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 =0;
end
% There are a total of 17 entries in each of the rate and state variable arrays.
% There are a total of 18 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 (second)');
    LEGEND_STATES(:,1) = strpad('T in component T (dimensionless)');
    LEGEND_CONSTANTS(:,1) = strpad('delta in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,2) = strpad('gamma in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,3) = strpad('lambda in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,2) = strpad('v in component v (dimensionless)');
    LEGEND_STATES(:,3) = strpad('I in component I (dimensionless)');
    LEGEND_CONSTANTS(:,4) = strpad('alpha in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,5) = strpad('p in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,4) = strpad('z in component z (dimensionless)');
    LEGEND_STATES(:,5) = strpad('w in component w (dimensionless)');
    LEGEND_STATES(:,6) = strpad('x in component x (dimensionless)');
    LEGEND_CONSTANTS(:,6) = strpad('r in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,7) = strpad('y in component y (dimensionless)');
    LEGEND_CONSTANTS(:,7) = strpad('k in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,8) = strpad('d in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,9) = strpad('beta in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,10) = strpad('a in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,11) = strpad('u in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,12) = strpad('eta in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,13) = strpad('xi in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,14) = strpad('rho in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,15) = strpad('phi in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,8) = strpad('m_9 in component m_9 (dimensionless)');
    LEGEND_STATES(:,9) = strpad('m_8 in component m_8 (dimensionless)');
    LEGEND_STATES(:,10) = strpad('m_7 in component m_7 (dimensionless)');
    LEGEND_STATES(:,11) = strpad('m_6 in component m_6 (dimensionless)');
    LEGEND_STATES(:,12) = strpad('m_5 in component m_5 (dimensionless)');
    LEGEND_STATES(:,13) = strpad('m_4 in component m_4 (dimensionless)');
    LEGEND_STATES(:,14) = strpad('m_3 in component m_3 (dimensionless)');
    LEGEND_STATES(:,15) = strpad('m_2 in component m_2 (dimensionless)');
    LEGEND_STATES(:,16) = strpad('m_1 in component m_1 (dimensionless)');
    LEGEND_STATES(:,17) = strpad('m_0 in component m_0 (dimensionless)');
    LEGEND_CONSTANTS(:,16) = strpad('b in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,17) = strpad('epsilon in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,18) = strpad('c in component model_parameters (first_order_rate_constant)');
    LEGEND_RATES(:,1) = strpad('d/dt T in component T (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt I in component I (dimensionless)');
    LEGEND_RATES(:,6) = strpad('d/dt x in component x (dimensionless)');
    LEGEND_RATES(:,7) = strpad('d/dt y in component y (dimensionless)');
    LEGEND_RATES(:,2) = strpad('d/dt v in component v (dimensionless)');
    LEGEND_RATES(:,5) = strpad('d/dt w in component w (dimensionless)');
    LEGEND_RATES(:,8) = strpad('d/dt m_9 in component m_9 (dimensionless)');
    LEGEND_RATES(:,9) = strpad('d/dt m_8 in component m_8 (dimensionless)');
    LEGEND_RATES(:,10) = strpad('d/dt m_7 in component m_7 (dimensionless)');
    LEGEND_RATES(:,11) = strpad('d/dt m_6 in component m_6 (dimensionless)');
    LEGEND_RATES(:,12) = strpad('d/dt m_5 in component m_5 (dimensionless)');
    LEGEND_RATES(:,13) = strpad('d/dt m_4 in component m_4 (dimensionless)');
    LEGEND_RATES(:,14) = strpad('d/dt m_3 in component m_3 (dimensionless)');
    LEGEND_RATES(:,15) = strpad('d/dt m_2 in component m_2 (dimensionless)');
    LEGEND_RATES(:,16) = strpad('d/dt m_1 in component m_1 (dimensionless)');
    LEGEND_RATES(:,17) = strpad('d/dt m_0 in component m_0 (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt z in component z (dimensionless)');
    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) = 1000.0;
    CONSTANTS(:,1) = 0.01;
    CONSTANTS(:,2) = 0.01;
    CONSTANTS(:,3) = 1.0;
    STATES(:,2) = 0.0001;
    STATES(:,3) = 0.0001;
    CONSTANTS(:,4) = 0.2;
    CONSTANTS(:,5) = 45.0;
    STATES(:,4) = 0.0;
    STATES(:,5) = 0.0;
    STATES(:,6) = 10.0;
    CONSTANTS(:,6) = 1.0;
    STATES(:,7) = 0.0;
    CONSTANTS(:,7) = 10.0;
    CONSTANTS(:,8) = 0.001;
    CONSTANTS(:,9) = 0.3;
    CONSTANTS(:,10) = 0.2;
    CONSTANTS(:,11) = 1.0;
    CONSTANTS(:,12) = 1.0;
    CONSTANTS(:,13) = 0.01;
    CONSTANTS(:,14) = 0.3;
    CONSTANTS(:,15) = 1.5;
    STATES(:,8) = 0.0;
    STATES(:,9) = 0.0;
    STATES(:,10) = 0.0;
    STATES(:,11) = 0.0;
    STATES(:,12) = 0.0;
    STATES(:,13) = 0.0;
    STATES(:,14) = 0.0;
    STATES(:,15) = 0.0;
    STATES(:,16) = 0.0;
    STATES(:,17) = 0.1;
    CONSTANTS(:,16) = 0.1;
    CONSTANTS(:,17) = 1.0;
    CONSTANTS(:,18) = 1.0;
    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(:,3) - ( CONSTANTS(:,1).*STATES(:,1)+ CONSTANTS(:,2).*STATES(:,1).*STATES(:,2));
    RATES(:,3) =  CONSTANTS(:,2).*STATES(:,1).*STATES(:,2) - ( CONSTANTS(:,4).*STATES(:,3)+ CONSTANTS(:,5).*STATES(:,3).*(STATES(:,4)+STATES(:,5)));
    RATES(:,6) =  CONSTANTS(:,6).*STATES(:,6).*STATES(:,2).*(1.00000 - (STATES(:,6)+STATES(:,7))./CONSTANTS(:,7)) - ( CONSTANTS(:,8).*STATES(:,6)+ CONSTANTS(:,9).*STATES(:,6).*STATES(:,2));
    RATES(:,7) = ( CONSTANTS(:,9).*STATES(:,6).*STATES(:,2)+ CONSTANTS(:,6).*STATES(:,7).*STATES(:,2).*(1.00000 - (STATES(:,6)+STATES(:,7))./CONSTANTS(:,7))) - ( CONSTANTS(:,10).*STATES(:,7)+ CONSTANTS(:,5).*STATES(:,7).*(STATES(:,4)+STATES(:,5)));
    RATES(:,2) =  CONSTANTS(:,12).*(STATES(:,7)+STATES(:,3)) -  CONSTANTS(:,11).*STATES(:,2);
    RATES(:,5) =  2.00000.*CONSTANTS(:,14).*STATES(:,8) - ( CONSTANTS(:,13).*STATES(:,5)+ CONSTANTS(:,15).*STATES(:,5));
    RATES(:,8) =  2.00000.*CONSTANTS(:,14).*STATES(:,9) -  CONSTANTS(:,14).*STATES(:,8);
    RATES(:,9) =  2.00000.*CONSTANTS(:,14).*STATES(:,10) -  CONSTANTS(:,14).*STATES(:,9);
    RATES(:,10) =  2.00000.*CONSTANTS(:,14).*STATES(:,11) -  CONSTANTS(:,14).*STATES(:,10);
    RATES(:,11) =  2.00000.*CONSTANTS(:,14).*STATES(:,12) -  CONSTANTS(:,14).*STATES(:,11);
    RATES(:,12) =  2.00000.*CONSTANTS(:,14).*STATES(:,13) -  CONSTANTS(:,14).*STATES(:,12);
    RATES(:,13) =  2.00000.*CONSTANTS(:,14).*STATES(:,14) -  CONSTANTS(:,14).*STATES(:,13);
    RATES(:,14) =  2.00000.*CONSTANTS(:,14).*STATES(:,15) -  CONSTANTS(:,14).*STATES(:,14);
    RATES(:,15) =  2.00000.*CONSTANTS(:,14).*STATES(:,16) -  CONSTANTS(:,14).*STATES(:,15);
    RATES(:,16) =  2.00000.*CONSTANTS(:,14).*STATES(:,17) -  CONSTANTS(:,14).*STATES(:,16);
    RATES(:,17) =  - ( CONSTANTS(:,14).*STATES(:,17));
    RATES(:,4) = ( CONSTANTS(:,13).*STATES(:,5)+ CONSTANTS(:,18).*STATES(:,6).*(STATES(:,7)+STATES(:,3)).*(STATES(:,4)./( CONSTANTS(:,17).*STATES(:,6)+1.00000))) -  CONSTANTS(:,16).*STATES(:,4);
   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
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