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 1 entries in each of the rate and state variable arrays.
% There are a total of 19 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 (minute)');
    LEGEND_CONSTANTS(:,16) = strpad('C in component C (nanomolar)');
    LEGEND_CONSTANTS(:,1) = strpad('kf1 in component model_parameters (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,13) = strpad('kr1 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,14) = strpad('k_x1 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,2) = strpad('kt in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,3) = strpad('ke in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,4) = strpad('L in component model_parameters (nanomolar)');
    LEGEND_CONSTANTS(:,17) = strpad('R in component R (nanomolar)');
    LEGEND_CONSTANTS(:,15) = strpad('K_X in component D (per_nanomolar)');
    LEGEND_CONSTANTS(:,18) = strpad('D in component D (nanomolar)');
    LEGEND_CONSTANTS(:,5) = strpad('kx2 in component model_parameters (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,6) = strpad('k_x2 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,7) = strpad('R_initial in component R (nanomolar)');
    LEGEND_CONSTANTS(:,8) = strpad('krec in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,9) = strpad('kdeg in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,1) = strpad('Ri in component Ri (nanomolar)');
    LEGEND_CONSTANTS(:,19) = strpad('signal in component signal (dimensionless)');
    LEGEND_CONSTANTS(:,10) = strpad('kappaE in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,11) = strpad('Vs in component model_parameters (flux)');
    LEGEND_CONSTANTS(:,12) = strpad('KD in component model_parameters (nanomolar)');
    LEGEND_RATES(:,1) = strpad('d/dt Ri in component Ri (nanomolar)');
    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 = [];
    CONSTANTS(:,1) = 0.1;
    CONSTANTS(:,2) = 0.005;
    CONSTANTS(:,3) = 0.10;
    CONSTANTS(:,4) = 0.01;
    CONSTANTS(:,5) = 4.83;
    CONSTANTS(:,6) = 0.016;
    CONSTANTS(:,7) = 2000.0;
    CONSTANTS(:,8) = 0.0;
    CONSTANTS(:,9) = 0.05;
    STATES(:,1) = 200.0;
    CONSTANTS(:,10) = 0.20;
    CONSTANTS(:,11) = 10.0;
    CONSTANTS(:,12) = 1.0;
    CONSTANTS(:,13) =  CONSTANTS(:,12).*CONSTANTS(:,1);
    CONSTANTS(:,14) =  0.0100000.*CONSTANTS(:,13);
    CONSTANTS(:,15) = CONSTANTS(:,5)./(CONSTANTS(:,6)+CONSTANTS(:,14)+CONSTANTS(:,3));
    [CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS, STATES, ALGEBRAIC);
    CONSTANTS(:,19) = (( 2.00000.*CONSTANTS(:,18))./200.000)./(CONSTANTS(:,10)+( 2.00000.*CONSTANTS(:,18))./200.000);
    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(:,2).*(CONSTANTS(:,17)+CONSTANTS(:,16)) -  (CONSTANTS(:,8)+CONSTANTS(:,9)).*STATES(:,1);
   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

% Functions required for solving differential algebraic equation
function [CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS_IN, STATES_IN, ALGEBRAIC_IN)
    ALGEBRAIC = ALGEBRAIC_IN;
    CONSTANTS = CONSTANTS_IN;
    STATES = STATES_IN;
    global initialGuess_0;
    if (length(initialGuess_0) ~= 3), initialGuess_0 = [0.1,0.1,0.1];, end
    options = optimset('Display', 'off', 'TolX', 1E-6);
    if length(VOI) == 1
        residualfn = @(algebraicCandidate)residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES);
        soln = fsolve(residualfn, initialGuess_0, options);
        initialGuess_0 = soln;
        CONSTANTS(:,16) = soln(1);
        CONSTANTS(:,17) = soln(2);
        CONSTANTS(:,18) = soln(3);
    else
        SET_CONSTANTS(:,16) = logical(1);
        SET_CONSTANTS(:,17) = logical(1);
        SET_CONSTANTS(:,18) = logical(1);
        for i=1:length(VOI)
            residualfn = @(algebraicCandidate)residualSN_0(algebraicCandidate, ALGEBRAIC(i,:), VOI(i), CONSTANTS, STATES(i,:));
            soln = fsolve(residualfn, initialGuess_0, options);
            initialGuess_0 = soln;
            TEMP_CONSTANTS(:,16) = soln(1);
            TEMP_CONSTANTS(:,17) = soln(2);
            TEMP_CONSTANTS(:,18) = soln(3);
            ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
        end
    end
end

function resid = residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
    CONSTANTS(:,16) = algebraicCandidate(1);
    CONSTANTS(:,17) = algebraicCandidate(2);
    CONSTANTS(:,18) = algebraicCandidate(3);
    resid(1) = CONSTANTS(:,16) - ( CONSTANTS(:,1).*CONSTANTS(:,4).*CONSTANTS(:,17))./(CONSTANTS(:,13)+CONSTANTS(:,2)+ (CONSTANTS(:,14)+CONSTANTS(:,3)).*CONSTANTS(:,15).*CONSTANTS(:,17));
    resid(2) = CONSTANTS(:,18) -  CONSTANTS(:,15).*CONSTANTS(:,17).*CONSTANTS(:,16);
    resid(3) = CONSTANTS(:,17) - (CONSTANTS(:,7) - (CONSTANTS(:,16)+ 2.00000.*(CONSTANTS(:,3)./CONSTANTS(:,2)).*(1.00000+CONSTANTS(:,8)./CONSTANTS(:,9)).*CONSTANTS(:,18)));
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