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 =26;
end
% There are a total of 4 entries in each of the rate and state variable arrays.
% There are a total of 27 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('VEC in component capillary_dynamics (litre)');
    LEGEND_CONSTANTS(:,2) = strpad('PPD in component capillary_dynamics (gram_per_minute)');
    LEGEND_CONSTANTS(:,3) = strpad('RVS in component capillary_dynamics (mmHg_minute_per_L)');
    LEGEND_CONSTANTS(:,4) = strpad('DFP in component capillary_dynamics (L_per_minute)');
    LEGEND_CONSTANTS(:,5) = strpad('VPF in component capillary_dynamics (litre)');
    LEGEND_CONSTANTS(:,6) = strpad('BFN in component capillary_dynamics (L_per_minute)');
    LEGEND_CONSTANTS(:,7) = strpad('PVS in component capillary_dynamics (mmHg)');
    LEGEND_CONSTANTS(:,25) = strpad('PC in component capillary_pressure (mmHg)');
    LEGEND_ALGEBRAIC(:,16) = strpad('PGH in component hydrostatic_pressure_of_tissue_gel (mmHg)');
    LEGEND_ALGEBRAIC(:,14) = strpad('PTC in component total_osmotic_pressure_of_tissue_gel (mmHg)');
    LEGEND_ALGEBRAIC(:,4) = strpad('PPC in component plasma_colloid_osmotic_pressure (mmHg)');
    LEGEND_CONSTANTS(:,27) = strpad('VTCPL in component plasma_leakage (L_per_minute)');
    LEGEND_ALGEBRAIC(:,17) = strpad('VTC in component rate_of_fluid_out_of_capillaries (L_per_minute)');
    LEGEND_CONSTANTS(:,8) = strpad('CFC in component parameter_values (L_per_minute_per_mmHg)');
    LEGEND_ALGEBRAIC(:,22) = strpad('VTL in component lymph_flow (L_per_minute)');
    LEGEND_STATES(:,1) = strpad('VP in component plasma_volume (litre)');
    LEGEND_CONSTANTS(:,9) = strpad('TRPL in component parameter_values (L_per_minute)');
    LEGEND_ALGEBRAIC(:,23) = strpad('VPD in component plasma_volume (L_per_minute)');
    LEGEND_STATES(:,2) = strpad('PRP in component total_plasma_protein (gram)');
    LEGEND_ALGEBRAIC(:,1) = strpad('CPP in component plasma_protein_concentration (gram_per_L)');
    LEGEND_ALGEBRAIC(:,3) = strpad('DLP in component protein_destruction_and_formation (gram_per_minute)');
    LEGEND_CONSTANTS(:,10) = strpad('CPR in component parameter_values (gram_per_L)');
    LEGEND_CONSTANTS(:,11) = strpad('LPPR in component parameter_values (gram_per_minute)');
    LEGEND_CONSTANTS(:,12) = strpad('LPDE in component parameter_values (dimensionless)');
    LEGEND_CONSTANTS(:,13) = strpad('LPK in component parameter_values (L_per_minute)');
    LEGEND_ALGEBRAIC(:,2) = strpad('CPPD in component protein_destruction_and_formation (gram_per_L)');
    LEGEND_CONSTANTS(:,14) = strpad('PCR in component parameter_values (mmHg)');
    LEGEND_CONSTANTS(:,15) = strpad('CPK in component parameter_values (L_per_minute_per_mmHg)');
    LEGEND_CONSTANTS(:,16) = strpad('PCE in component parameter_values (dimensionless)');
    LEGEND_CONSTANTS(:,26) = strpad('PRCD in component plasma_leakage (mmHg)');
    LEGEND_ALGEBRAIC(:,8) = strpad('CPI in component interstitial_protein_concentration (gram_per_L)');
    LEGEND_ALGEBRAIC(:,10) = strpad('DPC in component protein_influx_into_interstitium (gram_per_minute)');
    LEGEND_ALGEBRAIC(:,24) = strpad('DPL in component lymph_protein_flow (gram_per_minute)');
    LEGEND_ALGEBRAIC(:,25) = strpad('DPP in component total_plasma_protein (gram_per_minute)');
    LEGEND_ALGEBRAIC(:,5) = strpad('VTS in component total_systemic_fluid_volume (litre)');
    LEGEND_ALGEBRAIC(:,6) = strpad('VTS1 in component interstitial_fluid_volume (litre)');
    LEGEND_CONSTANTS(:,17) = strpad('TSSLML in component parameter_values (dimensionless)');
    LEGEND_CONSTANTS(:,18) = strpad('TSSLTC in component parameter_values (per_minute)');
    LEGEND_STATES(:,3) = strpad('VTS2 in component interstitial_fluid_volume (litre)');
    LEGEND_STATES(:,4) = strpad('TSP in component total_interstitial_protein (gram)');
    LEGEND_ALGEBRAIC(:,26) = strpad('DPI in component total_interstitial_protein (gram_per_minute)');
    LEGEND_ALGEBRAIC(:,11) = strpad('PTCPR in component interstitial_colloid_osmotic_pressure (mmHg)');
    LEGEND_ALGEBRAIC(:,15) = strpad('PTT in component total_tissue_pressure (mmHg)');
    LEGEND_ALGEBRAIC(:,12) = strpad('CHY in component hydrostatic_pressure_of_tissue_gel (gram_per_L)');
    LEGEND_CONSTANTS(:,19) = strpad('HYL in component parameter_values (gram)');
    LEGEND_CONSTANTS(:,20) = strpad('CMPTSS in component parameter_values (dimensionless)');
    LEGEND_CONSTANTS(:,21) = strpad('PGHF in component parameter_values (L_mmHg_per_gram)');
    LEGEND_ALGEBRAIC(:,13) = strpad('POSHYL in component total_osmotic_pressure_of_tissue_gel (mmHg)');
    LEGEND_CONSTANTS(:,22) = strpad('GCOPF in component parameter_values (per_mmHg)');
    LEGEND_CONSTANTS(:,23) = strpad('VTSF in component parameter_values (litre)');
    LEGEND_ALGEBRAIC(:,18) = strpad('PIF in component interstial_free_fluid_pressure (mmHg)');
    LEGEND_ALGEBRAIC(:,20) = strpad('PTS in component interstitial_solid_tissue_pressure (mmHg)');
    LEGEND_CONSTANTS(:,24) = strpad('PLDF in component parameter_values (mmHg)');
    LEGEND_ALGEBRAIC(:,19) = strpad('PLD1 in component lymph_flow (mmHg)');
    LEGEND_ALGEBRAIC(:,21) = strpad('PLD in component lymph_flow (mmHg)');
    LEGEND_ALGEBRAIC(:,7) = strpad('VG in component interstitial_gel_volume (litre)');
    LEGEND_ALGEBRAIC(:,9) = strpad('VIF in component interstitial_free_fluid_volume (litre)');
    LEGEND_RATES(:,1) = strpad('d/dt VP in component plasma_volume (litre)');
    LEGEND_RATES(:,2) = strpad('d/dt PRP in component total_plasma_protein (gram)');
    LEGEND_RATES(:,3) = strpad('d/dt VTS2 in component interstitial_fluid_volume (litre)');
    LEGEND_RATES(:,4) = strpad('d/dt TSP in component total_interstitial_protein (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) = 14.8548;
    CONSTANTS(:,2) = 4.4805e-06;
    CONSTANTS(:,3) = 2.77751;
    CONSTANTS(:,4) = -4.078e-07;
    CONSTANTS(:,5) = 0.0123238;
    CONSTANTS(:,6) = 2.79521;
    CONSTANTS(:,7) = 3.71612;
    CONSTANTS(:,8) = 0.01167;
    STATES(:,1) = 3.00449;
    CONSTANTS(:,9) = 0;
    STATES(:,2) = 216.243;
    CONSTANTS(:,10) = 40;
    CONSTANTS(:,11) = 0.03;
    CONSTANTS(:,12) = 8;
    CONSTANTS(:,13) = 2.728e-14;
    CONSTANTS(:,14) = 15;
    CONSTANTS(:,15) = 0.000253;
    CONSTANTS(:,16) = 1;
    CONSTANTS(:,17) = 0.15;
    CONSTANTS(:,18) = 0.005;
    STATES(:,3) = 0.0;
    STATES(:,4) = 279.945;
    CONSTANTS(:,19) = 60;
    CONSTANTS(:,20) = 2;
    CONSTANTS(:,21) = -2;
    CONSTANTS(:,22) = 0.8092;
    CONSTANTS(:,23) = 6;
    CONSTANTS(:,24) = 4.2;
    CONSTANTS(:,25) =  CONSTANTS(:,3).*1.70000.*CONSTANTS(:,6)+CONSTANTS(:,7);
    CONSTANTS(:,26) = piecewise({CONSTANTS(:,25) - CONSTANTS(:,14)<0.00000, 0.00000 }, CONSTANTS(:,25) - CONSTANTS(:,14));
    CONSTANTS(:,27) = power( CONSTANTS(:,26).*CONSTANTS(:,15), CONSTANTS(:,16));
    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) = (CONSTANTS(:,1) - STATES(:,1)) - CONSTANTS(:,5);
    RATES(:,3) =  ( (ALGEBRAIC(:,5) - 12.0000).*CONSTANTS(:,17) - STATES(:,3)).*CONSTANTS(:,18);
    ALGEBRAIC(:,6) = ALGEBRAIC(:,5) - STATES(:,3);
    ALGEBRAIC(:,15) =  power((ALGEBRAIC(:,6) - CONSTANTS(:,23))./CONSTANTS(:,23), 2.00000).*1.00000;
    ALGEBRAIC(:,12) = power((CONSTANTS(:,19)./ALGEBRAIC(:,5))./5.00000, CONSTANTS(:,20));
    ALGEBRAIC(:,16) =  ALGEBRAIC(:,12).*CONSTANTS(:,21)+ALGEBRAIC(:,15);
    ALGEBRAIC(:,8) = STATES(:,4)./ALGEBRAIC(:,5);
    ALGEBRAIC(:,11) =  0.280000.*ALGEBRAIC(:,8)+ 0.00190000.*power(ALGEBRAIC(:,8), 2.00000);
    ALGEBRAIC(:,13) =  ALGEBRAIC(:,12).*2.00000;
    ALGEBRAIC(:,14) =  ALGEBRAIC(:,13).*ALGEBRAIC(:,11).*CONSTANTS(:,22);
    ALGEBRAIC(:,1) = STATES(:,2)./STATES(:,1);
    ALGEBRAIC(:,4) =  0.280000.*ALGEBRAIC(:,1)+ 0.00190000.*power(ALGEBRAIC(:,1), 2.00000);
    ALGEBRAIC(:,17) =  (((CONSTANTS(:,25) - ALGEBRAIC(:,4)) - ALGEBRAIC(:,16))+ALGEBRAIC(:,14)).*CONSTANTS(:,8)+CONSTANTS(:,27);
    ALGEBRAIC(:,18) = ALGEBRAIC(:,16) - ALGEBRAIC(:,13);
    ALGEBRAIC(:,19) = (ALGEBRAIC(:,18)+CONSTANTS(:,24)) - ALGEBRAIC(:,15);
    ALGEBRAIC(:,21) = piecewise({ALGEBRAIC(:,19)>7.00000, 7.00000 }, ALGEBRAIC(:,19));
    ALGEBRAIC(:,22) = piecewise({ALGEBRAIC(:,21)<0.00000, 0.00000 },  ALGEBRAIC(:,21).*0.0200000);
    ALGEBRAIC(:,23) = ((ALGEBRAIC(:,22) - ALGEBRAIC(:,17)) - CONSTANTS(:,4))+CONSTANTS(:,9);
    RATES(:,1) = ALGEBRAIC(:,23);
    ALGEBRAIC(:,2) = piecewise({ALGEBRAIC(:,1) - CONSTANTS(:,10)<0.00000, 0.00000 }, ALGEBRAIC(:,1) - CONSTANTS(:,10));
    ALGEBRAIC(:,3) = CONSTANTS(:,11) -  power(ALGEBRAIC(:,2), CONSTANTS(:,12)).*CONSTANTS(:,13);
    ALGEBRAIC(:,10) =  CONSTANTS(:,27).*ALGEBRAIC(:,1)+ (ALGEBRAIC(:,1) - ALGEBRAIC(:,8)).*0.00104000;
    ALGEBRAIC(:,24) =  ALGEBRAIC(:,8).*ALGEBRAIC(:,22);
    ALGEBRAIC(:,25) = (((ALGEBRAIC(:,3)+ALGEBRAIC(:,24)) - ALGEBRAIC(:,10)) - CONSTANTS(:,2))+ CONSTANTS(:,9).*72.0000;
    RATES(:,2) = ALGEBRAIC(:,25);
    ALGEBRAIC(:,26) = ALGEBRAIC(:,10) - ALGEBRAIC(:,24);
    RATES(:,4) = ALGEBRAIC(:,26);
   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) = (CONSTANTS(:,1) - STATES(:,1)) - CONSTANTS(:,5);
    ALGEBRAIC(:,6) = ALGEBRAIC(:,5) - STATES(:,3);
    ALGEBRAIC(:,15) =  power((ALGEBRAIC(:,6) - CONSTANTS(:,23))./CONSTANTS(:,23), 2.00000).*1.00000;
    ALGEBRAIC(:,12) = power((CONSTANTS(:,19)./ALGEBRAIC(:,5))./5.00000, CONSTANTS(:,20));
    ALGEBRAIC(:,16) =  ALGEBRAIC(:,12).*CONSTANTS(:,21)+ALGEBRAIC(:,15);
    ALGEBRAIC(:,8) = STATES(:,4)./ALGEBRAIC(:,5);
    ALGEBRAIC(:,11) =  0.280000.*ALGEBRAIC(:,8)+ 0.00190000.*power(ALGEBRAIC(:,8), 2.00000);
    ALGEBRAIC(:,13) =  ALGEBRAIC(:,12).*2.00000;
    ALGEBRAIC(:,14) =  ALGEBRAIC(:,13).*ALGEBRAIC(:,11).*CONSTANTS(:,22);
    ALGEBRAIC(:,1) = STATES(:,2)./STATES(:,1);
    ALGEBRAIC(:,4) =  0.280000.*ALGEBRAIC(:,1)+ 0.00190000.*power(ALGEBRAIC(:,1), 2.00000);
    ALGEBRAIC(:,17) =  (((CONSTANTS(:,25) - ALGEBRAIC(:,4)) - ALGEBRAIC(:,16))+ALGEBRAIC(:,14)).*CONSTANTS(:,8)+CONSTANTS(:,27);
    ALGEBRAIC(:,18) = ALGEBRAIC(:,16) - ALGEBRAIC(:,13);
    ALGEBRAIC(:,19) = (ALGEBRAIC(:,18)+CONSTANTS(:,24)) - ALGEBRAIC(:,15);
    ALGEBRAIC(:,21) = piecewise({ALGEBRAIC(:,19)>7.00000, 7.00000 }, ALGEBRAIC(:,19));
    ALGEBRAIC(:,22) = piecewise({ALGEBRAIC(:,21)<0.00000, 0.00000 },  ALGEBRAIC(:,21).*0.0200000);
    ALGEBRAIC(:,23) = ((ALGEBRAIC(:,22) - ALGEBRAIC(:,17)) - CONSTANTS(:,4))+CONSTANTS(:,9);
    ALGEBRAIC(:,2) = piecewise({ALGEBRAIC(:,1) - CONSTANTS(:,10)<0.00000, 0.00000 }, ALGEBRAIC(:,1) - CONSTANTS(:,10));
    ALGEBRAIC(:,3) = CONSTANTS(:,11) -  power(ALGEBRAIC(:,2), CONSTANTS(:,12)).*CONSTANTS(:,13);
    ALGEBRAIC(:,10) =  CONSTANTS(:,27).*ALGEBRAIC(:,1)+ (ALGEBRAIC(:,1) - ALGEBRAIC(:,8)).*0.00104000;
    ALGEBRAIC(:,24) =  ALGEBRAIC(:,8).*ALGEBRAIC(:,22);
    ALGEBRAIC(:,25) = (((ALGEBRAIC(:,3)+ALGEBRAIC(:,24)) - ALGEBRAIC(:,10)) - CONSTANTS(:,2))+ CONSTANTS(:,9).*72.0000;
    ALGEBRAIC(:,26) = ALGEBRAIC(:,10) - ALGEBRAIC(:,24);
    ALGEBRAIC(:,7) = piecewise({ALGEBRAIC(:,5)<=0.00000, 0.00000 , ALGEBRAIC(:,5)>0.00000&ALGEBRAIC(:,5)<=12.0000, 0.00000+( (11.4000 - 0.00000).*(ALGEBRAIC(:,5) - 0.00000))./(12.0000 - 0.00000) , ALGEBRAIC(:,5)>12.0000&ALGEBRAIC(:,5)<=15.0000, 11.4000+( (14.0000 - 11.4000).*(ALGEBRAIC(:,5) - 12.0000))./(15.0000 - 12.0000) , ALGEBRAIC(:,5)>15.0000&ALGEBRAIC(:,5)<=18.0000, 14.0000+( (16.0000 - 14.0000).*(ALGEBRAIC(:,5) - 15.0000))./(18.0000 - 15.0000) , ALGEBRAIC(:,5)>18.0000&ALGEBRAIC(:,5)<=21.0000, 16.0000+( (17.3000 - 16.0000).*(ALGEBRAIC(:,5) - 18.0000))./(21.0000 - 18.0000) , ALGEBRAIC(:,5)>21.0000&ALGEBRAIC(:,5)<=24.0000, 17.3000+( (18.0000 - 17.3000).*(ALGEBRAIC(:,5) - 21.0000))./(24.0000 - 21.0000) }, 18.0000);
    ALGEBRAIC(:,9) = ALGEBRAIC(:,5) - ALGEBRAIC(:,7);
    ALGEBRAIC(:,20) = ALGEBRAIC(:,15) - ALGEBRAIC(:,18);
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