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 5 entries in each of the rate and state variable arrays.
% There are a total of 12 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('P in component P (picomolar)');
    LEGEND_CONSTANTS(:,1) = strpad('k1 in component model_parameters (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,2) = strpad('k1_ in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,3) = strpad('k2 in component model_parameters (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,4) = strpad('k2_ in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,5) = strpad('kcl in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,12) = strpad('D in component model_parameters (flux)');
    LEGEND_STATES(:,2) = strpad('Ca in component Ca (picomolar)');
    LEGEND_STATES(:,3) = strpad('Ci in component Ci (picomolar)');
    LEGEND_STATES(:,4) = strpad('Ra in component Ra (picomolar)');
    LEGEND_STATES(:,5) = strpad('Ri in component Ri (picomolar)');
    LEGEND_CONSTANTS(:,6) = strpad('k3 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,7) = strpad('k3_ in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,8) = strpad('k4 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,9) = strpad('k4_ in component model_parameters (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,1) = strpad('rho in component rho (dimensionless)');
    LEGEND_CONSTANTS(:,10) = strpad('De in component model_parameters (flux)');
    LEGEND_CONSTANTS(:,11) = strpad('Dd in component model_parameters (flux)');
    LEGEND_RATES(:,1) = strpad('d/dt P in component P (picomolar)');
    LEGEND_RATES(:,4) = strpad('d/dt Ra in component Ra (picomolar)');
    LEGEND_RATES(:,5) = strpad('d/dt Ri in component Ri (picomolar)');
    LEGEND_RATES(:,2) = strpad('d/dt Ca in component Ca (picomolar)');
    LEGEND_RATES(:,3) = strpad('d/dt Ci in component Ci (picomolar)');
    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) = 3;
    CONSTANTS(:,1) = 1e-6;
    CONSTANTS(:,2) = 1e-3;
    CONSTANTS(:,3) = 1e-7;
    CONSTANTS(:,4) = 1e-3;
    CONSTANTS(:,5) = 5e-3;
    STATES(:,2) = 4e-4;
    STATES(:,3) = 0.05;
    STATES(:,4) = 16.9;
    STATES(:,5) = 1.7;
    CONSTANTS(:,6) = 1e-3;
    CONSTANTS(:,7) = 1e-4;
    CONSTANTS(:,8) = 2e-3;
    CONSTANTS(:,9) = 0.4;
    CONSTANTS(:,10) = 0;
    CONSTANTS(:,11) = 0.015;
    CONSTANTS(:,12) = CONSTANTS(:,10)+CONSTANTS(:,11);
    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).*STATES(:,2)+ CONSTANTS(:,4).*STATES(:,3)+CONSTANTS(:,12)) - ( CONSTANTS(:,1).*STATES(:,4).*STATES(:,1)+ CONSTANTS(:,3).*STATES(:,5).*STATES(:,1)+ CONSTANTS(:,5).*STATES(:,1));
    RATES(:,4) = ( CONSTANTS(:,2).*STATES(:,2)+ CONSTANTS(:,6).*STATES(:,5)) - ( CONSTANTS(:,1).*STATES(:,4).*STATES(:,1)+ CONSTANTS(:,7).*STATES(:,4));
    RATES(:,5) = ( CONSTANTS(:,4).*STATES(:,3)+ CONSTANTS(:,7).*STATES(:,4)) - ( CONSTANTS(:,3).*STATES(:,5).*STATES(:,1)+ CONSTANTS(:,6).*STATES(:,5));
    RATES(:,2) = ( CONSTANTS(:,1).*STATES(:,4).*STATES(:,1)+ CONSTANTS(:,8).*STATES(:,3)) - ( CONSTANTS(:,2).*STATES(:,2)+ CONSTANTS(:,9).*STATES(:,2));
    RATES(:,3) = ( CONSTANTS(:,3).*STATES(:,5).*STATES(:,1)+ CONSTANTS(:,9).*STATES(:,2)) - ( CONSTANTS(:,4).*STATES(:,3)+ CONSTANTS(:,8).*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) = (STATES(:,4)+STATES(:,2))./(STATES(:,4)+STATES(:,2)+STATES(:,5)+STATES(:,3));
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