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 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 (minute)');
    LEGEND_CONSTANTS(:,1) = strpad('V_0 in component Vin (micromolar_per_minute)');
    LEGEND_CONSTANTS(:,2) = strpad('V_1 in component Vin (micromolar_per_minute)');
    LEGEND_CONSTANTS(:,3) = strpad('beta in component Vin (dimensionless)');
    LEGEND_CONSTANTS(:,20) = strpad('V_in in component Vin (micromolar_per_minute)');
    LEGEND_CONSTANTS(:,4) = strpad('V_M2 in component V2 (micromolar_per_minute)');
    LEGEND_STATES(:,1) = strpad('Z in component cytosol (micromolar)');
    LEGEND_CONSTANTS(:,5) = strpad('K_2 in component V2 (micromolar)');
    LEGEND_ALGEBRAIC(:,1) = strpad('V_2 in component V2 (micromolar_per_minute)');
    LEGEND_CONSTANTS(:,6) = strpad('V_M3 in component V3 (micromolar_per_minute)');
    LEGEND_CONSTANTS(:,7) = strpad('K_Z in component V3 (micromolar)');
    LEGEND_CONSTANTS(:,8) = strpad('K_A in component V3 (micromolar)');
    LEGEND_CONSTANTS(:,9) = strpad('K_Y in component V3 (micromolar)');
    LEGEND_CONSTANTS(:,10) = strpad('m in component V3 (dimensionless)');
    LEGEND_STATES(:,2) = strpad('Y in component internal_pool (micromolar)');
    LEGEND_STATES(:,3) = strpad('A in component InsP3_conc (micromolar)');
    LEGEND_ALGEBRAIC(:,3) = strpad('V_3 in component V3 (micromolar_per_minute)');
    LEGEND_CONSTANTS(:,11) = strpad('V_M5 in component V5 (micromolar_per_minute)');
    LEGEND_CONSTANTS(:,12) = strpad('K_5 in component V5 (micromolar)');
    LEGEND_CONSTANTS(:,13) = strpad('K_d in component V5 (micromolar)');
    LEGEND_CONSTANTS(:,14) = strpad('p in component V5 (dimensionless)');
    LEGEND_CONSTANTS(:,15) = strpad('n in component V5 (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('V_5 in component V5 (micromolar_per_minute)');
    LEGEND_CONSTANTS(:,16) = strpad('k in component cytosol (per_minute)');
    LEGEND_CONSTANTS(:,17) = strpad('k_f in component cytosol (per_minute)');
    LEGEND_CONSTANTS(:,18) = strpad('epsilon in component InsP3_conc (per_minute)');
    LEGEND_CONSTANTS(:,19) = strpad('V_4 in component InsP3_conc (micromolar_per_minute)');
    LEGEND_RATES(:,1) = strpad('d/dt Z in component cytosol (micromolar)');
    LEGEND_RATES(:,2) = strpad('d/dt Y in component internal_pool (micromolar)');
    LEGEND_RATES(:,3) = strpad('d/dt A in component InsP3_conc (micromolar)');
    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) = 2;
    CONSTANTS(:,2) = 2;
    CONSTANTS(:,3) = 0.6;
    CONSTANTS(:,4) = 6;
    STATES(:,1) = 0.15;
    CONSTANTS(:,5) = 0.1;
    CONSTANTS(:,6) = 20;
    CONSTANTS(:,7) = 0.5;
    CONSTANTS(:,8) = 0.2;
    CONSTANTS(:,9) = 0.2;
    CONSTANTS(:,10) = 2;
    STATES(:,2) = 1;
    STATES(:,3) = 0.42;
    CONSTANTS(:,11) = 5;
    CONSTANTS(:,12) = 1;
    CONSTANTS(:,13) = 0.4;
    CONSTANTS(:,14) = 2;
    CONSTANTS(:,15) = 4;
    CONSTANTS(:,16) = 10;
    CONSTANTS(:,17) = 1;
    CONSTANTS(:,18) = 0.1;
    CONSTANTS(:,19) = 2;
    CONSTANTS(:,20) = CONSTANTS(:,1)+ CONSTANTS(:,2).*CONSTANTS(:,3);
    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(:,11).*power(STATES(:,3), CONSTANTS(:,14)))./(power(CONSTANTS(:,12), CONSTANTS(:,14))+power(STATES(:,3), CONSTANTS(:,14)))).*power(STATES(:,1), CONSTANTS(:,15)))./(power(CONSTANTS(:,13), CONSTANTS(:,15))+power(STATES(:,1), CONSTANTS(:,15)));
    RATES(:,3) = ( CONSTANTS(:,3).*CONSTANTS(:,19) - ALGEBRAIC(:,2)) -  CONSTANTS(:,18).*STATES(:,3);
    ALGEBRAIC(:,1) = ( CONSTANTS(:,4).*power(STATES(:,1), 2.00000))./(power(CONSTANTS(:,5), 2.00000)+power(STATES(:,1), 2.00000));
    ALGEBRAIC(:,3) = ( (( (( CONSTANTS(:,6).*power(STATES(:,1), CONSTANTS(:,10)))./(power(CONSTANTS(:,7), CONSTANTS(:,10))+power(STATES(:,1), CONSTANTS(:,10)))).*power(STATES(:,2), 2.00000))./(power(CONSTANTS(:,9), 2.00000)+power(STATES(:,2), 2.00000))).*power(STATES(:,3), 4.00000))./(power(CONSTANTS(:,8), 4.00000)+power(STATES(:,3), 4.00000));
    RATES(:,1) = ((CONSTANTS(:,20) - ALGEBRAIC(:,1))+ALGEBRAIC(:,3)+ CONSTANTS(:,17).*STATES(:,2)) -  CONSTANTS(:,16).*STATES(:,1);
    RATES(:,2) = (ALGEBRAIC(:,1) - ALGEBRAIC(:,3)) -  CONSTANTS(:,17).*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(:,11).*power(STATES(:,3), CONSTANTS(:,14)))./(power(CONSTANTS(:,12), CONSTANTS(:,14))+power(STATES(:,3), CONSTANTS(:,14)))).*power(STATES(:,1), CONSTANTS(:,15)))./(power(CONSTANTS(:,13), CONSTANTS(:,15))+power(STATES(:,1), CONSTANTS(:,15)));
    ALGEBRAIC(:,1) = ( CONSTANTS(:,4).*power(STATES(:,1), 2.00000))./(power(CONSTANTS(:,5), 2.00000)+power(STATES(:,1), 2.00000));
    ALGEBRAIC(:,3) = ( (( (( CONSTANTS(:,6).*power(STATES(:,1), CONSTANTS(:,10)))./(power(CONSTANTS(:,7), CONSTANTS(:,10))+power(STATES(:,1), CONSTANTS(:,10)))).*power(STATES(:,2), 2.00000))./(power(CONSTANTS(:,9), 2.00000)+power(STATES(:,2), 2.00000))).*power(STATES(:,3), 4.00000))./(power(CONSTANTS(:,8), 4.00000)+power(STATES(:,3), 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