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 =1;
end
% There are a total of 3 entries in each of the rate and state variable arrays.
% There are a total of 11 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_STATES(:,1) = strpad('phi_I in component phi_I (cells_per_mm3)');
    LEGEND_CONSTANTS(:,1) = strpad('alpha in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,2) = strpad('k1 in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,3) = strpad('k2 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,4) = strpad('k3 in component model_parameters (per_cells_per_mm3)');
    LEGEND_CONSTANTS(:,5) = strpad('d1 in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,2) = strpad('phi_R in component phi_R (cells_per_mm3)');
    LEGEND_ALGEBRAIC(:,1) = strpad('K_T in component K_T (cells_per_mm3_day)');
    LEGEND_STATES(:,3) = strpad('T in component T (pg_per_mm3)');
    LEGEND_CONSTANTS(:,6) = strpad('k4 in component model_parameters (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,7) = strpad('d2 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,8) = strpad('tau1 in component K_T (mm6_cells_per_pg3_day)');
    LEGEND_CONSTANTS(:,9) = strpad('tau2 in component K_T (mm3_cells_per_pg2_day)');
    LEGEND_CONSTANTS(:,10) = strpad('tau3 in component K_T (cells_per_pg_day)');
    LEGEND_CONSTANTS(:,11) = strpad('tau4 in component K_T (cells_per_mm3_day)');
    LEGEND_RATES(:,1) = strpad('d/dt phi_I in component phi_I (cells_per_mm3)');
    LEGEND_RATES(:,2) = strpad('d/dt phi_R in component phi_R (cells_per_mm3)');
    LEGEND_RATES(:,3) = strpad('d/dt T in component T (pg_per_mm3)');
    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 = [];
    STATES(:,1) = 200.0;
    CONSTANTS(:,1) = 0.5;
    CONSTANTS(:,2) = 0.05;
    CONSTANTS(:,3) = 0.693;
    CONSTANTS(:,4) = 0.002;
    CONSTANTS(:,5) = 0.2;
    STATES(:,2) = 200.0;
    STATES(:,3) = 6.0;
    CONSTANTS(:,6) = 0.07;
    CONSTANTS(:,7) = 9.1;
    CONSTANTS(:,8) = -2.47;
    CONSTANTS(:,9) = 21.94;
    CONSTANTS(:,10) = 6.41;
    CONSTANTS(:,11) = 1.75;
    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(:,3) =  CONSTANTS(:,6).*STATES(:,1) -  CONSTANTS(:,7).*STATES(:,3);
    ALGEBRAIC(:,1) =  CONSTANTS(:,8).*power(STATES(:,3), 3.00000)+ CONSTANTS(:,9).*power(STATES(:,3), 2.00000)+ CONSTANTS(:,10).*STATES(:,3)+CONSTANTS(:,11);
    RATES(:,1) = ( CONSTANTS(:,1).*ALGEBRAIC(:,1)+ CONSTANTS(:,2).*CONSTANTS(:,3).*STATES(:,1).*(1.00000 -  CONSTANTS(:,4).*(STATES(:,1)+STATES(:,2)))) -  CONSTANTS(:,5).*STATES(:,1);
    RATES(:,2) = ( (1.00000 - CONSTANTS(:,1)).*ALGEBRAIC(:,1)+ CONSTANTS(:,2).*CONSTANTS(:,3).*STATES(:,2).*(1.00000 -  CONSTANTS(:,4).*(STATES(:,1)+STATES(:,2)))) -  CONSTANTS(:,5).*STATES(:,2);
   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(:,8).*power(STATES(:,3), 3.00000)+ CONSTANTS(:,9).*power(STATES(:,3), 2.00000)+ CONSTANTS(:,10).*STATES(:,3)+CONSTANTS(:,11);
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