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 =9;
end
% There are a total of 4 entries in each of the rate and state variable arrays.
% There are a total of 16 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('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_ALGEBRAIC(:,3) = strpad('J_ERch in component J_ERch (micromolar)');
    LEGEND_ALGEBRAIC(:,4) = strpad('J_ERpump in component J_ERpump (micromolar)');
    LEGEND_ALGEBRAIC(:,5) = strpad('J_ERleak in component J_ERleak (micromolar)');
    LEGEND_ALGEBRAIC(:,7) = strpad('J_CaPr in component J_CaPr (micromolar)');
    LEGEND_ALGEBRAIC(:,9) = strpad('J_Pr in component J_Pr (micromolar)');
    LEGEND_CONSTANTS(:,5) = strpad('rho_m in component Ca_cyt (dimensionless)');
    LEGEND_CONSTANTS(:,6) = strpad('beta_m in component Ca_cyt (dimensionless)');
    LEGEND_STATES(:,3) = strpad('Ca_tot in component Ca_tot (micromolar)');
    LEGEND_STATES(:,4) = strpad('Ca_ER in component Ca_ER (micromolar)');
    LEGEND_CONSTANTS(:,7) = strpad('rho_ER in component Ca_ER (dimensionless)');
    LEGEND_CONSTANTS(:,8) = strpad('beta_ER in component Ca_ER (dimensionless)');
    LEGEND_ALGEBRAIC(:,6) = strpad('CaPr in component CaPr (micromolar)');
    LEGEND_CONSTANTS(:,9) = strpad('k_ERch in component J_ERch (micromolar)');
    LEGEND_CONSTANTS(:,10) = strpad('K_ch in component J_ERch (micromolar)');
    LEGEND_CONSTANTS(:,11) = strpad('k_ERpump in component J_ERpump (per_second)');
    LEGEND_CONSTANTS(:,12) = strpad('k_ERleak in component J_ERleak (per_second)');
    LEGEND_CONSTANTS(:,13) = strpad('k_min in component J_CaPr (per_second)');
    LEGEND_CONSTANTS(:,14) = strpad('k_plus in component J_Pr (per_micromolar_per_second)');
    LEGEND_ALGEBRAIC(:,8) = strpad('Pr in component Pr (micromolar)');
    LEGEND_CONSTANTS(:,15) = strpad('Ca_tot in component CaPr (micromolar)');
    LEGEND_CONSTANTS(:,16) = strpad('Pr_tot in component Pr (micromolar)');
    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(:,3) = strpad('d/dt Ca_tot in component Ca_tot (micromolar)');
    LEGEND_RATES(:,4) = strpad('d/dt Ca_ER in component Ca_ER (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;
    CONSTANTS(:,5) = 0.01;
    CONSTANTS(:,6) = 0.025;
    STATES(:,3) = 0.01;
    STATES(:,4) = 20;
    CONSTANTS(:,7) = 0.01;
    CONSTANTS(:,8) = 0.0025;
    CONSTANTS(:,9) = 0.001;
    CONSTANTS(:,10) = 5;
    CONSTANTS(:,11) = 20;
    CONSTANTS(:,12) = 0.05;
    CONSTANTS(:,13) = 0.01;
    CONSTANTS(:,14) = 0.1;
    CONSTANTS(:,15) = 90;
    CONSTANTS(:,16) = 120;
    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(:,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);
    ALGEBRAIC(:,3) =  (( CONSTANTS(:,9).*power(STATES(:,2), 2.00000))./(power(CONSTANTS(:,10), 2.00000)+power(STATES(:,2), 2.00000))).*(STATES(:,4) - STATES(:,2));
    ALGEBRAIC(:,4) =  CONSTANTS(:,11).*STATES(:,2);
    ALGEBRAIC(:,5) =  CONSTANTS(:,12).*(STATES(:,4) - STATES(:,2));
    RATES(:,4) =  (CONSTANTS(:,8)./CONSTANTS(:,7)).*((ALGEBRAIC(:,4) - ALGEBRAIC(:,5)) - ALGEBRAIC(:,3)).*1.00000;
    ALGEBRAIC(:,6) = CONSTANTS(:,15) - (STATES(:,2)+ (CONSTANTS(:,7)./CONSTANTS(:,8)).*STATES(:,4));
    RATES(:,3) = STATES(:,2)+ (CONSTANTS(:,7)./CONSTANTS(:,8)).*STATES(:,4)+ (CONSTANTS(:,5)./CONSTANTS(:,6)).*STATES(:,1)+ALGEBRAIC(:,6);
    ALGEBRAIC(:,7) =  CONSTANTS(:,13).*ALGEBRAIC(:,6);
    ALGEBRAIC(:,8) = CONSTANTS(:,16) - ALGEBRAIC(:,6);
    ALGEBRAIC(:,9) =  CONSTANTS(:,14).*STATES(:,2).*ALGEBRAIC(:,8);
    RATES(:,2) =  ((((ALGEBRAIC(:,3) - ALGEBRAIC(:,4))+ALGEBRAIC(:,5)+ALGEBRAIC(:,7)) - ALGEBRAIC(:,9))+ (CONSTANTS(:,5)./CONSTANTS(:,6)).*(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;
    ALGEBRAIC(:,3) =  (( CONSTANTS(:,9).*power(STATES(:,2), 2.00000))./(power(CONSTANTS(:,10), 2.00000)+power(STATES(:,2), 2.00000))).*(STATES(:,4) - STATES(:,2));
    ALGEBRAIC(:,4) =  CONSTANTS(:,11).*STATES(:,2);
    ALGEBRAIC(:,5) =  CONSTANTS(:,12).*(STATES(:,4) - STATES(:,2));
    ALGEBRAIC(:,6) = CONSTANTS(:,15) - (STATES(:,2)+ (CONSTANTS(:,7)./CONSTANTS(:,8)).*STATES(:,4));
    ALGEBRAIC(:,7) =  CONSTANTS(:,13).*ALGEBRAIC(:,6);
    ALGEBRAIC(:,8) = CONSTANTS(:,16) - ALGEBRAIC(:,6);
    ALGEBRAIC(:,9) =  CONSTANTS(:,14).*STATES(:,2).*ALGEBRAIC(:,8);
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