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 27 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('R in component R (picomolar)');
    LEGEND_CONSTANTS(:,1) = strpad('DR in component model_parameters (flux)');
    LEGEND_ALGEBRAIC(:,3) = strpad('pi_C in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,23) = strpad('DB in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,2) = strpad('B in component B (picomolar)');
    LEGEND_CONSTANTS(:,2) = strpad('kB in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,3) = strpad('C in component C (picomolar)');
    LEGEND_CONSTANTS(:,3) = strpad('DC in component model_parameters (flux)');
    LEGEND_ALGEBRAIC(:,2) = strpad('pi_L in component pi_L (dimensionless)');
    LEGEND_CONSTANTS(:,4) = strpad('DA in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,5) = strpad('k1 in component pi_L (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,6) = strpad('k2 in component pi_L (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,7) = strpad('k3 in component pi_L (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,8) = strpad('k4 in component pi_L (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,9) = strpad('K in component pi_L (picomolar)');
    LEGEND_CONSTANTS(:,10) = strpad('ko in component pi_L (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,1) = strpad('Io in component pi_L (flux)');
    LEGEND_CONSTANTS(:,11) = strpad('IL in component pi_L (flux)');
    LEGEND_CONSTANTS(:,12) = strpad('rL in component pi_L (flux)');
    LEGEND_CONSTANTS(:,13) = strpad('KOP in component pi_L (picomole_day_picomole_cells)');
    LEGEND_CONSTANTS(:,14) = strpad('KLP in component pi_L (picomole_picomole_cells)');
    LEGEND_CONSTANTS(:,27) = strpad('pi_P in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,15) = strpad('f0 in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,16) = strpad('dB in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,17) = strpad('IP in component model_parameters (flux)');
    LEGEND_CONSTANTS(:,18) = strpad('kP in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,24) = strpad('P in component model_parameters (picomolar)');
    LEGEND_CONSTANTS(:,25) = strpad('P_0 in component model_parameters (picomolar)');
    LEGEND_CONSTANTS(:,26) = strpad('P_s in component model_parameters (picomolar)');
    LEGEND_CONSTANTS(:,19) = strpad('C_s in component model_parameters (picomolar)');
    LEGEND_CONSTANTS(:,20) = strpad('SP in component model_parameters (flux)');
    LEGEND_CONSTANTS(:,21) = strpad('k5 in component model_parameters (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,22) = strpad('k6 in component model_parameters (first_order_rate_constant)');
    LEGEND_RATES(:,1) = strpad('d/dt R in component R (picomolar)');
    LEGEND_RATES(:,2) = strpad('d/dt B in component B (picomolar)');
    LEGEND_RATES(:,3) = strpad('d/dt C in component C (picomolar)');
    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) = 0.00;
    CONSTANTS(:,1) = 7E-4;
    STATES(:,2) = 0.00;
    CONSTANTS(:,2) = 0.189;
    STATES(:,3) = 0.00;
    CONSTANTS(:,3) = 2.1E-3;
    CONSTANTS(:,4) = 0.7;
    CONSTANTS(:,5) = 1E-2;
    CONSTANTS(:,6) = 10.0;
    CONSTANTS(:,7) = 5.8E-4;
    CONSTANTS(:,8) = 1.7E-2;
    CONSTANTS(:,9) = 10.0;
    CONSTANTS(:,10) = 0.35;
    CONSTANTS(:,11) = 0.0;
    CONSTANTS(:,12) = 1E3;
    CONSTANTS(:,13) = 2E5;
    CONSTANTS(:,14) = 3E6;
    CONSTANTS(:,15) = 0.05;
    CONSTANTS(:,16) = 0.7;
    CONSTANTS(:,17) = 0.0;
    CONSTANTS(:,18) = 86.0;
    CONSTANTS(:,19) = 5E-3;
    CONSTANTS(:,20) = 250.0;
    CONSTANTS(:,21) = 0.02;
    CONSTANTS(:,22) = 3.0;
    CONSTANTS(:,23) =  CONSTANTS(:,15).*CONSTANTS(:,16);
    CONSTANTS(:,24) = CONSTANTS(:,17)./CONSTANTS(:,18);
    CONSTANTS(:,25) = CONSTANTS(:,20)./CONSTANTS(:,18);
    CONSTANTS(:,26) = CONSTANTS(:,22)./CONSTANTS(:,21);
    CONSTANTS(:,27) = (CONSTANTS(:,24)+CONSTANTS(:,25))./(CONSTANTS(:,24)+CONSTANTS(:,26));
    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
    ALGEBRAIC(:,3) = (STATES(:,3)+ CONSTANTS(:,15).*CONSTANTS(:,19))./(STATES(:,3)+CONSTANTS(:,19));
    RATES(:,1) =  CONSTANTS(:,1).*ALGEBRAIC(:,3) -  (CONSTANTS(:,23)./ALGEBRAIC(:,3)).*STATES(:,1);
    RATES(:,2) =  (CONSTANTS(:,23)./ALGEBRAIC(:,3)).*STATES(:,1) -  CONSTANTS(:,2).*STATES(:,2);
    ALGEBRAIC(:,1) = piecewise({VOI>20.0000&VOI<=80.0000, 200000. }, 0.00000);
    ALGEBRAIC(:,2) =  (CONSTANTS(:,7)./CONSTANTS(:,8)).*(( CONSTANTS(:,14).*CONSTANTS(:,27).*STATES(:,2))./(1.00000+( CONSTANTS(:,7).*CONSTANTS(:,9))./CONSTANTS(:,8)+ (CONSTANTS(:,5)./( CONSTANTS(:,6).*CONSTANTS(:,10))).*( (CONSTANTS(:,13)./CONSTANTS(:,27)).*STATES(:,1)+ALGEBRAIC(:,1)))).*(1.00000+CONSTANTS(:,11)./CONSTANTS(:,12));
    RATES(:,3) =  CONSTANTS(:,3).*ALGEBRAIC(:,2) -  CONSTANTS(:,4).*ALGEBRAIC(:,3).*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(:,3) = (STATES(:,3)+ CONSTANTS(:,15).*CONSTANTS(:,19))./(STATES(:,3)+CONSTANTS(:,19));
    ALGEBRAIC(:,1) = piecewise({VOI>20.0000&VOI<=80.0000, 200000. }, 0.00000);
    ALGEBRAIC(:,2) =  (CONSTANTS(:,7)./CONSTANTS(:,8)).*(( CONSTANTS(:,14).*CONSTANTS(:,27).*STATES(:,2))./(1.00000+( CONSTANTS(:,7).*CONSTANTS(:,9))./CONSTANTS(:,8)+ (CONSTANTS(:,5)./( CONSTANTS(:,6).*CONSTANTS(:,10))).*( (CONSTANTS(:,13)./CONSTANTS(:,27)).*STATES(:,1)+ALGEBRAIC(:,1)))).*(1.00000+CONSTANTS(:,11)./CONSTANTS(:,12));
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