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 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 (s)');
    LEGEND_STATES(:,1) = strpad('Z in component Ca (uM)');
    LEGEND_STATES(:,2) = strpad('Y in component Ca (uM)');
    LEGEND_CONSTANTS(:,1) = strpad('v_0 in component Ca (uM_per_s)');
    LEGEND_CONSTANTS(:,2) = strpad('v_1 in component Ca (uM_per_s)');
    LEGEND_ALGEBRAIC(:,1) = strpad('v_2 in component v_2 (uM_per_s)');
    LEGEND_ALGEBRAIC(:,3) = strpad('v_3 in component v_3 (uM_per_s)');
    LEGEND_CONSTANTS(:,3) = strpad('k in component Ca (per_s)');
    LEGEND_CONSTANTS(:,4) = strpad('k_f in component Ca (per_s)');
    LEGEND_CONSTANTS(:,5) = strpad('beta in component Ca (dimensionless)');
    LEGEND_CONSTANTS(:,6) = strpad('V_M2 in component v_2 (uM_per_s)');
    LEGEND_CONSTANTS(:,7) = strpad('K_2 in component v_2 (uM)');
    LEGEND_CONSTANTS(:,8) = strpad('n in component v_2 (dimensionless)');
    LEGEND_CONSTANTS(:,9) = strpad('V_M3 in component v_3 (uM_per_s)');
    LEGEND_CONSTANTS(:,10) = strpad('K_R in component v_3 (uM)');
    LEGEND_CONSTANTS(:,11) = strpad('K_A in component v_3 (uM)');
    LEGEND_CONSTANTS(:,12) = strpad('m in component v_3 (dimensionless)');
    LEGEND_CONSTANTS(:,13) = strpad('p in component v_3 (dimensionless)');
    LEGEND_STATES(:,3) = strpad('W_star in component W_star (dimensionless)');
    LEGEND_CONSTANTS(:,14) = strpad('W_T in component W_star (uM)');
    LEGEND_CONSTANTS(:,15) = strpad('v_P in component W_star (uM_per_s)');
    LEGEND_ALGEBRAIC(:,2) = strpad('v_K in component v_K (uM_per_s)');
    LEGEND_CONSTANTS(:,16) = strpad('K_1 in component W_star (dimensionless)');
    LEGEND_CONSTANTS(:,17) = strpad('K_2 in component W_star (dimensionless)');
    LEGEND_CONSTANTS(:,18) = strpad('V_MK in component v_K (uM_per_s)');
    LEGEND_CONSTANTS(:,19) = strpad('K_a in component v_K (uM)');
    LEGEND_RATES(:,1) = strpad('d/dt Z in component Ca (uM)');
    LEGEND_RATES(:,2) = strpad('d/dt Y in component Ca (uM)');
    LEGEND_RATES(:,3) = strpad('d/dt W_star in component W_star (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) = 0.5;
    STATES(:,2) = 1.75;
    CONSTANTS(:,1) = 1;
    CONSTANTS(:,2) = 7.3;
    CONSTANTS(:,3) = 10;
    CONSTANTS(:,4) = 1;
    CONSTANTS(:,5) = 0.301;
    CONSTANTS(:,6) = 65;
    CONSTANTS(:,7) = 1;
    CONSTANTS(:,8) = 2;
    CONSTANTS(:,9) = 500;
    CONSTANTS(:,10) = 2;
    CONSTANTS(:,11) = 0.9;
    CONSTANTS(:,12) = 2;
    CONSTANTS(:,13) = 4;
    STATES(:,3) = 0;
    CONSTANTS(:,14) = 1;
    CONSTANTS(:,15) = 5;
    CONSTANTS(:,16) = 0.1;
    CONSTANTS(:,17) = 0.1;
    CONSTANTS(:,18) = 40;
    CONSTANTS(:,19) = 2.5;
    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(:,2) =  CONSTANTS(:,18).*(STATES(:,1)./(CONSTANTS(:,19)+STATES(:,1)));
    RATES(:,3) =  (CONSTANTS(:,15)./CONSTANTS(:,14)).*( (ALGEBRAIC(:,2)./CONSTANTS(:,15)).*((1.00000 - STATES(:,3))./(CONSTANTS(:,16)+1.00000+ - STATES(:,3))) - STATES(:,3)./(CONSTANTS(:,17)+STATES(:,3)));
    ALGEBRAIC(:,1) =  CONSTANTS(:,6).*(power(STATES(:,1), CONSTANTS(:,8))./(power(CONSTANTS(:,7), CONSTANTS(:,8))+power(STATES(:,1), CONSTANTS(:,8))));
    ALGEBRAIC(:,3) =  CONSTANTS(:,9).*(power(STATES(:,2), CONSTANTS(:,12))./(power(CONSTANTS(:,10), CONSTANTS(:,12))+power(STATES(:,2), CONSTANTS(:,12)))).*(power(STATES(:,1), CONSTANTS(:,13))./(power(CONSTANTS(:,11), CONSTANTS(:,13))+power(STATES(:,1), CONSTANTS(:,13))));
    RATES(:,1) = CONSTANTS(:,1)+ CONSTANTS(:,2).*CONSTANTS(:,5)+ - ALGEBRAIC(:,1)+ALGEBRAIC(:,3)+ CONSTANTS(:,4).*STATES(:,2)+ - ( CONSTANTS(:,3).*STATES(:,1));
    RATES(:,2) = ALGEBRAIC(:,1)+ - ALGEBRAIC(:,3)+ - ( CONSTANTS(:,4).*STATES(:,2));
   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(:,2) =  CONSTANTS(:,18).*(STATES(:,1)./(CONSTANTS(:,19)+STATES(:,1)));
    ALGEBRAIC(:,1) =  CONSTANTS(:,6).*(power(STATES(:,1), CONSTANTS(:,8))./(power(CONSTANTS(:,7), CONSTANTS(:,8))+power(STATES(:,1), CONSTANTS(:,8))));
    ALGEBRAIC(:,3) =  CONSTANTS(:,9).*(power(STATES(:,2), CONSTANTS(:,12))./(power(CONSTANTS(:,10), CONSTANTS(:,12))+power(STATES(:,2), CONSTANTS(:,12)))).*(power(STATES(:,1), CONSTANTS(:,13))./(power(CONSTANTS(:,11), CONSTANTS(:,13))+power(STATES(:,1), CONSTANTS(:,13))));
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