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 =11;
end
% There are a total of 2 entries in each of the rate and state variable arrays.
% There are a total of 11 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_CONSTANTS(:,1) = strpad('VPF in component pulmonary_O2_uptake (litre)');
    LEGEND_CONSTANTS(:,2) = strpad('DOB in component pulmonary_O2_uptake (mL_per_minute)');
    LEGEND_CONSTANTS(:,3) = strpad('QRO in component pulmonary_O2_uptake (L_per_minute)');
    LEGEND_CONSTANTS(:,4) = strpad('RMO in component pulmonary_O2_uptake (mL_per_minute)');
    LEGEND_CONSTANTS(:,5) = strpad('HM in component pulmonary_O2_uptake (dimensionless)');
    LEGEND_CONSTANTS(:,10) = strpad('O2UTIL in component total_O2_utilization (mL_per_minute)');
    LEGEND_ALGEBRAIC(:,6) = strpad('O2VAD2 in component progressive_chemoreceptor_adaptation_of_alveolar_ventilation (dimensionless)');
    LEGEND_ALGEBRAIC(:,5) = strpad('O2VTS2 in component acute_chemoreceptor_adaptation_of_alveolar_ventilation (dimensionless)');
    LEGEND_ALGEBRAIC(:,8) = strpad('ALVENT in component alveolar_ventilation (L_per_minute)');
    LEGEND_CONSTANTS(:,6) = strpad('VNTSTM in component parameter_values (dimensionless)');
    LEGEND_ALGEBRAIC(:,9) = strpad('PO2ALV in component alveolar_PO2 (mmHg)');
    LEGEND_CONSTANTS(:,7) = strpad('PO2AMB in component parameter_values (mmHg)');
    LEGEND_ALGEBRAIC(:,2) = strpad('PO2ART in component arterial_PO2 (mmHg)');
    LEGEND_ALGEBRAIC(:,10) = strpad('O2DFS in component respiratory_O2_diffusion_into_capillaries (mL_per_minute)');
    LEGEND_CONSTANTS(:,8) = strpad('PL2 in component parameter_values (L_mL_per_minute_per_mmHg)');
    LEGEND_CONSTANTS(:,9) = strpad('VPTISS in component parameter_values (litre)');
    LEGEND_CONSTANTS(:,11) = strpad('RSPDFC in component respiratory_O2_diffusion_into_capillaries (mL_per_minute_per_mmHg)');
    LEGEND_STATES(:,1) = strpad('OVA in component O2_volume_of_arterial_blood (mL_per_L)');
    LEGEND_ALGEBRAIC(:,11) = strpad('DOVA in component O2_volume_of_arterial_blood (mL_per_L_per_minute)');
    LEGEND_ALGEBRAIC(:,1) = strpad('OSA in component arterial_PO2 (dimensionless)');
    LEGEND_ALGEBRAIC(:,4) = strpad('O2VTST in component acute_chemoreceptor_adaptation_of_alveolar_ventilation (dimensionless)');
    LEGEND_ALGEBRAIC(:,3) = strpad('O2VTST1 in component acute_chemoreceptor_adaptation_of_alveolar_ventilation (dimensionless)');
    LEGEND_ALGEBRAIC(:,7) = strpad('DO2VAD in component progressive_chemoreceptor_adaptation_of_alveolar_ventilation (per_minute)');
    LEGEND_STATES(:,2) = strpad('O2VAD1 in component progressive_chemoreceptor_adaptation_of_alveolar_ventilation (dimensionless)');
    LEGEND_RATES(:,1) = strpad('d/dt OVA in component O2_volume_of_arterial_blood (mL_per_L)');
    LEGEND_RATES(:,2) = strpad('d/dt O2VAD1 in component progressive_chemoreceptor_adaptation_of_alveolar_ventilation (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) = 0.0123238;
    CONSTANTS(:,2) = 163.508;
    CONSTANTS(:,3) = 4.97838;
    CONSTANTS(:,4) = 56.8057;
    CONSTANTS(:,5) = 40.0381;
    CONSTANTS(:,6) = 1;
    CONSTANTS(:,7) = 150;
    CONSTANTS(:,8) = 1.8;
    CONSTANTS(:,9) = 0.0175;
    STATES(:,1) = 204.497;
    STATES(:,2) = 2.368e-07;
    CONSTANTS(:,10) = CONSTANTS(:,2)+CONSTANTS(:,4);
    CONSTANTS(:,11) = CONSTANTS(:,8)./(CONSTANTS(:,9)+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) = (STATES(:,1)./CONSTANTS(:,5))./5.25000;
    ALGEBRAIC(:,2) = piecewise({ALGEBRAIC(:,1)>1.00000, 114.000+ (ALGEBRAIC(:,1) - 1.00000).*6667.00 , ALGEBRAIC(:,1)>0.936000&ALGEBRAIC(:,1)<=1.00000, 74.0000+ (ALGEBRAIC(:,1) - 0.936000).*625.000 , ALGEBRAIC(:,1)>0.800000&ALGEBRAIC(:,1)<=0.936000, 46.0000+ (ALGEBRAIC(:,1) - 0.800000).*205.882 },  ALGEBRAIC(:,1).*57.5000);
    ALGEBRAIC(:,3) = (ALGEBRAIC(:,2) - 67.0000)./30.0000;
    ALGEBRAIC(:,4) = piecewise({ALGEBRAIC(:,3)>1.00000, 1.00000 , ALGEBRAIC(:,3)<0.600000, 0.600000 }, ALGEBRAIC(:,3));
    ALGEBRAIC(:,5) = 1.00000./ALGEBRAIC(:,4);
    ALGEBRAIC(:,7) =  ( (ALGEBRAIC(:,5) - 1.00000).*3.00000 - STATES(:,2)).*0.000500000;
    RATES(:,2) = ALGEBRAIC(:,7);
    ALGEBRAIC(:,6) = STATES(:,2)+1.00000;
    ALGEBRAIC(:,8) =  CONSTANTS(:,10).*CONSTANTS(:,6).*0.0266670.*ALGEBRAIC(:,5).*ALGEBRAIC(:,6);
    ALGEBRAIC(:,9) = CONSTANTS(:,7) - (CONSTANTS(:,10)./ALGEBRAIC(:,8))./0.761000;
    ALGEBRAIC(:,10) =  (ALGEBRAIC(:,9) - ALGEBRAIC(:,2)).*CONSTANTS(:,11);
    ALGEBRAIC(:,11) = (ALGEBRAIC(:,10) - CONSTANTS(:,10))./( CONSTANTS(:,3).*1.00000);
    RATES(:,1) = ALGEBRAIC(:,11);
   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(:,5))./5.25000;
    ALGEBRAIC(:,2) = piecewise({ALGEBRAIC(:,1)>1.00000, 114.000+ (ALGEBRAIC(:,1) - 1.00000).*6667.00 , ALGEBRAIC(:,1)>0.936000&ALGEBRAIC(:,1)<=1.00000, 74.0000+ (ALGEBRAIC(:,1) - 0.936000).*625.000 , ALGEBRAIC(:,1)>0.800000&ALGEBRAIC(:,1)<=0.936000, 46.0000+ (ALGEBRAIC(:,1) - 0.800000).*205.882 },  ALGEBRAIC(:,1).*57.5000);
    ALGEBRAIC(:,3) = (ALGEBRAIC(:,2) - 67.0000)./30.0000;
    ALGEBRAIC(:,4) = piecewise({ALGEBRAIC(:,3)>1.00000, 1.00000 , ALGEBRAIC(:,3)<0.600000, 0.600000 }, ALGEBRAIC(:,3));
    ALGEBRAIC(:,5) = 1.00000./ALGEBRAIC(:,4);
    ALGEBRAIC(:,7) =  ( (ALGEBRAIC(:,5) - 1.00000).*3.00000 - STATES(:,2)).*0.000500000;
    ALGEBRAIC(:,6) = STATES(:,2)+1.00000;
    ALGEBRAIC(:,8) =  CONSTANTS(:,10).*CONSTANTS(:,6).*0.0266670.*ALGEBRAIC(:,5).*ALGEBRAIC(:,6);
    ALGEBRAIC(:,9) = CONSTANTS(:,7) - (CONSTANTS(:,10)./ALGEBRAIC(:,8))./0.761000;
    ALGEBRAIC(:,10) =  (ALGEBRAIC(:,9) - ALGEBRAIC(:,2)).*CONSTANTS(:,11);
    ALGEBRAIC(:,11) = (ALGEBRAIC(:,10) - CONSTANTS(:,10))./( CONSTANTS(:,3).*1.00000);
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