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 =3;
end
% There are a total of 3 entries in each of the rate and state variable arrays.
% There are a total of 18 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 (day)');
    LEGEND_ALGEBRAIC(:,3) = strpad('S in component population_pharmacodynamics_model (units)');
    LEGEND_CONSTANTS(:,1) = strpad('S0 in component population_pharmacodynamics_model (units)');
    LEGEND_CONSTANTS(:,2) = strpad('alpha in component population_pharmacodynamics_model (units_per_day)');
    LEGEND_CONSTANTS(:,3) = strpad('epsilon in component population_pharmacodynamics_model (units)');
    LEGEND_ALGEBRAIC(:,1) = strpad('ADAS_Cog_p in component placebo_response_model (units)');
    LEGEND_CONSTANTS(:,15) = strpad('PD_CeA in component drug_response_model (units)');
    LEGEND_CONSTANTS(:,4) = strpad('beta_P in component placebo_response_model (units)');
    LEGEND_CONSTANTS(:,16) = strpad('Keq_p in component placebo_response_model (per_day)');
    LEGEND_CONSTANTS(:,17) = strpad('Kel_p in component placebo_response_model (per_day)');
    LEGEND_CONSTANTS(:,5) = strpad('t_half_el_p in component placebo_response_model (day)');
    LEGEND_CONSTANTS(:,6) = strpad('t_half_eq_p in component placebo_response_model (day)');
    LEGEND_CONSTANTS(:,18) = strpad('CL in component pharmacokinetic_model (litre_per_day)');
    LEGEND_CONSTANTS(:,7) = strpad('smk in component pharmacokinetic_model (dimensionless)');
    LEGEND_CONSTANTS(:,8) = strpad('age in component pharmacokinetic_model (year)');
    LEGEND_ALGEBRAIC(:,2) = strpad('Sv in component drop_out_model (dimensionless)');
    LEGEND_CONSTANTS(:,9) = strpad('beta_a in component drug_response_model (units_ml_per_ng)');
    LEGEND_CONSTANTS(:,10) = strpad('CeA in component drug_response_model (ng_per_ml)');
    LEGEND_STATES(:,1) = strpad('CC in component drug_clearance (mg_per_litre)');
    LEGEND_STATES(:,2) = strpad('PC in component drug_clearance (mg_per_litre)');
    LEGEND_CONSTANTS(:,11) = strpad('Vc in component drug_clearance (litre)');
    LEGEND_CONSTANTS(:,12) = strpad('Vp in component drug_clearance (litre)');
    LEGEND_STATES(:,3) = strpad('A_in in component drug_clearance (mg)');
    LEGEND_CONSTANTS(:,13) = strpad('k_ab in component drug_clearance (per_day)');
    LEGEND_CONSTANTS(:,14) = strpad('CL_ic in component drug_clearance (litre_per_day)');
    LEGEND_RATES(:,1) = strpad('d/dt CC in component drug_clearance (mg_per_litre)');
    LEGEND_RATES(:,2) = strpad('d/dt PC in component drug_clearance (mg_per_litre)');
    LEGEND_RATES(:,3) = strpad('d/dt A_in in component drug_clearance (mg)');
    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) = 30;
    CONSTANTS(:,2) = 0.0164;
    CONSTANTS(:,3) = 0.0;
    CONSTANTS(:,4) = -3;
    CONSTANTS(:,5) = 7;
    CONSTANTS(:,6) = 6;
    CONSTANTS(:,7) = 1;
    CONSTANTS(:,8) = 40;
    CONSTANTS(:,9) = -0.047;
    CONSTANTS(:,10) = 25;
    STATES(:,1) = 0;
    STATES(:,2) = 0;
    CONSTANTS(:,11) = 172;
    CONSTANTS(:,12) = 222;
    STATES(:,3) = 25;
    CONSTANTS(:,13) = 115.44;
    CONSTANTS(:,14) = 763.2;
    CONSTANTS(:,15) =  CONSTANTS(:,9).*CONSTANTS(:,10);
    CONSTANTS(:,16) = log(2.00000)./CONSTANTS(:,6);
    CONSTANTS(:,17) = log(2.00000)./CONSTANTS(:,5);
    CONSTANTS(:,18) =  2268.00.*exp(  - 0.0135000.*(CONSTANTS(:,8) - 40.0000)).*CONSTANTS(:,7);
    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
    RATES(:,1) = ( CONSTANTS(:,13).*STATES(:,3) - ( CONSTANTS(:,18).*STATES(:,1)+ CONSTANTS(:,14).*(STATES(:,1) - STATES(:,2))))./CONSTANTS(:,11);
    RATES(:,2) = ( CONSTANTS(:,14).*(STATES(:,1) - STATES(:,2)))./CONSTANTS(:,12);
    RATES(:,3) =   - 115.440.*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(:,4).*CONSTANTS(:,16))./(CONSTANTS(:,16) - CONSTANTS(:,17))).*(exp(  - CONSTANTS(:,17).*VOI) - exp(  - CONSTANTS(:,16).*VOI));
    ALGEBRAIC(:,2) = exp(  - 0.00145000.*VOI);
    ALGEBRAIC(:,3) = CONSTANTS(:,1)+ CONSTANTS(:,2).*VOI+ALGEBRAIC(:,1)+CONSTANTS(:,15)+CONSTANTS(:,3);
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