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 =9;
end
% There are a total of 8 entries in each of the rate and state variable arrays.
% There are a total of 20 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_CONSTANTS(:,1) = strpad('mu_T in component uninfected_CD4 (per_day)');
    LEGEND_CONSTANTS(:,2) = strpad('r in component uninfected_CD4 (per_day)');
    LEGEND_STATES(:,1) = strpad('T_1 in component latently_infected_CD4 (per_micro_L)');
    LEGEND_CONSTANTS(:,3) = strpad('T_max in component uninfected_CD4 (per_micro_L)');
    LEGEND_CONSTANTS(:,4) = strpad('k_1 in component HIV1 (micro_L_per_day)');
    LEGEND_STATES(:,2) = strpad('V in component HIV1 (per_micro_L)');
    LEGEND_CONSTANTS(:,5) = strpad('k_1_ in component hybrid_HIV1 (micro_L_per_day)');
    LEGEND_STATES(:,3) = strpad('V_ in component hybrid_HIV1 (per_micro_L)');
    LEGEND_CONSTANTS(:,6) = strpad('s_0 in component uninfected_CD4 (per_micro_L_day)');
    LEGEND_CONSTANTS(:,7) = strpad('theta in component uninfected_CD4 (per_micro_L)');
    LEGEND_ALGEBRAIC(:,1) = strpad('s_V in component uninfected_CD4 (per_micro_L_day)');
    LEGEND_STATES(:,4) = strpad('T in component uninfected_CD4 (per_micro_L)');
    LEGEND_CONSTANTS(:,8) = strpad('k_2 in component latently_infected_CD4 (per_day)');
    LEGEND_CONSTANTS(:,9) = strpad('k_1D in component actively_infected_CD4 (micro_L_per_day)');
    LEGEND_ALGEBRAIC(:,2) = strpad('D in component DIV (per_micro_L)');
    LEGEND_CONSTANTS(:,10) = strpad('mu_b in component actively_infected_CD4 (per_day)');
    LEGEND_STATES(:,5) = strpad('T_2 in component actively_infected_CD4 (per_micro_L)');
    LEGEND_CONSTANTS(:,11) = strpad('k_s in component actively_coinfected_CD4 (per_day)');
    LEGEND_CONSTANTS(:,12) = strpad('mu_bD in component actively_coinfected_CD4 (per_day)');
    LEGEND_STATES(:,6) = strpad('T_D2 in component actively_coinfected_CD4 (per_micro_L)');
    LEGEND_CONSTANTS(:,13) = strpad('mu_TD in component stably_coinfected_CD4 (per_day)');
    LEGEND_STATES(:,7) = strpad('T_D1 in component stably_coinfected_CD4 (per_micro_L)');
    LEGEND_ALGEBRAIC(:,5) = strpad('N_D_t in component DIV (dimensionless)');
    LEGEND_ALGEBRAIC(:,8) = strpad('pi_D_t in component DIV (per_day)');
    LEGEND_CONSTANTS(:,14) = strpad('mu_D in component DIV (per_day)');
    LEGEND_ALGEBRAIC(:,3) = strpad('N_t in component production_function (dimensionless)');
    LEGEND_CONSTANTS(:,15) = strpad('t_DIV in component DIV (day)');
    LEGEND_STATES(:,8) = strpad('D_ode in component DIV (per_micro_L)');
    LEGEND_CONSTANTS(:,16) = strpad('D_0 in component DIV (per_micro_L)');
    LEGEND_ALGEBRAIC(:,6) = strpad('N_2_t in component HIV1 (dimensionless)');
    LEGEND_CONSTANTS(:,17) = strpad('mu_V in component HIV1 (per_day)');
    LEGEND_ALGEBRAIC(:,7) = strpad('N_t_ in component hybrid_HIV1 (dimensionless)');
    LEGEND_ALGEBRAIC(:,9) = strpad('pi_t_ in component hybrid_HIV1 (per_day)');
    LEGEND_CONSTANTS(:,18) = strpad('N_0 in component production_function (dimensionless)');
    LEGEND_CONSTANTS(:,19) = strpad('gamma in component production_function (dimensionless)');
    LEGEND_CONSTANTS(:,20) = strpad('t_c in component production_function (day)');
    LEGEND_ALGEBRAIC(:,4) = strpad('T_tot in component cell_population (per_micro_L)');
    LEGEND_RATES(:,4) = strpad('d/dt T in component uninfected_CD4 (per_micro_L)');
    LEGEND_RATES(:,1) = strpad('d/dt T_1 in component latently_infected_CD4 (per_micro_L)');
    LEGEND_RATES(:,5) = strpad('d/dt T_2 in component actively_infected_CD4 (per_micro_L)');
    LEGEND_RATES(:,6) = strpad('d/dt T_D2 in component actively_coinfected_CD4 (per_micro_L)');
    LEGEND_RATES(:,7) = strpad('d/dt T_D1 in component stably_coinfected_CD4 (per_micro_L)');
    LEGEND_RATES(:,8) = strpad('d/dt D_ode in component DIV (per_micro_L)');
    LEGEND_RATES(:,2) = strpad('d/dt V in component HIV1 (per_micro_L)');
    LEGEND_RATES(:,3) = strpad('d/dt V_ in component hybrid_HIV1 (per_micro_L)');
    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) = 0.02;
    CONSTANTS(:,2) = 0.03;
    STATES(:,1) = 0;
    CONSTANTS(:,3) = 1500;
    CONSTANTS(:,4) = 2.4E-5;
    STATES(:,2) = 1E-3;
    CONSTANTS(:,5) = 2.4E-7;
    STATES(:,3) = 0;
    CONSTANTS(:,6) = 10;
    CONSTANTS(:,7) = 1;
    STATES(:,4) = 1000;
    CONSTANTS(:,8) = 0.017;
    CONSTANTS(:,9) = 2.4E-5;
    CONSTANTS(:,10) = 0.24;
    STATES(:,5) = 0;
    CONSTANTS(:,11) = 0.48;
    CONSTANTS(:,12) = 0.12;
    STATES(:,6) = 0;
    CONSTANTS(:,13) = 0.02;
    STATES(:,7) = 0;
    CONSTANTS(:,14) = 0.76;
    CONSTANTS(:,15) = 2557;
    STATES(:,8) = 0;
    CONSTANTS(:,16) = 0.1;
    CONSTANTS(:,17) = 2.4;
    CONSTANTS(:,18) = 300;
    CONSTANTS(:,19) = 25;
    CONSTANTS(:,20) = 7305;
    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(:,4).*STATES(:,2).*STATES(:,4)+ CONSTANTS(:,5).*STATES(:,3).*STATES(:,4)) -  CONSTANTS(:,1).*STATES(:,1)) -  CONSTANTS(:,8).*STATES(:,1);
    RATES(:,7) =  CONSTANTS(:,11).*STATES(:,6) -  CONSTANTS(:,13).*STATES(:,7);
    ALGEBRAIC(:,1) = ( CONSTANTS(:,6).*CONSTANTS(:,7))./(CONSTANTS(:,7)+STATES(:,2));
    RATES(:,4) = (((ALGEBRAIC(:,1) -  CONSTANTS(:,1).*STATES(:,4))+ CONSTANTS(:,2).*STATES(:,4).*(1.00000 - (STATES(:,4)+STATES(:,1))./CONSTANTS(:,3))) -  CONSTANTS(:,4).*STATES(:,2).*STATES(:,4)) -  CONSTANTS(:,5).*STATES(:,3).*STATES(:,4);
    ALGEBRAIC(:,2) = piecewise({VOI<CONSTANTS(:,15), 0.00000 }, STATES(:,8));
    RATES(:,5) = ( CONSTANTS(:,8).*STATES(:,1) -  CONSTANTS(:,9).*ALGEBRAIC(:,2).*STATES(:,5)) -  CONSTANTS(:,10).*STATES(:,5);
    RATES(:,6) = ( CONSTANTS(:,9).*ALGEBRAIC(:,2).*STATES(:,5) -  CONSTANTS(:,11).*STATES(:,6)) -  CONSTANTS(:,12).*STATES(:,6);
    ALGEBRAIC(:,3) =  CONSTANTS(:,18).*(1.00000+ CONSTANTS(:,19).*(power(VOI, 2.00000)./(power(VOI, 2.00000)+power(CONSTANTS(:,20), 2.00000))));
    ALGEBRAIC(:,6) =  0.100000.*ALGEBRAIC(:,3);
    RATES(:,2) = (( ALGEBRAIC(:,3).*CONSTANTS(:,10).*STATES(:,5)+ ALGEBRAIC(:,6).*CONSTANTS(:,12).*STATES(:,6)) -  CONSTANTS(:,4).*STATES(:,2).*STATES(:,4)) -  CONSTANTS(:,17).*STATES(:,2);
    ALGEBRAIC(:,5) =  0.200000.*ALGEBRAIC(:,3);
    ALGEBRAIC(:,8) =  0.500000.*CONSTANTS(:,10).*ALGEBRAIC(:,3);
    RATES(:,8) = piecewise({VOI<CONSTANTS(:,15), CONSTANTS(:,16)./CONSTANTS(:,15) }, ( ALGEBRAIC(:,5).*CONSTANTS(:,12).*STATES(:,6)+ ALGEBRAIC(:,8).*STATES(:,7)) -  CONSTANTS(:,14).*STATES(:,8));
    ALGEBRAIC(:,7) =  0.100000.*ALGEBRAIC(:,3);
    ALGEBRAIC(:,9) =  0.0100000.*CONSTANTS(:,10).*ALGEBRAIC(:,3);
    RATES(:,3) = (( ALGEBRAIC(:,7).*CONSTANTS(:,12).*STATES(:,6)+ ALGEBRAIC(:,9).*STATES(:,7)) -  CONSTANTS(:,17).*STATES(:,3)) -  CONSTANTS(:,5).*STATES(:,4).*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(:,6).*CONSTANTS(:,7))./(CONSTANTS(:,7)+STATES(:,2));
    ALGEBRAIC(:,2) = piecewise({VOI<CONSTANTS(:,15), 0.00000 }, STATES(:,8));
    ALGEBRAIC(:,3) =  CONSTANTS(:,18).*(1.00000+ CONSTANTS(:,19).*(power(VOI, 2.00000)./(power(VOI, 2.00000)+power(CONSTANTS(:,20), 2.00000))));
    ALGEBRAIC(:,6) =  0.100000.*ALGEBRAIC(:,3);
    ALGEBRAIC(:,5) =  0.200000.*ALGEBRAIC(:,3);
    ALGEBRAIC(:,8) =  0.500000.*CONSTANTS(:,10).*ALGEBRAIC(:,3);
    ALGEBRAIC(:,7) =  0.100000.*ALGEBRAIC(:,3);
    ALGEBRAIC(:,9) =  0.0100000.*CONSTANTS(:,10).*ALGEBRAIC(:,3);
    ALGEBRAIC(:,4) = STATES(:,4)+STATES(:,1)+STATES(:,5)+STATES(:,6)+STATES(:,7);
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