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 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 (day)');
    LEGEND_CONSTANTS(:,1) = strpad('tau in component model_parameters (day)');
    LEGEND_CONSTANTS(:,2) = strpad('delta in component model_parameters (cells_per_day)');
    LEGEND_CONSTANTS(:,3) = strpad('np in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,4) = strpad('c in component model_parameters (virons_per_day)');
    LEGEND_CONSTANTS(:,5) = strpad('k in component model_parameters (ml_per_virons_per_day)');
    LEGEND_CONSTANTS(:,6) = strpad('N in component model_parameters (virons_per_cell)');
    LEGEND_CONSTANTS(:,7) = strpad('m in component model_parameters (per_day)');
    LEGEND_CONSTANTS(:,8) = strpad('T in component uninfected_T_cells (cells_per_ml)');
    LEGEND_STATES(:,1) = strpad('T_star in component infected_T_cells (cells_per_ml)');
    LEGEND_STATES(:,2) = strpad('VI in component infectious_virus (virons_per_ml)');
    LEGEND_ALGEBRAIC(:,1) = strpad('log_VI in component infectious_virus (dimensionless)');
    LEGEND_STATES(:,3) = strpad('VNI in component non_infectious_virus (virons_per_ml)');
    LEGEND_ALGEBRAIC(:,2) = strpad('virus_total in component total_virus (virons_per_ml)');
    LEGEND_ALGEBRAIC(:,3) = strpad('log_virus_total in component total_virus (dimensionless)');
    LEGEND_RATES(:,1) = strpad('d/dt T_star in component infected_T_cells (cells_per_ml)');
    LEGEND_RATES(:,2) = strpad('d/dt VI in component infectious_virus (virons_per_ml)');
    LEGEND_RATES(:,3) = strpad('d/dt VNI in component non_infectious_virus (virons_per_ml)');
    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) = 1.0;
    CONSTANTS(:,2) = 0.5;
    CONSTANTS(:,3) = 1;
    CONSTANTS(:,4) = 3;
    CONSTANTS(:,5) = 3.43e-5;
    CONSTANTS(:,6) = 480;
    CONSTANTS(:,7) = 0.01;
    STATES(:,1) = 3.6;
    STATES(:,2) = 134e3;
    STATES(:,3) = 0;
    CONSTANTS(:,8) = 180.000;
    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(:,5).*CONSTANTS(:,8).*STATES(:,2).*(VOI - CONSTANTS(:,1)).*exp(  - CONSTANTS(:,7).*CONSTANTS(:,1)).*1.00000 -  (CONSTANTS(:,2)./1.00000).*STATES(:,1);
    RATES(:,2) = ( (1.00000 - CONSTANTS(:,3)).*CONSTANTS(:,6).*CONSTANTS(:,2).*STATES(:,1))./1.00000 - ( CONSTANTS(:,4).*STATES(:,2))./1.00000;
    RATES(:,3) = ( CONSTANTS(:,3).*CONSTANTS(:,6).*CONSTANTS(:,2).*STATES(:,1))./1.00000 - ( CONSTANTS(:,4).*STATES(:,3))./1.00000;
   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) = arbitrary_log(STATES(:,2)./1.00000, 10);
    ALGEBRAIC(:,2) = STATES(:,2)+STATES(:,3);
    ALGEBRAIC(:,3) = arbitrary_log(ALGEBRAIC(:,2)./1.00000, 10);
end

% Compute a logarithm to any base" +
function x = arbitrary_log(a, base)
    x = log(a) ./ log(base);
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