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 =17;
end
% There are a total of 13 entries in each of the rate and state variable arrays.
% There are a total of 38 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('t in component all (s)');
    LEGEND_STATES(:,1) = strpad('Ca in component all (uM)');
    LEGEND_ALGEBRAIC(:,11) = strpad('L in component all (uM)');
    LEGEND_CONSTANTS(:,1) = strpad('Ls in component all (uM)');
    LEGEND_CONSTANTS(:,2) = strpad('ts in component all (s)');
    LEGEND_STATES(:,2) = strpad('Gd in component all (per_um2)');
    LEGEND_STATES(:,3) = strpad('Gt in component all (per_um2)');
    LEGEND_STATES(:,4) = strpad('R in component all (per_um2)');
    LEGEND_STATES(:,5) = strpad('Rl in component all (per_um2)');
    LEGEND_STATES(:,6) = strpad('Rg in component all (per_um2)');
    LEGEND_STATES(:,7) = strpad('Rlg in component all (per_um2)');
    LEGEND_STATES(:,8) = strpad('Rlgp in component all (per_um2)');
    LEGEND_STATES(:,9) = strpad('IP3 in component all (uM)');
    LEGEND_CONSTANTS(:,3) = strpad('PIP2 in component all (per_um2)');
    LEGEND_STATES(:,10) = strpad('Pc in component all (per_um2)');
    LEGEND_STATES(:,11) = strpad('Pcg in component all (per_um2)');
    LEGEND_STATES(:,12) = strpad('P in component all (per_um2)');
    LEGEND_STATES(:,13) = strpad('Pg in component all (per_um2)');
    LEGEND_ALGEBRAIC(:,12) = strpad('J1 in component all (per_um2_per_s)');
    LEGEND_CONSTANTS(:,4) = strpad('kf1 in component all (per_uM_per_s)');
    LEGEND_CONSTANTS(:,32) = strpad('kr1 in component all (per_s)');
    LEGEND_CONSTANTS(:,5) = strpad('Kd1 in component all (uM)');
    LEGEND_ALGEBRAIC(:,13) = strpad('J2 in component all (per_um2_per_s)');
    LEGEND_CONSTANTS(:,6) = strpad('kf2 in component all (um2_per_s)');
    LEGEND_CONSTANTS(:,33) = strpad('kr2 in component all (per_s)');
    LEGEND_CONSTANTS(:,7) = strpad('Kd2 in component all (per_um2)');
    LEGEND_ALGEBRAIC(:,14) = strpad('J3 in component all (per_um2_per_s)');
    LEGEND_CONSTANTS(:,8) = strpad('kf3 in component all (um2_per_s)');
    LEGEND_CONSTANTS(:,9) = strpad('kr3 in component all (per_s)');
    LEGEND_ALGEBRAIC(:,15) = strpad('J4 in component all (per_um2_per_s)');
    LEGEND_CONSTANTS(:,10) = strpad('kf4 in component all (per_uM_per_s)');
    LEGEND_CONSTANTS(:,34) = strpad('kr4 in component all (per_s)');
    LEGEND_CONSTANTS(:,11) = strpad('Kd4 in component all (uM)');
    LEGEND_ALGEBRAIC(:,16) = strpad('J5 in component all (per_um2_per_s)');
    LEGEND_CONSTANTS(:,12) = strpad('kf5 in component all (per_s)');
    LEGEND_ALGEBRAIC(:,17) = strpad('J6 in component all (per_um2_per_s)');
    LEGEND_CONSTANTS(:,13) = strpad('kf6 in component all (per_s)');
    LEGEND_ALGEBRAIC(:,10) = strpad('J7 in component all (per_um2_per_s)');
    LEGEND_CONSTANTS(:,14) = strpad('kf7 in component all (per_s)');
    LEGEND_ALGEBRAIC(:,8) = strpad('J8 in component all (per_um2_per_s)');
    LEGEND_CONSTANTS(:,15) = strpad('kf8 in component all (per_uM_per_s)');
    LEGEND_CONSTANTS(:,16) = strpad('kr8 in component all (per_s)');
    LEGEND_ALGEBRAIC(:,9) = strpad('J9 in component all (per_um2_per_s)');
    LEGEND_CONSTANTS(:,17) = strpad('kf9 in component all (um2_per_s)');
    LEGEND_CONSTANTS(:,18) = strpad('kr9 in component all (per_s)');
    LEGEND_ALGEBRAIC(:,7) = strpad('J10 in component all (per_um2_per_s)');
    LEGEND_CONSTANTS(:,19) = strpad('kf10 in component all (um2_per_s)');
    LEGEND_CONSTANTS(:,20) = strpad('kr10 in component all (per_s)');
    LEGEND_ALGEBRAIC(:,5) = strpad('J11 in component all (per_um2_per_s)');
    LEGEND_CONSTANTS(:,21) = strpad('kf11 in component all (per_uM_per_s)');
    LEGEND_CONSTANTS(:,35) = strpad('kr11 in component all (per_s)');
    LEGEND_CONSTANTS(:,22) = strpad('Kd11 in component all (uM)');
    LEGEND_ALGEBRAIC(:,3) = strpad('J12 in component all (per_um2_per_s)');
    LEGEND_CONSTANTS(:,23) = strpad('kf12 in component all (per_s)');
    LEGEND_ALGEBRAIC(:,1) = strpad('J13 in component all (per_um2_per_s)');
    LEGEND_CONSTANTS(:,24) = strpad('kf13 in component all (per_s)');
    LEGEND_ALGEBRAIC(:,4) = strpad('J14 in component all (per_um2_per_s)');
    LEGEND_CONSTANTS(:,25) = strpad('kf14 in component all (per_s)');
    LEGEND_CONSTANTS(:,26) = strpad('Km14 in component all (uM)');
    LEGEND_ALGEBRAIC(:,6) = strpad('J15 in component all (per_um2_per_s)');
    LEGEND_CONSTANTS(:,27) = strpad('kf15 in component all (per_s)');
    LEGEND_CONSTANTS(:,28) = strpad('Km15 in component all (uM)');
    LEGEND_ALGEBRAIC(:,2) = strpad('J16 in component all (uM_per_s)');
    LEGEND_CONSTANTS(:,29) = strpad('kf16 in component all (per_s)');
    LEGEND_CONSTANTS(:,38) = strpad('Cpc in component all (uM_um2)');
    LEGEND_CONSTANTS(:,36) = strpad('Cc in component all (uM)');
    LEGEND_CONSTANTS(:,37) = strpad('Cp in component all (per_um2)');
    LEGEND_CONSTANTS(:,30) = strpad('Vc in component all (um3)');
    LEGEND_CONSTANTS(:,31) = strpad('Rpc in component all (per_um)');
    LEGEND_RATES(:,12) = strpad('d/dt P in component all (per_um2)');
    LEGEND_RATES(:,13) = strpad('d/dt Pg in component all (per_um2)');
    LEGEND_RATES(:,10) = strpad('d/dt Pc in component all (per_um2)');
    LEGEND_RATES(:,11) = strpad('d/dt Pcg in component all (per_um2)');
    LEGEND_RATES(:,9) = strpad('d/dt IP3 in component all (uM)');
    LEGEND_RATES(:,2) = strpad('d/dt Gd in component all (per_um2)');
    LEGEND_RATES(:,3) = strpad('d/dt Gt in component all (per_um2)');
    LEGEND_RATES(:,1) = strpad('d/dt Ca in component all (uM)');
    LEGEND_RATES(:,4) = strpad('d/dt R in component all (per_um2)');
    LEGEND_RATES(:,5) = strpad('d/dt Rl in component all (per_um2)');
    LEGEND_RATES(:,6) = strpad('d/dt Rg in component all (per_um2)');
    LEGEND_RATES(:,8) = strpad('d/dt Rlgp in component all (per_um2)');
    LEGEND_RATES(:,7) = strpad('d/dt Rlg in component all (per_um2)');
    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) = 0.1;
    CONSTANTS(:,2) = 10;
    STATES(:,2) = 10000;
    STATES(:,3) = 0;
    STATES(:,4) = 13.9;
    STATES(:,5) = 0;
    STATES(:,6) = 5.06;
    STATES(:,7) = 0;
    STATES(:,8) = 0;
    STATES(:,9) = 0.015;
    CONSTANTS(:,3) = 4000;
    STATES(:,10) = 9.09;
    STATES(:,11) = 0;
    STATES(:,12) = 90.9;
    STATES(:,13) = 0;
    CONSTANTS(:,4) = 0.0003;
    CONSTANTS(:,5) = 3e-5;
    CONSTANTS(:,6) = 2.75e-4;
    CONSTANTS(:,7) = 27500;
    CONSTANTS(:,8) = 1;
    CONSTANTS(:,9) = 0.001;
    CONSTANTS(:,10) = 0.3;
    CONSTANTS(:,11) = 3e-5;
    CONSTANTS(:,12) = 0.0004;
    CONSTANTS(:,13) = 1;
    CONSTANTS(:,14) = 0.15;
    CONSTANTS(:,15) = 0.0167;
    CONSTANTS(:,16) = 0.0167;
    CONSTANTS(:,17) = 0.0042;
    CONSTANTS(:,18) = 1;
    CONSTANTS(:,19) = 0.042;
    CONSTANTS(:,20) = 1;
    CONSTANTS(:,21) = 0.0334;
    CONSTANTS(:,22) = 0.1;
    CONSTANTS(:,23) = 6;
    CONSTANTS(:,24) = 6;
    CONSTANTS(:,25) = 0.444;
    CONSTANTS(:,26) = 19.8;
    CONSTANTS(:,27) = 3.8;
    CONSTANTS(:,28) = 5;
    CONSTANTS(:,29) = 1.25;
    CONSTANTS(:,30) = 2550;
    CONSTANTS(:,31) = 4.61;
    CONSTANTS(:,32) =  CONSTANTS(:,4).*CONSTANTS(:,5);
    CONSTANTS(:,33) =  CONSTANTS(:,6).*CONSTANTS(:,7);
    CONSTANTS(:,34) =  CONSTANTS(:,10).*CONSTANTS(:,11);
    CONSTANTS(:,35) =  CONSTANTS(:,21).*CONSTANTS(:,22);
    CONSTANTS(:,36) = 1.00000./( CONSTANTS(:,30).*602.200);
    CONSTANTS(:,37) = 1.00000./( CONSTANTS(:,30).*CONSTANTS(:,31));
    CONSTANTS(:,38) = CONSTANTS(:,36)./CONSTANTS(:,37);
    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(:,4) = ( CONSTANTS(:,25).*STATES(:,10).*CONSTANTS(:,3))./(CONSTANTS(:,26)./CONSTANTS(:,38)+CONSTANTS(:,3));
    ALGEBRAIC(:,6) = ( CONSTANTS(:,27).*STATES(:,11).*CONSTANTS(:,3))./(CONSTANTS(:,28)./CONSTANTS(:,38)+CONSTANTS(:,3));
    ALGEBRAIC(:,2) =  CONSTANTS(:,29).*STATES(:,9);
    RATES(:,9) =  CONSTANTS(:,38).*(ALGEBRAIC(:,4)+ALGEBRAIC(:,6)) - ALGEBRAIC(:,2);
    ALGEBRAIC(:,7) =  CONSTANTS(:,19).*STATES(:,10).*STATES(:,3) -  CONSTANTS(:,20).*STATES(:,11);
    ALGEBRAIC(:,5) =  CONSTANTS(:,21).*STATES(:,13).*STATES(:,1) -  CONSTANTS(:,35).*STATES(:,11);
    ALGEBRAIC(:,3) =  CONSTANTS(:,23).*STATES(:,11);
    RATES(:,11) = (ALGEBRAIC(:,7)+ALGEBRAIC(:,5)) - ALGEBRAIC(:,3);
    ALGEBRAIC(:,8) =  CONSTANTS(:,15).*STATES(:,12).*STATES(:,1) -  CONSTANTS(:,16).*STATES(:,10);
    RATES(:,10) = (ALGEBRAIC(:,8)+ALGEBRAIC(:,3)) - ALGEBRAIC(:,7);
    RATES(:,1) =  CONSTANTS(:,38).* - 1.00000.*(ALGEBRAIC(:,8)+ALGEBRAIC(:,5));
    ALGEBRAIC(:,9) =  CONSTANTS(:,17).*STATES(:,12).*STATES(:,3) -  CONSTANTS(:,18).*STATES(:,13);
    ALGEBRAIC(:,1) =  CONSTANTS(:,24).*STATES(:,13);
    RATES(:,12) = ALGEBRAIC(:,1) - (ALGEBRAIC(:,9)+ALGEBRAIC(:,8));
    RATES(:,13) = ALGEBRAIC(:,9) - (ALGEBRAIC(:,5)+ALGEBRAIC(:,1));
    ALGEBRAIC(:,11) = piecewise({VOI<CONSTANTS(:,2)+0.150000&VOI>=CONSTANTS(:,2), CONSTANTS(:,1)./(1.00000+exp(  - 80.0000.*((VOI - CONSTANTS(:,2)) - 0.0500000))) , VOI>=CONSTANTS(:,2)+0.150000, CONSTANTS(:,1) }, 0.00000);
    ALGEBRAIC(:,12) =  CONSTANTS(:,4).*STATES(:,4).*ALGEBRAIC(:,11) -  CONSTANTS(:,32).*STATES(:,5);
    ALGEBRAIC(:,13) =  CONSTANTS(:,6).*STATES(:,4).*STATES(:,2) -  CONSTANTS(:,33).*STATES(:,6);
    RATES(:,4) =   - 1.00000.*(ALGEBRAIC(:,12)+ALGEBRAIC(:,13));
    ALGEBRAIC(:,14) =  CONSTANTS(:,8).*STATES(:,5).*STATES(:,2) -  CONSTANTS(:,9).*STATES(:,7);
    ALGEBRAIC(:,10) =  CONSTANTS(:,14).*STATES(:,3);
    RATES(:,2) = (ALGEBRAIC(:,10)+ALGEBRAIC(:,1)+ALGEBRAIC(:,3)) - (ALGEBRAIC(:,13)+ALGEBRAIC(:,14));
    ALGEBRAIC(:,15) =  CONSTANTS(:,10).*ALGEBRAIC(:,11).*STATES(:,6) -  CONSTANTS(:,34).*STATES(:,7);
    RATES(:,6) = ALGEBRAIC(:,13) - ALGEBRAIC(:,15);
    ALGEBRAIC(:,16) =  CONSTANTS(:,12).*STATES(:,7);
    RATES(:,8) = ALGEBRAIC(:,16);
    ALGEBRAIC(:,17) =  CONSTANTS(:,13).*STATES(:,7);
    RATES(:,3) = ALGEBRAIC(:,17) - (ALGEBRAIC(:,10)+ALGEBRAIC(:,9)+ALGEBRAIC(:,7));
    RATES(:,5) = (ALGEBRAIC(:,12)+ALGEBRAIC(:,17)) - ALGEBRAIC(:,14);
    RATES(:,7) = ((ALGEBRAIC(:,14) - ALGEBRAIC(:,16))+ALGEBRAIC(:,15)) - ALGEBRAIC(:,17);
   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(:,4) = ( CONSTANTS(:,25).*STATES(:,10).*CONSTANTS(:,3))./(CONSTANTS(:,26)./CONSTANTS(:,38)+CONSTANTS(:,3));
    ALGEBRAIC(:,6) = ( CONSTANTS(:,27).*STATES(:,11).*CONSTANTS(:,3))./(CONSTANTS(:,28)./CONSTANTS(:,38)+CONSTANTS(:,3));
    ALGEBRAIC(:,2) =  CONSTANTS(:,29).*STATES(:,9);
    ALGEBRAIC(:,7) =  CONSTANTS(:,19).*STATES(:,10).*STATES(:,3) -  CONSTANTS(:,20).*STATES(:,11);
    ALGEBRAIC(:,5) =  CONSTANTS(:,21).*STATES(:,13).*STATES(:,1) -  CONSTANTS(:,35).*STATES(:,11);
    ALGEBRAIC(:,3) =  CONSTANTS(:,23).*STATES(:,11);
    ALGEBRAIC(:,8) =  CONSTANTS(:,15).*STATES(:,12).*STATES(:,1) -  CONSTANTS(:,16).*STATES(:,10);
    ALGEBRAIC(:,9) =  CONSTANTS(:,17).*STATES(:,12).*STATES(:,3) -  CONSTANTS(:,18).*STATES(:,13);
    ALGEBRAIC(:,1) =  CONSTANTS(:,24).*STATES(:,13);
    ALGEBRAIC(:,11) = piecewise({VOI<CONSTANTS(:,2)+0.150000&VOI>=CONSTANTS(:,2), CONSTANTS(:,1)./(1.00000+exp(  - 80.0000.*((VOI - CONSTANTS(:,2)) - 0.0500000))) , VOI>=CONSTANTS(:,2)+0.150000, CONSTANTS(:,1) }, 0.00000);
    ALGEBRAIC(:,12) =  CONSTANTS(:,4).*STATES(:,4).*ALGEBRAIC(:,11) -  CONSTANTS(:,32).*STATES(:,5);
    ALGEBRAIC(:,13) =  CONSTANTS(:,6).*STATES(:,4).*STATES(:,2) -  CONSTANTS(:,33).*STATES(:,6);
    ALGEBRAIC(:,14) =  CONSTANTS(:,8).*STATES(:,5).*STATES(:,2) -  CONSTANTS(:,9).*STATES(:,7);
    ALGEBRAIC(:,10) =  CONSTANTS(:,14).*STATES(:,3);
    ALGEBRAIC(:,15) =  CONSTANTS(:,10).*ALGEBRAIC(:,11).*STATES(:,6) -  CONSTANTS(:,34).*STATES(:,7);
    ALGEBRAIC(:,16) =  CONSTANTS(:,12).*STATES(:,7);
    ALGEBRAIC(:,17) =  CONSTANTS(:,13).*STATES(:,7);
end

% Compute result of a piecewise function
function x = piecewise(cases, default)
    set = [0];
    for i = 1:2:length(cases)
        if (length(cases{i+1}) == 1)
            x(cases{i} & ~set,:) = cases{i+1};
        else
            x(cases{i} & ~set,:) = cases{i+1}(cases{i} & ~set);
        end
        set = set | cases{i};
        if(set), break, end
    end
    if (length(default) == 1)
        x(~set,:) = default;
    else
        x(~set,:) = default(~set);
    end
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