,4) = strpad('kinc in component model_parameters (W_per_kg_C2)');
    LEGEND_CONSTANTS(:,5) = strpad('tdose1 in component model_parameters (hour)');
    LEGEND_CONSTANTS(:,6) = strpad('tdose2 in component model_parameters (hour)');
    LEGEND_CONSTANTS(:,7) = strpad('tdose3 in component model_parameters (hour)');
    LEGEND_ALGEBRAIC(:,6) = strpad('M_c in component M_c (W_per_kg)');
    LEGEND_CONSTANTS(:,8) = strpad('t_day in component M_c (hour)');
    LEGEND_CONSTANTS(:,9) = strpad('t_night in component M_c (hour)');
    LEGEND_ALGEBRAIC(:,2) = strpad('tprime in component M_c (second)');
    LEGEND_CONSTANTS(:,10) = strpad('day_length in component M_c (second)');
    LEGEND_CONSTANTS(:,36) = strpad('M_day in component M_day (W_per_kg)');
    LEGEND_ALGEBRAIC(:,4) = strpad('M_night in component M_night (W_per_kg)');
    LEGEND_STATES(:,1) = strpad('M in component M (W_per_kg)');
    LEGEND_CONSTANTS(:,11) = strpad('km in component M (per_hour)');
    LEGEND_STATES(:,2) = strpad('T in component T (celsius)');
    LEGEND_CONSTANTS(:,12) = strpad('c in component T (kJ_per_kg_C)');
    LEGEND_ALGEBRAIC(:,1) = strpad('k in component k (W_per_kg_C)');
    LEGEND_STATES(:,3) = strpad('BR in component k (dimensionless)');
    LEGEND_CONSTANTS(:,13) = strpad('pEtot in component k (dimensionless)');
    LEGEND_CONSTANTS(:,14) = strpad('kR in component k (per_day)');
    LEGEND_CONSTANTS(:,15) = strpad('AMT_dose in component k (mg_per_kg)');
    LEGEND_CONSTANTS(:,16) = strpad('pEf1 in component k (per_day)');
    LEGEND_CONSTANTS(:,17) = strpad('pEs1 in component k (kg_per_day_mg)');
    LEGEND_CONSTANTS(:,18) = strpad('pEf2 in component k (per_day)');
    LEGEND_CONSTANTS(:,19) = strpad('pEs2 in component k (kg_per_day_mg)');
    LEGEND_CONSTANTS(:,20) = strpad('pEf3 in component k (per_day)');
    LEGEND_CONSTANTS(:,21) = strpad('pEs3 in component k (kg_per_day_mg)');
    LEGEND_ALGEBRAIC(:,14) = strpad('E_slow in component k (per_day)');
    LEGEND_ALGEBRAIC(:,16) = strpad('E_fast in component k (per_day)');
    LEGEND_CONSTANTS(:,31) = strpad('f2_drug in component k (W_per_kg_C)');
    LEGEND_CONSTANTS(:,35) = strpad('kb in component kb (W_per_kg_C)');
    LEGEND_ALGEBRAIC(:,3) = strpad('f_prime in component M_night (dimensionless)');
    LEGEND_ALGEBRAIC(:,7) = strpad('gNsTs1 in component gNT (dimensionless)');
    LEGEND_ALGEBRAIC(:,10) = strpad('gNsTs2 in component gNT (dimensionless)');
    LEGEND_ALGEBRAIC(:,13) = strpad('gNsTs3 in component gNT (dimensionless)');
    LEGEND_ALGEBRAIC(:,8) = strpad('gNfTf1 in component gNT (dimensionless)');
    LEGEND_ALGEBRAIC(:,11) = strpad('gNfTf2 in component gNT (dimensionless)');
    LEGEND_ALGEBRAIC(:,15) = strpad('gNfTf3 in component gNT (dimensionless)');
    LEGEND_CONSTANTS(:,30) = strpad('T_day in component T_day (celsius)');
    LEGEND_CONSTANTS(:,33) = strpad('T_night in component T_night (celsius)');
    LEGEND_CONSTANTS(:,22) = strpad('M_b in component kb (W_per_kg)');
    LEGEND_CONSTANTS(:,23) = strpad('t_prime in component M_night (hour)');
    LEGEND_CONSTANTS(:,24) = strpad('alpha in component M_night (per_hour)');
    LEGEND_CONSTANTS(:,25) = strpad('delta_high_dose in component M_night (dimensionless)');
    LEGEND_CONSTANTS(:,37) = strpad('M_night_baseline in component M_night (W_per_kg)');
    LEGEND_CONSTANTS(:,26) = strpad('Ns in component gNT (dimensionless)');
    LEGEND_CONSTANTS(:,27) = strpad('Nf in component gNT (dimensionless)');
    LEGEND_CONSTANTS(:,28) = strpad('Ts in component gNT (day)');
    LEGEND_CONSTANTS(:,29) = strpad('Tf in component gNT (day)');
    LEGEND_ALGEBRAIC(:,5) = strpad('X1 in component gNT (day)');
    LEGEND_ALGEBRAIC(:,9) = strpad('X2 in component gNT (day)');
    LEGEND_ALGEBRAIC(:,12) = strpad('X3 in component gNT (day)');
    LEGEND_CONSTANTS(:,32) = strpad('Kf in component gNT (per_day)');
    LEGEND_CONSTANTS(:,34) = strpad('Ks in component gNT (per_day)');
    LEGEND_RATES(:,1) = strpad('d/dt M in component M (W_per_kg)');
    LEGEND_RATES(:,2) = strpad('d/dt T in component T (celsius)');
    LEGEND_RATES(:,3) = strpad('d/dt BR in component k (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 = [];
    CONSTANTS(:,1) = 21.0;
    CONSTANTS(:,2) = 38.0;
    CONSTANTS(:,3) = 1.57;
    CONSTANTS(:,4) = 0.0258;
    CONSTANTS(:,5) = 24.0;
    CONSTANTS(:,6) = 72.0;
    CONSTANTS(:,7) = 120.0;
    CONSTANTS(:,8) = 17.5;
    CONSTANTS(:,9) = 6.73;
    CONSTANTS(:,10) = 86400;
    STATES(:,1) = 3.5;
    CONSTANTS(:,11) = 1.1375;
    STATES(:,2) = 38.785;
    CONSTANTS(:,12) = 3.47;
    STATES(:,3) = 0.0;
    CONSTANTS(:,13) = 0.144;
    CONSTANTS(:,14) = 5.35;
    CONSTANTS(:,15) = 3.0;
    CONSTANTS(:,16) = 1.0;
    CONSTANTS(:,17) = 0.2;
    CONSTANTS(:,18) = 3.57;
    CONSTANTS(:,19) = 2.43;
    CONSTANTS(:,20) = 8.0;
    CONSTANTS(:,21) = 50.0;
    CONSTANTS(:,22) = 3.0;
    CONSTANTS(:,23) = 45.12;
    CONSTANTS(:,24) = 0.2229166;
    CONSTANTS(:,25) = 1.0;
    CONSTANTS(:,26) = 4.0;
    CONSTANTS(:,27) = 4.0;
    CONSTANTS(:,28) = 2.45;
    CONSTANTS(:,29) = 0.368;
    CONSTANTS(:,30) = CONSTANTS(:,2)+CONSTANTS(:,3)./2.00000;
    CONSTANTS(:,31) = 0.00000;
    CONSTANTS(:,32) = CONSTANTS(:,27)./CONSTANTS(:,29);
    CONSTANTS(:,33) = CONSTANTS(:,2) - CONSTANTS(:,3)./2.00000;
    CONSTANTS(:,34) = CONSTANTS(:,26)./CONSTANTS(:,28);
    CONSTANTS(:,35) = CONSTANTS(:,22)./(CONSTANTS(:,2) - CONSTANTS(:,1));
    CONSTANTS(:,36) =  (CONSTANTS(:,35)+ CONSTANTS(:,4).*(CONSTANTS(:,30) - CONSTANTS(:,2))).*(CONSTANTS(:,30) - CONSTANTS(:,1));
    CONSTANTS(:,37) =  (CONSTANTS(:,35)+ CONSTANTS(:,4).*(CONSTANTS(:,33) - CONSTANTS(:,2))).*(CONSTANTS(:,33) - CONSTANTS(:,1));
    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(:,35)+ CONSTANTS(:,4).*(STATES(:,2) -  CONSTANTS(:,2).*(1.00000+ CONSTANTS(:,13).*STATES(:,3)))+CONSTANTS(:,31);
    RATES(:,2) =  power(CONSTANTS(:,12), -1.00000).*(STATES(:,1) -  ALGEBRAIC(:,1).*(STATES(:,2) - CONSTANTS(:,1)));
    ALGEBRAIC(:,2) =  rem( VOI.*3600.00.*1.00000, CONSTANTS(:,10));
    ALGEBRAIC(:,3) =  CONSTANTS(:,25).*power(1.00000+exp(  - CONSTANTS(:,24).*(VOI - (CONSTANTS(:,5)+CONSTANTS(:,23)))), -1.00000);
    ALGEBRAIC(:,4) =  (1.00000 - ALGEBRAIC(:,3)).*CONSTANTS(:,37)+ ALGEBRAIC(:,3).*CONSTANTS(:,36);
    ALGEBRAIC(:,6) = piecewise({ALGEBRAIC(:,2)./3600.00>=CONSTANTS(:,9)&ALGEBRAIC(:,2)./3600.00<CONSTANTS(:,8), ALGEBRAIC(:,4) }, CONSTANTS(:,36));
    RATES(:,1) =   - CONSTANTS(:,11).*(STATES(:,1) - ALGEBRAIC(:,6));
    ALGEBRAIC(:,5) = (VOI - CONSTANTS(:,5))./24.0000;
    ALGEBRAIC(:,7) = piecewise({ALGEBRAIC(:,5)>0.00000,  (power(CONSTANTS(:,34), CONSTANTS(:,26))./6.00000).*exp(  - CONSTANTS(:,34).*ALGEBRAIC(:,5)).*power(ALGEBRAIC(:,5), CONSTANTS(:,26) - 1.00000) }, 0.00000);
    ALGEBRAIC(:,9) = (VOI - CONSTANTS(:,6))./24.0000;
    ALGEBRAIC(:,10) = piecewise({ALGEBRAIC(:,9)>0.00000,  (power(CONSTANTS(:,34), CONSTANTS(:,26))./6.00000).*exp(  - CONSTANTS(:,34).*ALGEBRAIC(:,9)).*power(ALGEBRAIC(:,9), CONSTANTS(:,26) - 1.00000) }, 0.00000);
    ALGEBRAIC(:,12) = (VOI - CONSTANTS(:,7))./24.0000;
    ALGEBRAIC(:,13) = piecewise({ALGEBRAIC(:,12)>0.00000,  (power(CONSTANTS(:,34), CONSTANTS(:,26))./6.00000).*exp(  - CONSTANTS(:,34).*ALGEBRAIC(:,12)).*power(ALGEBRAIC(:,12), CONSTANTS(:,26) - 1.00000) }, 0.00000);
    ALGEBRAIC(:,14) =  CONSTANTS(:,15).*CONSTANTS(:,19).*(ALGEBRAIC(:,7)+ALGEBRAIC(:,10)+ALGEBRAIC(:,13));
    ALGEBRAIC(:,8) = piecewise({ALGEBRAIC(:,5)>0.00000,  (power(CONSTANTS(:,32), CONSTANTS(:,27))./6.00000).*exp(  - CONSTANTS(:,32).*ALGEBRAIC(:,5)).*power(ALGEBRAIC(:,5), CONSTANTS(:,27) - 1.00000) }, 0.00000);
    ALGEBRAIC(:,11) = piecewise({ALGEBRAIC(:,9)>0.00000,  (power(CONSTANTS(:,32), CONSTANTS(:,27))./6.00000).*exp(  - CONSTANTS(:,32).*ALGEBRAIC(:,9)).*power(ALGEBRAIC(:,9), CONSTANTS(:,27) - 1.00000) }, 0.00000);
    ALGEBRAIC(:,15) = piecewise({ALGEBRAIC(:,12)>0.00000,  (power(CONSTANTS(:,32), CONSTANTS(:,27))./6.00000).*exp(  - CONSTANTS(:,32).*ALGEBRAIC(:,12)).*power(ALGEBRAIC(:,12), CONSTANTS(:,27) - 1.00000) }, 0.00000);
    ALGEBRAIC(:,16) =  CONSTANTS(:,18).*(ALGEBRAIC(:,8)+ALGEBRAIC(:,11)+ALGEBRAIC(:,15));
    RATES(:,3) =  ( ALGEBRAIC(:,3).*(ALGEBRAIC(:,14)+ALGEBRAIC(:,16))).*(1.00000 - STATES(:,3)) -  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(:,35)+ CONSTANTS(:,4).*(STATES(:,2) -  CONSTANTS(:,2).*(1.00000+ CONSTANTS(:,13).*STATES(:,3)))+CONSTANTS(:,31);
    ALGEBRAIC(:,2) =  rem( VOI.*3600.00.*1.00000, CONSTANTS(:,10));
    ALGEBRAIC(:,3) =  CONSTANTS(:,25).*power(1.00000+exp(  - CONSTANTS(:,24).*(VOI - (CONSTANTS(:,5)+CONSTANTS(:,23)))), -1.00000);
    ALGEBRAIC(:,4) =  (1.00000 - ALGEBRAIC(:,3)).*CONSTANTS(:,37)+ ALGEBRAIC(:,3).*CONSTANTS(:,36);
    ALGEBRAIC(:,6) = piecewise({ALGEBRAIC(:,2)./3600.00>=CONSTANTS(:,9)&ALGEBRAIC(:,2)./3600.00<CONSTANTS(:,8), ALGEBRAIC(:,4) }, CONSTANTS(:,36));
    ALGEBRAIC(:,5) = (VOI - CONSTANTS(:,5))./24.0000;
    ALGEBRAIC(:,7) = piecewise({ALGEBRAIC(:,5)>0.00000,  (power(CONSTANTS(:,34), CONSTANTS(:,26))./6.00000).*exp(  - CONSTANTS(:,34).*ALGEBRAIC(:,5)).*power(ALGEBRAIC(:,5), CONSTANTS(:,26) - 1.00000) }, 0.00000);
    ALGEBRAIC(:,9) = (VOI - CONSTANTS(:,6))./24.0000;
    ALGEBRAIC(:,10) = piecewise({ALGEBRAIC(:,9)>0.00000,  (power(CONSTANTS(:,34), CONSTANTS(:,26))./6.00000).*exp(  - CONSTANTS(:,34).*ALGEBRAIC(:,9)).*power(ALGEBRAIC(:,9), CONSTANTS(:,26) - 1.00000) }, 0.00000);
    ALGEBRAIC(:,12) = (VOI - CONSTANTS(:,7))./24.0000;
    ALGEBRAIC(:,13) = piecewise({ALGEBRAIC(:,12)>0.00000,  (power(CONSTANTS(:,34), CONSTANTS(:,26))./6.00000).*exp(  - CONSTANTS(:,34).*ALGEBRAIC(:,12)).*power(ALGEBRAIC(:,12), CONSTANTS(:,26) - 1.00000) }, 0.00000);
    ALGEBRAIC(:,14) =  CONSTANTS(:,15).*CONSTANTS(:,19).*(ALGEBRAIC(:,7)+ALGEBRAIC(:,10)+ALGEBRAIC(:,13));
    ALGEBRAIC(:,8) = piecewise({ALGEBRAIC(:,5)>0.00000,  (power(CONSTANTS(:,32), CONSTANTS(:,27))./6.00000).*exp(  - CONSTANTS(:,32).*ALGEBRAIC(:,5)).*power(ALGEBRAIC(:,5), CONSTANTS(:,27) - 1.00000) }, 0.00000);
    ALGEBRAIC(:,11) = piecewise({ALGEBRAIC(:,9)>0.00000,  (power(CONSTANTS(:,32), CONSTANTS(:,27))./6.00000).*exp(  - CONSTANTS(:,32).*ALGEBRAIC(:,9)).*power(ALGEBRAIC(:,9), CONSTANTS(:,27) - 1.00000) }, 0.00000);
    ALGEBRAIC(:,15) = piecewise({ALGEBRAIC(:,12)>0.00000,  (power(CONSTANTS(:,32), CONSTANTS(:,27))./6.00000).*exp(  - CONSTANTS(:,32).*ALGEBRAIC(:,12)).*power(ALGEBRAIC(:,12), CONSTANTS(:,27) - 1.00000) }, 0.00000);
    ALGEBRAIC(:,16) =  CONSTANTS(:,18).*(ALGEBRAIC(:,8)+ALGEBRAIC(:,11)+ALGEBRAIC(:,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