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 16 entries in each of the rate and state variable arrays.
% There are a total of 20 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 (hour)');
    LEGEND_STATES(:,1) = strpad('x in component x (dimensionless)');
    LEGEND_CONSTANTS(:,1) = strpad('d 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_CONSTANTS(:,4) = strpad('beta in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,2) = strpad('v in component v (dimensionless)');
    LEGEND_STATES(:,3) = strpad('y0 in component y0 (dimensionless)');
    LEGEND_CONSTANTS(:,5) = strpad('a0 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,6) = strpad('eta in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,7) = strpad('phi in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,4) = strpad('L in component L (dimensionless)');
    LEGEND_CONSTANTS(:,8) = strpad('pa in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,5) = strpad('za in component za (dimensionless)');
    LEGEND_CONSTANTS(:,9) = strpad('p_i in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,6) = strpad('zi in component zi (dimensionless)');
    LEGEND_STATES(:,7) = strpad('y1 in component y1 (dimensionless)');
    LEGEND_CONSTANTS(:,10) = strpad('a1 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,11) = strpad('k in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,12) = strpad('u in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,8) = strpad('m_8 in component m_8 (dimensionless)');
    LEGEND_CONSTANTS(:,13) = strpad('r in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,9) = strpad('m_7 in component m_7 (dimensionless)');
    LEGEND_STATES(:,10) = strpad('m_6 in component m_6 (dimensionless)');
    LEGEND_STATES(:,11) = strpad('m_5 in component m_5 (dimensionless)');
    LEGEND_STATES(:,12) = strpad('m_4 in component m_4 (dimensionless)');
    LEGEND_STATES(:,13) = strpad('m_3 in component m_3 (dimensionless)');
    LEGEND_STATES(:,14) = strpad('m_2 in component m_2 (dimensionless)');
    LEGEND_STATES(:,15) = strpad('m_1 in component m_1 (dimensionless)');
    LEGEND_STATES(:,16) = strpad('m_0 in component m_0 (dimensionless)');
    LEGEND_CONSTANTS(:,14) = strpad('alpha in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,15) = strpad('ca in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,16) = strpad('ba in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,17) = strpad('xi in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,18) = strpad('ci in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,19) = strpad('bi in component model_parameters (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,1) = strpad('log_zi in component zi (dimensionless)');
    LEGEND_CONSTANTS(:,20) = strpad('R0 in component R0 (dimensionless)');
    LEGEND_RATES(:,1) = strpad('d/dt x in component x (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt y0 in component y0 (dimensionless)');
    LEGEND_RATES(:,7) = strpad('d/dt y1 in component y1 (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt L in component L (dimensionless)');
    LEGEND_RATES(:,2) = strpad('d/dt v in component v (dimensionless)');
    LEGEND_RATES(:,8) = strpad('d/dt m_8 in component m_8 (dimensionless)');
    LEGEND_RATES(:,9) = strpad('d/dt m_7 in component m_7 (dimensionless)');
    LEGEND_RATES(:,10) = strpad('d/dt m_6 in component m_6 (dimensionless)');
    LEGEND_RATES(:,11) = strpad('d/dt m_5 in component m_5 (dimensionless)');
    LEGEND_RATES(:,12) = strpad('d/dt m_4 in component m_4 (dimensionless)');
    LEGEND_RATES(:,13) = strpad('d/dt m_3 in component m_3 (dimensionless)');
    LEGEND_RATES(:,14) = strpad('d/dt m_2 in component m_2 (dimensionless)');
    LEGEND_RATES(:,15) = strpad('d/dt m_1 in component m_1 (dimensionless)');
    LEGEND_RATES(:,16) = strpad('d/dt m_0 in component m_0 (dimensionless)');
    LEGEND_RATES(:,5) = strpad('d/dt za in component za (dimensionless)');
    LEGEND_RATES(:,6) = strpad('d/dt zi in component zi (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) = 1;
    CONSTANTS(:,1) = 0.1;
    CONSTANTS(:,2) = 0.5;
    CONSTANTS(:,3) = 10;
    CONSTANTS(:,4) = 0.1;
    STATES(:,2) = 1;
    STATES(:,3) = 0;
    CONSTANTS(:,5) = 0.1;
    CONSTANTS(:,6) = 0.01;
    CONSTANTS(:,7) = 0.1;
    STATES(:,4) = 0;
    CONSTANTS(:,8) = 0.000001;
    STATES(:,5) = 1;
    CONSTANTS(:,9) = 1;
    STATES(:,6) = 0.1;
    STATES(:,7) = 0;
    CONSTANTS(:,10) = 0.2;
    CONSTANTS(:,11) = 1;
    CONSTANTS(:,12) = 1;
    STATES(:,8) = 0;
    CONSTANTS(:,13) = 1;
    STATES(:,9) = 0;
    STATES(:,10) = 0;
    STATES(:,11) = 0;
    STATES(:,12) = 0;
    STATES(:,13) = 0;
    STATES(:,14) = 0;
    STATES(:,15) = 0;
    STATES(:,16) = 0;
    CONSTANTS(:,14) = 0.2;
    CONSTANTS(:,15) = 15.5;
    CONSTANTS(:,16) = 0.1;
    CONSTANTS(:,17) = 0.01;
    CONSTANTS(:,18) = 12;
    CONSTANTS(:,19) = 0.1;
    CONSTANTS(:,20) =  (( CONSTANTS(:,3).*CONSTANTS(:,6))./( CONSTANTS(:,1).*CONSTANTS(:,10).*(CONSTANTS(:,5)+CONSTANTS(:,6)))).*(CONSTANTS(:,4)+( CONSTANTS(:,2).*CONSTANTS(:,7))./(CONSTANTS(:,7)+CONSTANTS(:,1)));
    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(:,4).*STATES(:,1).*STATES(:,2)+ CONSTANTS(:,2).*STATES(:,1).*STATES(:,2));
    RATES(:,3) = ( CONSTANTS(:,4).*STATES(:,1).*STATES(:,2) - ( CONSTANTS(:,5).*STATES(:,3)+ CONSTANTS(:,6).*STATES(:,3)+ CONSTANTS(:,8).*STATES(:,3).*STATES(:,5)+ CONSTANTS(:,9).*STATES(:,3).*STATES(:,6)))+ CONSTANTS(:,7).*STATES(:,4);
    RATES(:,7) =  CONSTANTS(:,6).*STATES(:,3) - ( CONSTANTS(:,10).*STATES(:,7)+ CONSTANTS(:,8).*STATES(:,7).*STATES(:,5)+ CONSTANTS(:,9).*STATES(:,7).*STATES(:,6));
    RATES(:,4) =  CONSTANTS(:,2).*STATES(:,1).*STATES(:,2) - ( CONSTANTS(:,7).*STATES(:,4)+ CONSTANTS(:,1).*STATES(:,4));
    RATES(:,2) =  CONSTANTS(:,11).*STATES(:,7) -  CONSTANTS(:,12).*STATES(:,2);
    RATES(:,8) =  2.00000.*CONSTANTS(:,13).*STATES(:,9) -  CONSTANTS(:,13).*STATES(:,8);
    RATES(:,9) =  2.00000.*CONSTANTS(:,13).*STATES(:,10) -  CONSTANTS(:,13).*STATES(:,9);
    RATES(:,10) =  2.00000.*CONSTANTS(:,13).*STATES(:,11) -  CONSTANTS(:,13).*STATES(:,10);
    RATES(:,11) =  2.00000.*CONSTANTS(:,13).*STATES(:,12) -  CONSTANTS(:,13).*STATES(:,11);
    RATES(:,12) =  2.00000.*CONSTANTS(:,13).*STATES(:,13) -  CONSTANTS(:,13).*STATES(:,12);
    RATES(:,13) =  2.00000.*CONSTANTS(:,13).*STATES(:,14) -  CONSTANTS(:,13).*STATES(:,13);
    RATES(:,14) =  2.00000.*CONSTANTS(:,13).*STATES(:,15) -  CONSTANTS(:,13).*STATES(:,14);
    RATES(:,15) =  2.00000.*CONSTANTS(:,13).*STATES(:,16) -  CONSTANTS(:,13).*STATES(:,15);
    RATES(:,16) =   - CONSTANTS(:,13).*STATES(:,16);
    RATES(:,5) = ( CONSTANTS(:,14).*STATES(:,8)+ CONSTANTS(:,15).*(STATES(:,3)+STATES(:,7)).*STATES(:,5)) -  CONSTANTS(:,16).*STATES(:,5);
    RATES(:,6) = (CONSTANTS(:,17)+ CONSTANTS(:,18).*(STATES(:,3)+STATES(:,7)).*STATES(:,6)) -  CONSTANTS(:,19).*STATES(:,6);
   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(:,6), 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