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 =2;
end
% There are a total of 5 entries in each of the rate and state variable arrays.
% There are a total of 26 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('R in component R (dimensionless)');
    LEGEND_CONSTANTS(:,20) = strpad('phi_1 in component reaction_rate_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,21) = strpad('phi_2 in component reaction_rate_constants (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,22) = strpad('phi_2b in component reaction_rate_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,1) = strpad('k_1b in component reaction_rate_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,2) = strpad('l_2b in component reaction_rate_constants (first_order_rate_constant)');
    LEGEND_STATES(:,2) = strpad('I_1 in component I_1 (dimensionless)');
    LEGEND_STATES(:,3) = strpad('O in component O (dimensionless)');
    LEGEND_CONSTANTS(:,3) = strpad('p in component reaction_rate_constants (micromolar)');
    LEGEND_CONSTANTS(:,23) = strpad('phi_3 in component reaction_rate_constants (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,24) = strpad('phi_4 in component reaction_rate_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,25) = strpad('phi_4b in component reaction_rate_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,4) = strpad('k_3b in component reaction_rate_constants (first_order_rate_constant)');
    LEGEND_STATES(:,4) = strpad('A in component A (dimensionless)');
    LEGEND_ALGEBRAIC(:,1) = strpad('S in component S (dimensionless)');
    LEGEND_STATES(:,5) = strpad('I_2 in component I_2 (dimensionless)');
    LEGEND_CONSTANTS(:,26) = strpad('phi_5 in component reaction_rate_constants (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,2) = strpad('open_probability in component open_probability (dimensionless)');
    LEGEND_CONSTANTS(:,5) = strpad('k_1a in component reaction_rate_constants (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,6) = strpad('k_2a in component reaction_rate_constants (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,7) = strpad('k_2b in component reaction_rate_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,8) = strpad('k_3a in component reaction_rate_constants (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,9) = strpad('k_4a in component reaction_rate_constants (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,10) = strpad('k_4b in component reaction_rate_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,11) = strpad('l_2a in component reaction_rate_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,12) = strpad('l_4a in component reaction_rate_constants (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,13) = strpad('l_4b in component reaction_rate_constants (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,14) = strpad('l_6a in component reaction_rate_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,15) = strpad('l_6b in component reaction_rate_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,16) = strpad('L_1 in component reaction_rate_constants (micromolar)');
    LEGEND_CONSTANTS(:,17) = strpad('L_3 in component reaction_rate_constants (micromolar)');
    LEGEND_CONSTANTS(:,18) = strpad('L_5 in component reaction_rate_constants (micromolar)');
    LEGEND_CONSTANTS(:,19) = strpad('c in component reaction_rate_constants (micromolar)');
    LEGEND_RATES(:,1) = strpad('d/dt R in component R (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt O in component O (dimensionless)');
    LEGEND_RATES(:,2) = strpad('d/dt I_1 in component I_1 (dimensionless)');
    LEGEND_RATES(:,5) = strpad('d/dt I_2 in component I_2 (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt A in component A (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) = 0.04;
    CONSTANTS(:,2) = 0.8;
    STATES(:,2) = 0;
    STATES(:,3) = 0;
    CONSTANTS(:,3) = 10;
    CONSTANTS(:,4) = 29.8;
    STATES(:,4) = 0;
    STATES(:,5) = 0;
    CONSTANTS(:,5) = 0.64;
    CONSTANTS(:,6) = 37.4;
    CONSTANTS(:,7) = 1.4;
    CONSTANTS(:,8) = 0.11;
    CONSTANTS(:,9) = 4;
    CONSTANTS(:,10) = 0.54;
    CONSTANTS(:,11) = 1.7;
    CONSTANTS(:,12) = 1.7;
    CONSTANTS(:,13) = 2.5;
    CONSTANTS(:,14) = 4707;
    CONSTANTS(:,15) = 11.4;
    CONSTANTS(:,16) = 0.12;
    CONSTANTS(:,17) = 0.025;
    CONSTANTS(:,18) = 54.7;
    CONSTANTS(:,19) = 1;
    CONSTANTS(:,20) = ( ( CONSTANTS(:,5).*CONSTANTS(:,16)+CONSTANTS(:,11)).*CONSTANTS(:,19))./(CONSTANTS(:,16)+ CONSTANTS(:,19).*(1.00000+CONSTANTS(:,16)./CONSTANTS(:,17)));
    CONSTANTS(:,21) = ( CONSTANTS(:,6).*CONSTANTS(:,17)+ CONSTANTS(:,12).*CONSTANTS(:,19))./(CONSTANTS(:,17)+ CONSTANTS(:,19).*(1.00000+CONSTANTS(:,17)./CONSTANTS(:,16)));
    CONSTANTS(:,22) = (CONSTANTS(:,7)+ CONSTANTS(:,13).*CONSTANTS(:,19))./(1.00000+CONSTANTS(:,19)./CONSTANTS(:,18));
    CONSTANTS(:,23) = ( CONSTANTS(:,8).*CONSTANTS(:,18))./(CONSTANTS(:,19)+CONSTANTS(:,18));
    CONSTANTS(:,24) = ( ( CONSTANTS(:,9).*CONSTANTS(:,18)+CONSTANTS(:,14)).*CONSTANTS(:,19))./(CONSTANTS(:,19)+CONSTANTS(:,18));
    CONSTANTS(:,25) = ( CONSTANTS(:,16).*(CONSTANTS(:,10)+CONSTANTS(:,15)))./(CONSTANTS(:,19)+CONSTANTS(:,16));
    CONSTANTS(:,26) = ( ( CONSTANTS(:,5).*CONSTANTS(:,16)+CONSTANTS(:,11)).*CONSTANTS(:,19))./(CONSTANTS(:,19)+CONSTANTS(:,16));
    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(:,22).*STATES(:,3)+ (CONSTANTS(:,1)+CONSTANTS(:,2)).*STATES(:,2)) - ( CONSTANTS(:,21).*CONSTANTS(:,3).*STATES(:,1)+ CONSTANTS(:,20).*STATES(:,1));
    RATES(:,2) =  CONSTANTS(:,20).*STATES(:,1) -  (CONSTANTS(:,1)+CONSTANTS(:,2)).*STATES(:,2);
    RATES(:,5) =  CONSTANTS(:,26).*STATES(:,4) -  (CONSTANTS(:,1)+CONSTANTS(:,2)).*STATES(:,5);
    RATES(:,4) = ( CONSTANTS(:,24).*STATES(:,3)+ (CONSTANTS(:,1)+CONSTANTS(:,2)).*STATES(:,5)) - ( CONSTANTS(:,25).*STATES(:,4)+ CONSTANTS(:,26).*STATES(:,4));
    ALGEBRAIC(:,1) = 1.00000 - (STATES(:,1)+STATES(:,3)+STATES(:,4)+STATES(:,2)+STATES(:,5));
    RATES(:,3) = ( CONSTANTS(:,21).*CONSTANTS(:,3).*STATES(:,1)+ CONSTANTS(:,25).*STATES(:,4)+ CONSTANTS(:,4).*ALGEBRAIC(:,1)) -  (CONSTANTS(:,22)+CONSTANTS(:,24)+ 1.00000.*CONSTANTS(:,23)).*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(:,1) = 1.00000 - (STATES(:,1)+STATES(:,3)+STATES(:,4)+STATES(:,2)+STATES(:,5));
    ALGEBRAIC(:,2) = power( 0.100000.*STATES(:,3)+ 0.900000.*STATES(:,4), 4.00000);
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