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 16 entries in each of the rate and state variable arrays.
% There are a total of 14 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('B0 in component B0 (cells_per_GC)');
    LEGEND_CONSTANTS(:,1) = strpad('pr in component kinetic_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,2) = strpad('mu in component kinetic_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,3) = strpad('rho in component kinetic_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,4) = strpad('delta_B in component kinetic_parameters (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,1) = strpad('CT_star in component CT_star (cells_per_GC)');
    LEGEND_STATES(:,2) = strpad('B1 in component B1 (cells_per_GC)');
    LEGEND_ALGEBRAIC(:,5) = strpad('alpha_B in component alpha_B (dimensionless)');
    LEGEND_STATES(:,3) = strpad('B2 in component B2 (cells_per_GC)');
    LEGEND_STATES(:,4) = strpad('B3 in component B3 (cells_per_GC)');
    LEGEND_STATES(:,5) = strpad('B4 in component B4 (cells_per_GC)');
    LEGEND_STATES(:,6) = strpad('B5 in component B5 (cells_per_GC)');
    LEGEND_STATES(:,7) = strpad('B6 in component B6 (cells_per_GC)');
    LEGEND_STATES(:,8) = strpad('B7 in component B7 (cells_per_GC)');
    LEGEND_STATES(:,9) = strpad('B8 in component B8 (cells_per_GC)');
    LEGEND_STATES(:,10) = strpad('B9 in component B9 (cells_per_GC)');
    LEGEND_STATES(:,11) = strpad('B10 in component B10 (cells_per_GC)');
    LEGEND_ALGEBRAIC(:,2) = strpad('B_sum in component centroblasts_sum (cells_per_GC)');
    LEGEND_STATES(:,12) = strpad('C in component C (cells_per_GC)');
    LEGEND_CONSTANTS(:,5) = strpad('d in component C (first_order_rate_constant)');
    LEGEND_STATES(:,13) = strpad('C_star in component C_star (cells_per_GC)');
    LEGEND_ALGEBRAIC(:,3) = strpad('CA in component CA (cells_per_GC)');
    LEGEND_ALGEBRAIC(:,6) = strpad('C_starsum in component centrocytes_sum (cells_per_GC)');
    LEGEND_STATES(:,14) = strpad('M in component M (cells_per_GC)');
    LEGEND_STATES(:,15) = strpad('A in component A (cells_per_GC)');
    LEGEND_CONSTANTS(:,6) = strpad('z in component A (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,7) = strpad('u in component A (dimensionless)');
    LEGEND_ALGEBRAIC(:,4) = strpad('log_A in component A (dimensionless)');
    LEGEND_STATES(:,16) = strpad('T in component T (cells_per_GC)');
    LEGEND_CONSTANTS(:,8) = strpad('p in component T (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,9) = strpad('sigma in component T (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,10) = strpad('delta_T in component T (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,7) = strpad('alpha_T in component alpha_T (dimensionless)');
    LEGEND_CONSTANTS(:,11) = strpad('SA in component CA (dimensionless)');
    LEGEND_CONSTANTS(:,12) = strpad('ST in component CT_star (dimensionless)');
    LEGEND_CONSTANTS(:,13) = strpad('KB in component alpha_B (dimensionless)');
    LEGEND_CONSTANTS(:,14) = strpad('KT in component alpha_T (dimensionless)');
    LEGEND_ALGEBRAIC(:,8) = strpad('total in component total (cells_per_GC)');
    LEGEND_ALGEBRAIC(:,9) = strpad('log_total in component total (dimensionless)');
    LEGEND_RATES(:,1) = strpad('d/dt B0 in component B0 (cells_per_GC)');
    LEGEND_RATES(:,2) = strpad('d/dt B1 in component B1 (cells_per_GC)');
    LEGEND_RATES(:,3) = strpad('d/dt B2 in component B2 (cells_per_GC)');
    LEGEND_RATES(:,4) = strpad('d/dt B3 in component B3 (cells_per_GC)');
    LEGEND_RATES(:,5) = strpad('d/dt B4 in component B4 (cells_per_GC)');
    LEGEND_RATES(:,6) = strpad('d/dt B5 in component B5 (cells_per_GC)');
    LEGEND_RATES(:,7) = strpad('d/dt B6 in component B6 (cells_per_GC)');
    LEGEND_RATES(:,8) = strpad('d/dt B7 in component B7 (cells_per_GC)');
    LEGEND_RATES(:,9) = strpad('d/dt B8 in component B8 (cells_per_GC)');
    LEGEND_RATES(:,10) = strpad('d/dt B9 in component B9 (cells_per_GC)');
    LEGEND_RATES(:,11) = strpad('d/dt B10 in component B10 (cells_per_GC)');
    LEGEND_RATES(:,12) = strpad('d/dt C in component C (cells_per_GC)');
    LEGEND_RATES(:,13) = strpad('d/dt C_star in component C_star (cells_per_GC)');
    LEGEND_RATES(:,14) = strpad('d/dt M in component M (cells_per_GC)');
    LEGEND_RATES(:,15) = strpad('d/dt A in component A (cells_per_GC)');
    LEGEND_RATES(:,16) = strpad('d/dt T in component T (cells_per_GC)');
    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) = 3;
    CONSTANTS(:,1) = 0.15;
    CONSTANTS(:,2) = 3;
    CONSTANTS(:,3) = 4;
    CONSTANTS(:,4) = 0.8;
    STATES(:,2) = 0;
    STATES(:,3) = 0;
    STATES(:,4) = 0;
    STATES(:,5) = 0;
    STATES(:,6) = 0;
    STATES(:,7) = 0;
    STATES(:,8) = 0;
    STATES(:,9) = 0;
    STATES(:,10) = 0;
    STATES(:,11) = 0;
    STATES(:,12) = 0;
    CONSTANTS(:,5) = 2;
    STATES(:,13) = 0;
    STATES(:,14) = 0;
    STATES(:,15) = 500;
    CONSTANTS(:,6) = 0.02;
    CONSTANTS(:,7) = 0.15;
    STATES(:,16) = 0;
    CONSTANTS(:,8) = 2;
    CONSTANTS(:,9) = 5;
    CONSTANTS(:,10) = 0.8;
    CONSTANTS(:,11) = 500;
    CONSTANTS(:,12) = 50;
    CONSTANTS(:,13) = 1e4;
    CONSTANTS(:,14) = 100;
    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(:,12) =  CONSTANTS(:,5).*CONSTANTS(:,3).*STATES(:,11).*1.00000 -  CONSTANTS(:,2).*STATES(:,12);
    ALGEBRAIC(:,1) = ( STATES(:,13).*STATES(:,16))./( CONSTANTS(:,12).*1.00000+STATES(:,13));
    RATES(:,1) =  CONSTANTS(:,1).*CONSTANTS(:,2).*ALGEBRAIC(:,1) - ( CONSTANTS(:,3).*STATES(:,1)+ CONSTANTS(:,4).*STATES(:,1));
    ALGEBRAIC(:,3) = ( STATES(:,12).*STATES(:,15))./( CONSTANTS(:,11).*1.00000+STATES(:,15));
    RATES(:,13) =  CONSTANTS(:,2).*ALGEBRAIC(:,3) -  CONSTANTS(:,2).*STATES(:,13);
    RATES(:,14) =  (1.00000 - CONSTANTS(:,1)).*CONSTANTS(:,2).*ALGEBRAIC(:,1);
    RATES(:,15) =   - CONSTANTS(:,6).*STATES(:,15) -  CONSTANTS(:,7).*ALGEBRAIC(:,3).*1.00000;
    ALGEBRAIC(:,2) = STATES(:,2)+STATES(:,2)+STATES(:,4)+STATES(:,5)+STATES(:,6)+STATES(:,7)+STATES(:,7)+STATES(:,8)+STATES(:,9)+STATES(:,10)+STATES(:,11);
    ALGEBRAIC(:,5) = CONSTANTS(:,13)./(CONSTANTS(:,13)+ALGEBRAIC(:,2)./1.00000);
    RATES(:,2) =  CONSTANTS(:,3).*(1.00000+ALGEBRAIC(:,5)).*STATES(:,1) - ( CONSTANTS(:,3).*STATES(:,2)+ CONSTANTS(:,4).*STATES(:,2));
    RATES(:,3) =  CONSTANTS(:,3).*(1.00000+ALGEBRAIC(:,5)).*STATES(:,2) - ( CONSTANTS(:,3).*STATES(:,3)+ CONSTANTS(:,4).*STATES(:,3));
    RATES(:,4) =  CONSTANTS(:,3).*(1.00000+ALGEBRAIC(:,5)).*STATES(:,3) - ( CONSTANTS(:,3).*STATES(:,4)+ CONSTANTS(:,4).*STATES(:,4));
    RATES(:,5) =  CONSTANTS(:,3).*(1.00000+ALGEBRAIC(:,5)).*STATES(:,4) - ( CONSTANTS(:,3).*STATES(:,5)+ CONSTANTS(:,4).*STATES(:,5));
    RATES(:,6) =  CONSTANTS(:,3).*(1.00000+ALGEBRAIC(:,5)).*STATES(:,5) - ( CONSTANTS(:,3).*STATES(:,6)+ CONSTANTS(:,4).*STATES(:,6));
    RATES(:,7) =  CONSTANTS(:,3).*(1.00000+ALGEBRAIC(:,5)).*STATES(:,6) - ( CONSTANTS(:,3).*STATES(:,7)+ CONSTANTS(:,4).*STATES(:,7));
    RATES(:,8) =  CONSTANTS(:,3).*(1.00000+ALGEBRAIC(:,5)).*STATES(:,7) - ( CONSTANTS(:,3).*STATES(:,8)+ CONSTANTS(:,4).*STATES(:,8));
    RATES(:,9) =  CONSTANTS(:,3).*(1.00000+ALGEBRAIC(:,5)).*STATES(:,8) - ( CONSTANTS(:,3).*STATES(:,9)+ CONSTANTS(:,4).*STATES(:,9));
    RATES(:,10) =  CONSTANTS(:,3).*(1.00000+ALGEBRAIC(:,5)).*STATES(:,9) - ( CONSTANTS(:,3).*STATES(:,10)+ CONSTANTS(:,4).*STATES(:,10));
    RATES(:,11) =  CONSTANTS(:,3).*(1.00000+ALGEBRAIC(:,5)).*STATES(:,10) - ( CONSTANTS(:,3).*STATES(:,11)+ CONSTANTS(:,4).*STATES(:,11));
    ALGEBRAIC(:,7) = CONSTANTS(:,14)./(CONSTANTS(:,14)+STATES(:,16)./1.00000);
    RATES(:,16) = ( CONSTANTS(:,9).*1.00000+ CONSTANTS(:,8).*ALGEBRAIC(:,7).*ALGEBRAIC(:,1)) -  CONSTANTS(:,10).*STATES(:,16);
   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) = ( STATES(:,13).*STATES(:,16))./( CONSTANTS(:,12).*1.00000+STATES(:,13));
    ALGEBRAIC(:,3) = ( STATES(:,12).*STATES(:,15))./( CONSTANTS(:,11).*1.00000+STATES(:,15));
    ALGEBRAIC(:,2) = STATES(:,2)+STATES(:,2)+STATES(:,4)+STATES(:,5)+STATES(:,6)+STATES(:,7)+STATES(:,7)+STATES(:,8)+STATES(:,9)+STATES(:,10)+STATES(:,11);
    ALGEBRAIC(:,5) = CONSTANTS(:,13)./(CONSTANTS(:,13)+ALGEBRAIC(:,2)./1.00000);
    ALGEBRAIC(:,7) = CONSTANTS(:,14)./(CONSTANTS(:,14)+STATES(:,16)./1.00000);
    ALGEBRAIC(:,4) = arbitrary_log(STATES(:,15)./1.00000, 10);
    ALGEBRAIC(:,6) = STATES(:,12)+STATES(:,13);
    ALGEBRAIC(:,8) = ALGEBRAIC(:,2)+ALGEBRAIC(:,6);
    ALGEBRAIC(:,9) = arbitrary_log(ALGEBRAIC(:,8)./1.00000+1.00000e-12, 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