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 =4;
end
% There are a total of 2 entries in each of the rate and state variable arrays.
% There are a total of 13 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_ALGEBRAIC(:,1) = strpad('B in component B (micromolar)');
    LEGEND_CONSTANTS(:,1) = strpad('F in component B (micromolar)');
    LEGEND_CONSTANTS(:,2) = strpad('n2 in component B (dimensionless)');
    LEGEND_CONSTANTS(:,3) = strpad('K2 in component B (per_micromolar)');
    LEGEND_STATES(:,1) = strpad('Ca in component Ca (micromolar)');
    LEGEND_ALGEBRAIC(:,4) = strpad('R in component R (flux)');
    LEGEND_CONSTANTS(:,4) = strpad('Vmax in component R (flux)');
    LEGEND_CONSTANTS(:,5) = strpad('Km in component R (micromolar)');
    LEGEND_ALGEBRAIC(:,3) = strpad('fu in component R (dimensionless)');
    LEGEND_CONSTANTS(:,13) = strpad('ISF in component R (dimensionless)');
    LEGEND_CONSTANTS(:,6) = strpad('age in component R (dimensionless)');
    LEGEND_STATES(:,2) = strpad('C in component C (micromolar)');
    LEGEND_CONSTANTS(:,7) = strpad('Va in component Ca (ml)');
    LEGEND_CONSTANTS(:,8) = strpad('Vv in component Ca (ml)');
    LEGEND_CONSTANTS(:,9) = strpad('Qc in component model_constants (flow)');
    LEGEND_ALGEBRAIC(:,2) = strpad('Cv in component Cv (micromolar)');
    LEGEND_CONSTANTS(:,10) = strpad('Q in component model_constants (flow)');
    LEGEND_CONSTANTS(:,11) = strpad('P in component model_constants (dimensionless)');
    LEGEND_CONSTANTS(:,12) = strpad('V in component C (ml)');
    LEGEND_RATES(:,1) = strpad('d/dt Ca in component Ca (micromolar)');
    LEGEND_RATES(:,2) = strpad('d/dt C in component C (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) = 0.48;
    CONSTANTS(:,2) = 1;
    CONSTANTS(:,3) = 0.8532;
    STATES(:,1) = 6.6685;
    CONSTANTS(:,4) = 9.433e-3;
    CONSTANTS(:,5) = 198;
    CONSTANTS(:,6) = 5;
    STATES(:,2) = 0;
    CONSTANTS(:,7) = 2148;
    CONSTANTS(:,8) = 3431;
    CONSTANTS(:,9) = 6445.65;
    CONSTANTS(:,10) = 1221.34;
    CONSTANTS(:,11) = 15.61;
    CONSTANTS(:,12) = 1454;
    CONSTANTS(:,13) =  - 8.32120+ 2.04010.*CONSTANTS(:,6)+ 4.19620.*arbitrary_log( CONSTANTS(:,6).*365.000, 10);
    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(:,10).*STATES(:,2))./CONSTANTS(:,11))./CONSTANTS(:,9);
    RATES(:,1) = ( CONSTANTS(:,9).*(ALGEBRAIC(:,2) - STATES(:,1)))./(CONSTANTS(:,7)+CONSTANTS(:,8));
    ALGEBRAIC(:,1) = ( CONSTANTS(:,1).*CONSTANTS(:,2).*CONSTANTS(:,3).*STATES(:,1))./(1.00000+ CONSTANTS(:,3).*CONSTANTS(:,1));
    ALGEBRAIC(:,3) = CONSTANTS(:,1)./(CONSTANTS(:,1)+ALGEBRAIC(:,1));
    ALGEBRAIC(:,4) = ( CONSTANTS(:,13).*CONSTANTS(:,4).*ALGEBRAIC(:,3).*STATES(:,2))./(CONSTANTS(:,5)+ ALGEBRAIC(:,3).*STATES(:,2));
    RATES(:,2) = ( CONSTANTS(:,10).*(STATES(:,1) - STATES(:,2)./CONSTANTS(:,11)) -  ALGEBRAIC(:,4).*1.00000)./CONSTANTS(:,12);
   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(:,10).*STATES(:,2))./CONSTANTS(:,11))./CONSTANTS(:,9);
    ALGEBRAIC(:,1) = ( CONSTANTS(:,1).*CONSTANTS(:,2).*CONSTANTS(:,3).*STATES(:,1))./(1.00000+ CONSTANTS(:,3).*CONSTANTS(:,1));
    ALGEBRAIC(:,3) = CONSTANTS(:,1)./(CONSTANTS(:,1)+ALGEBRAIC(:,1));
    ALGEBRAIC(:,4) = ( CONSTANTS(:,13).*CONSTANTS(:,4).*ALGEBRAIC(:,3).*STATES(:,2))./(CONSTANTS(:,5)+ ALGEBRAIC(:,3).*STATES(:,2));
end

% Compute a logarithm to any base" +
function x = arbitrary_log(a, base)
    x = log(a) ./ log(base);
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