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 =2;
end
% There are a total of 8 entries in each of the rate and state variable arrays.
% There are a total of 14 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_STATES(:,1) = strpad('Ca_m in component Ca_m (micromolar)');
    LEGEND_ALGEBRAIC(:,1) = strpad('J_min in component J_min (micromolar)');
    LEGEND_ALGEBRAIC(:,2) = strpad('J_mout in component J_mout (micromolar)');
    LEGEND_CONSTANTS(:,1) = strpad('k_min in component J_min (micromolar)');
    LEGEND_STATES(:,2) = strpad('Ca_cyt in component Ca_cyt (micromolar)');
    LEGEND_CONSTANTS(:,2) = strpad('K_m in component J_min (micromolar)');
    LEGEND_CONSTANTS(:,3) = strpad('n in component J_min (micromolar)');
    LEGEND_CONSTANTS(:,4) = strpad('k_mout in component J_mout (micromolar)');
    LEGEND_STATES(:,3) = strpad('J_ERch in component J_ERch (micromolar)');
    LEGEND_STATES(:,4) = strpad('J_ERpump in component J_ERpump (micromolar)');
    LEGEND_STATES(:,5) = strpad('J_ERleak in component J_ERleak (micromolar)');
    LEGEND_STATES(:,6) = strpad('J_in in component J_in (micromolar)');
    LEGEND_STATES(:,7) = strpad('J_out in component J_out (micromolar)');
    LEGEND_STATES(:,8) = strpad('Ca_ER in component Ca_ER (micromolar)');
    LEGEND_CONSTANTS(:,5) = strpad('beta in component J_ERch (dimensionless)');
    LEGEND_CONSTANTS(:,6) = strpad('k_0ch in component J_ERch (micromolar_per_minute)');
    LEGEND_CONSTANTS(:,7) = strpad('K_chcyt in component J_ERch (micromolar)');
    LEGEND_CONSTANTS(:,8) = strpad('K_chER in component J_ERch (micromolar)');
    LEGEND_CONSTANTS(:,9) = strpad('K_ERpump in component J_ERpump (micromolar)');
    LEGEND_CONSTANTS(:,10) = strpad('K_pump in component J_ERpump (micromolar)');
    LEGEND_CONSTANTS(:,11) = strpad('K_ERleak in component J_ERleak (per_minute)');
    LEGEND_CONSTANTS(:,12) = strpad('K_0in in component J_in (micromolar_per_minute)');
    LEGEND_CONSTANTS(:,13) = strpad('K_out in component J_out (per_minute)');
    LEGEND_RATES(:,1) = strpad('d/dt Ca_m in component Ca_m (micromolar)');
    LEGEND_RATES(:,2) = strpad('d/dt Ca_cyt in component Ca_cyt (micromolar)');
    LEGEND_RATES(:,8) = strpad('d/dt Ca_ER in component Ca_ER (micromolar)');
    LEGEND_RATES(:,3) = strpad('d/dt J_ERch in component J_ERch (micromolar)');
    LEGEND_RATES(:,4) = strpad('d/dt J_ERpump in component J_ERpump (micromolar)');
    LEGEND_RATES(:,5) = strpad('d/dt J_ERleak in component J_ERleak (micromolar)');
    LEGEND_RATES(:,6) = strpad('d/dt J_in in component J_in (micromolar)');
    LEGEND_RATES(:,7) = strpad('d/dt J_out in component J_out (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 = [];
    STATES(:,1) = 0.1;
    CONSTANTS(:,1) = 330;
    STATES(:,2) = 0.01;
    CONSTANTS(:,2) = 1.6;
    CONSTANTS(:,3) = 8;
    CONSTANTS(:,4) = 0.5;
    STATES(:,3) = 0.1;
    STATES(:,4) = 0.1;
    STATES(:,5) = 0.1;
    STATES(:,6) = 0.1;
    STATES(:,7) = 0.1;
    STATES(:,8) = 20;
    CONSTANTS(:,5) = 1.7;
    CONSTANTS(:,6) = 325;
    CONSTANTS(:,7) = 0.45;
    CONSTANTS(:,8) = 1;
    CONSTANTS(:,9) = 25;
    CONSTANTS(:,10) = 0.5;
    CONSTANTS(:,11) = 1;
    CONSTANTS(:,12) = 1.7;
    CONSTANTS(:,13) = 10;
    CONSTANTS(:,13) =  CONSTANTS(:,12).*1.00000;
    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(:,6) = CONSTANTS(:,13);
    RATES(:,8) =  ((STATES(:,4) - STATES(:,5)) - STATES(:,3)).*1.00000;
    RATES(:,3) =  CONSTANTS(:,5).*CONSTANTS(:,6).*( (power(STATES(:,2), 4.00000)./(power(CONSTANTS(:,7), 4.00000)+power(STATES(:,2), 4.00000))).*(power(STATES(:,8), 2.00000)./(power(CONSTANTS(:,8), 2.00000)+power(STATES(:,8), 2.00000)))).*1.00000;
    RATES(:,4) =  CONSTANTS(:,9).*(power(STATES(:,2), 2.00000)./(power(CONSTANTS(:,10), 2.00000)+power(STATES(:,2), 2.00000)));
    RATES(:,5) =  (( CONSTANTS(:,11).*STATES(:,8))./1.00000).*1.00000;
    RATES(:,7) =  (( CONSTANTS(:,13).*STATES(:,2))./1.00000).*1.00000;
    ALGEBRAIC(:,1) = ( CONSTANTS(:,1).*power(STATES(:,2), CONSTANTS(:,3)))./(power(CONSTANTS(:,2), CONSTANTS(:,3))+power(STATES(:,2), CONSTANTS(:,3)));
    ALGEBRAIC(:,2) = ( CONSTANTS(:,4).*STATES(:,1))./1.00000;
    RATES(:,1) = ALGEBRAIC(:,1) - ALGEBRAIC(:,2);
    RATES(:,2) =  (((((STATES(:,3) - STATES(:,4))+STATES(:,5)+STATES(:,6)) - STATES(:,7))+ALGEBRAIC(:,2)) - ALGEBRAIC(:,1)).*1.00000;
   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) = ( CONSTANTS(:,1).*power(STATES(:,2), CONSTANTS(:,3)))./(power(CONSTANTS(:,2), CONSTANTS(:,3))+power(STATES(:,2), CONSTANTS(:,3)));
    ALGEBRAIC(:,2) = ( CONSTANTS(:,4).*STATES(:,1))./1.00000;
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