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 =13;
end
% There are a total of 2 entries in each of the rate and state variable arrays.
% There are a total of 8 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('PPC in component pulmonary_fluid_dynamics (mmHg)');
    LEGEND_CONSTANTS(:,2) = strpad('PPA in component pulmonary_fluid_dynamics (mmHg)');
    LEGEND_CONSTANTS(:,3) = strpad('PLA in component pulmonary_fluid_dynamics (mmHg)');
    LEGEND_CONSTANTS(:,4) = strpad('CPP in component pulmonary_fluid_dynamics (gram_per_L)');
    LEGEND_CONSTANTS(:,5) = strpad('RPV in component pulmonary_fluid_dynamics (mmHg_minute_per_L)');
    LEGEND_CONSTANTS(:,6) = strpad('RPA in component pulmonary_fluid_dynamics (mmHg_minute_per_L)');
    LEGEND_CONSTANTS(:,8) = strpad('PCP in component pulmonary_capillary_pressure (mmHg)');
    LEGEND_ALGEBRAIC(:,5) = strpad('POS in component colloid_osmotic_pressure_of_pulmonary_interstitium (mmHg)');
    LEGEND_ALGEBRAIC(:,2) = strpad('PPI in component pulmonary_interstitial_fluid_pressure (mmHg)');
    LEGEND_ALGEBRAIC(:,6) = strpad('PFI in component fluid_filtration_into_pulmonary_interstitium (L_per_minute)');
    LEGEND_CONSTANTS(:,7) = strpad('CPF in component parameter_values (L_per_minute_per_mmHg)');
    LEGEND_ALGEBRAIC(:,8) = strpad('PLF in component lung_lymphatic_protein_flow (L_per_minute)');
    LEGEND_ALGEBRAIC(:,11) = strpad('DFP in component pulmonary_interstitial_free_fluid_volume (L_per_minute)');
    LEGEND_ALGEBRAIC(:,1) = strpad('VPF in component pulmonary_interstitial_free_fluid_volume (litre)');
    LEGEND_ALGEBRAIC(:,9) = strpad('DFZ in component pulmonary_interstitial_free_fluid_volume (L_per_minute)');
    LEGEND_STATES(:,1) = strpad('VPF1 in component pulmonary_interstitial_free_fluid_volume (litre)');
    LEGEND_ALGEBRAIC(:,10) = strpad('PPO in component lung_lymphatic_protein_flow (gram_per_minute)');
    LEGEND_ALGEBRAIC(:,7) = strpad('PPN in component protein_leakage_into_pulmonary_interstitium (gram_per_minute)');
    LEGEND_ALGEBRAIC(:,13) = strpad('PPD in component concentration_of_protein_in_pulmonary_interstitium (gram_per_minute)');
    LEGEND_ALGEBRAIC(:,4) = strpad('CPN in component concentration_of_protein_in_pulmonary_interstitium (gram_per_L)');
    LEGEND_ALGEBRAIC(:,12) = strpad('PPZ in component concentration_of_protein_in_pulmonary_interstitium (gram_per_minute)');
    LEGEND_STATES(:,2) = strpad('PPR1 in component concentration_of_protein_in_pulmonary_interstitium (gram)');
    LEGEND_ALGEBRAIC(:,3) = strpad('PPR in component concentration_of_protein_in_pulmonary_interstitium (gram)');
    LEGEND_RATES(:,1) = strpad('d/dt VPF1 in component pulmonary_interstitial_free_fluid_volume (litre)');
    LEGEND_RATES(:,2) = strpad('d/dt PPR1 in component concentration_of_protein_in_pulmonary_interstitium (gram)');
    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) = 29.9941;
    CONSTANTS(:,2) = 15.6376;
    CONSTANTS(:,3) = 2;
    CONSTANTS(:,4) = 71.9719;
    CONSTANTS(:,5) = 1.55719;
    CONSTANTS(:,6) = 1.5683;
    CONSTANTS(:,7) = 0.0003;
    STATES(:,1) = 0.0123238;
    STATES(:,2) = 0.419998;
    CONSTANTS(:,8) = ( (CONSTANTS(:,2) - CONSTANTS(:,3)).*CONSTANTS(:,5))./(CONSTANTS(:,5)+CONSTANTS(:,6))+CONSTANTS(:,3);
    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) = piecewise({STATES(:,1)<0.00100000, 0.00100000 }, STATES(:,1));
    ALGEBRAIC(:,3) = piecewise({STATES(:,2)<0.0250000, 0.0250000 }, STATES(:,2));
    ALGEBRAIC(:,4) = ALGEBRAIC(:,3)./ALGEBRAIC(:,1);
    ALGEBRAIC(:,5) =  ALGEBRAIC(:,4).*0.400000;
    ALGEBRAIC(:,2) = 2.00000 - 0.150000./ALGEBRAIC(:,1);
    ALGEBRAIC(:,6) =  (((CONSTANTS(:,8) - ALGEBRAIC(:,2))+ALGEBRAIC(:,5)) - CONSTANTS(:,1)).*CONSTANTS(:,7);
    ALGEBRAIC(:,8) =  (ALGEBRAIC(:,2)+11.0000).*0.000300000;
    ALGEBRAIC(:,9) = ALGEBRAIC(:,6) - ALGEBRAIC(:,8);
    ALGEBRAIC(:,11) = ALGEBRAIC(:,9);
    RATES(:,1) = ALGEBRAIC(:,11);
    ALGEBRAIC(:,10) =  ALGEBRAIC(:,8).*ALGEBRAIC(:,4);
    ALGEBRAIC(:,7) =  (CONSTANTS(:,4) - ALGEBRAIC(:,4)).*0.000225000;
    ALGEBRAIC(:,12) = ALGEBRAIC(:,7) - ALGEBRAIC(:,10);
    ALGEBRAIC(:,13) = ALGEBRAIC(:,12);
    RATES(:,2) = ALGEBRAIC(:,13);
   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) = piecewise({STATES(:,1)<0.00100000, 0.00100000 }, STATES(:,1));
    ALGEBRAIC(:,3) = piecewise({STATES(:,2)<0.0250000, 0.0250000 }, STATES(:,2));
    ALGEBRAIC(:,4) = ALGEBRAIC(:,3)./ALGEBRAIC(:,1);
    ALGEBRAIC(:,5) =  ALGEBRAIC(:,4).*0.400000;
    ALGEBRAIC(:,2) = 2.00000 - 0.150000./ALGEBRAIC(:,1);
    ALGEBRAIC(:,6) =  (((CONSTANTS(:,8) - ALGEBRAIC(:,2))+ALGEBRAIC(:,5)) - CONSTANTS(:,1)).*CONSTANTS(:,7);
    ALGEBRAIC(:,8) =  (ALGEBRAIC(:,2)+11.0000).*0.000300000;
    ALGEBRAIC(:,9) = ALGEBRAIC(:,6) - ALGEBRAIC(:,8);
    ALGEBRAIC(:,11) = ALGEBRAIC(:,9);
    ALGEBRAIC(:,10) =  ALGEBRAIC(:,8).*ALGEBRAIC(:,4);
    ALGEBRAIC(:,7) =  (CONSTANTS(:,4) - ALGEBRAIC(:,4)).*0.000225000;
    ALGEBRAIC(:,12) = ALGEBRAIC(:,7) - ALGEBRAIC(:,10);
    ALGEBRAIC(:,13) = ALGEBRAIC(:,12);
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