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 =15;
end
% There are a total of 7 entries in each of the rate and state variable arrays.
% There are a total of 40 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_CONSTANTS(:,1) = strpad('cap in component parameters (nanofarad)');
    LEGEND_CONSTANTS(:,2) = strpad('cc1lin in component parameters (per_second)');
    LEGEND_CONSTANTS(:,3) = strpad('cc_2 in component parameters (per_second)');
    LEGEND_CONSTANTS(:,4) = strpad('ck1lin in component parameters (per_second)');
    LEGEND_CONSTANTS(:,5) = strpad('ck_2 in component parameters (per_second)');
    LEGEND_CONSTANTS(:,6) = strpad('clmax in component parameters (nanosiemens)');
    LEGEND_CONSTANTS(:,7) = strpad('cnmax in component parameters (nanosiemens)');
    LEGEND_CONSTANTS(:,8) = strpad('cx1lin in component parameters (per_second)');
    LEGEND_CONSTANTS(:,9) = strpad('cx2 in component parameters (per_second)');
    LEGEND_CONSTANTS(:,10) = strpad('ef in component parameters (per_second)');
    LEGEND_CONSTANTS(:,11) = strpad('gl in component parameters (nanosiemens)');
    LEGEND_CONSTANTS(:,12) = strpad('hmc_1 in component parameters (uM)');
    LEGEND_CONSTANTS(:,13) = strpad('hmc_2 in component parameters (uM)');
    LEGEND_CONSTANTS(:,14) = strpad('inf in component parameters (uM_per_picocoulomb)');
    LEGEND_CONSTANTS(:,15) = strpad('inhmax in component parameters (dimensionless)');
    LEGEND_CONSTANTS(:,16) = strpad('k_1 in component parameters (per_uM_per_second)');
    LEGEND_CONSTANTS(:,17) = strpad('k_2 in component parameters (per_second)');
    LEGEND_CONSTANTS(:,18) = strpad('kI in component parameters (uM)');
    LEGEND_CONSTANTS(:,19) = strpad('kinh in component parameters (uM)');
    LEGEND_CONSTANTS(:,20) = strpad('kinhcng in component parameters (uM)');
    LEGEND_CONSTANTS(:,21) = strpad('n_1 in component parameters (dimensionless)');
    LEGEND_CONSTANTS(:,22) = strpad('n_2 in component parameters (dimensionless)');
    LEGEND_CONSTANTS(:,23) = strpad('nI in component parameters (dimensionless)');
    LEGEND_CONSTANTS(:,24) = strpad('ninh in component parameters (dimensionless)');
    LEGEND_CONSTANTS(:,25) = strpad('ninhcng in component parameters (dimensionless)');
    LEGEND_CONSTANTS(:,26) = strpad('pd in component parameters (per_second)');
    LEGEND_CONSTANTS(:,27) = strpad('r_1 in component parameters (per_second)');
    LEGEND_CONSTANTS(:,28) = strpad('r_2 in component parameters (per_second)');
    LEGEND_CONSTANTS(:,29) = strpad('smax in component parameters (uM_per_second)');
    LEGEND_CONSTANTS(:,30) = strpad('V_Cl in component parameters (millivolt)');
    LEGEND_CONSTANTS(:,31) = strpad('V_cng in component parameters (millivolt)');
    LEGEND_CONSTANTS(:,32) = strpad('V_l in component parameters (millivolt)');
    LEGEND_CONSTANTS(:,40) = strpad('F_vol in component parameters (picocoulomb_per_uM)');
    LEGEND_CONSTANTS(:,33) = strpad('F in component parameters (coulombs_per_mole)');
    LEGEND_CONSTANTS(:,34) = strpad('C_vol in component parameters (liter)');
    LEGEND_ALGEBRAIC(:,10) = strpad('O_stim in component O_stim (uM)');
    LEGEND_CONSTANTS(:,35) = strpad('od in component O_stim (uM)');
    LEGEND_CONSTANTS(:,36) = strpad('t_0 in component O_stim (second)');
    LEGEND_CONSTANTS(:,37) = strpad('t_1 in component O_stim (second)');
    LEGEND_ALGEBRAIC(:,1) = strpad('H_0 in component O_stim (dimensionless)');
    LEGEND_ALGEBRAIC(:,6) = strpad('H_1 in component O_stim (dimensionless)');
    LEGEND_STATES(:,1) = strpad('bLR in component bLR (dimensionless)');
    LEGEND_CONSTANTS(:,38) = strpad('R_tot in component bLR (dimensionless)');
    LEGEND_STATES(:,2) = strpad('aG in component aG (dimensionless)');
    LEGEND_CONSTANTS(:,39) = strpad('G_tot in component aG (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('k_G in component k_G (per_second)');
    LEGEND_ALGEBRAIC(:,7) = strpad('r_G in component r_G (per_second)');
    LEGEND_STATES(:,3) = strpad('cAMP in component cAMP (uM)');
    LEGEND_ALGEBRAIC(:,3) = strpad('synth in component synth (uM_per_second)');
    LEGEND_ALGEBRAIC(:,8) = strpad('degrad in component degrad (uM_per_second)');
    LEGEND_STATES(:,4) = strpad('aCaMK in component aCaMK (uM)');
    LEGEND_STATES(:,5) = strpad('Ca in component Ca (uM)');
    LEGEND_ALGEBRAIC(:,11) = strpad('I_CNG in component I_CNG (nanoampere)');
    LEGEND_ALGEBRAIC(:,13) = strpad('J_NCX in component J_NCX (uM_per_second)');
    LEGEND_ALGEBRAIC(:,4) = strpad('cc_1 in component cc_1 (uM_per_second)');
    LEGEND_STATES(:,6) = strpad('CaCaM in component CaCaM (uM)');
    LEGEND_ALGEBRAIC(:,5) = strpad('ck_1 in component ck_1 (uM_per_second)');
    LEGEND_STATES(:,7) = strpad('V in component V (millivolt)');
    LEGEND_ALGEBRAIC(:,12) = strpad('I_ClCa in component I_ClCa (nanoampere)');
    LEGEND_ALGEBRAIC(:,14) = strpad('I_NCX in component I_NCX (nanoampere)');
    LEGEND_ALGEBRAIC(:,15) = strpad('I_other in component I_other (nanoampere)');
    LEGEND_ALGEBRAIC(:,9) = strpad('inhcng in component inhcng (dimensionless)');
    LEGEND_RATES(:,1) = strpad('d/dt bLR in component bLR (dimensionless)');
    LEGEND_RATES(:,2) = strpad('d/dt aG in component aG (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt cAMP in component cAMP (uM)');
    LEGEND_RATES(:,5) = strpad('d/dt Ca in component Ca (uM)');
    LEGEND_RATES(:,6) = strpad('d/dt CaCaM in component CaCaM (uM)');
    LEGEND_RATES(:,4) = strpad('d/dt aCaMK in component aCaMK (uM)');
    LEGEND_RATES(:,7) = strpad('d/dt V in component V (millivolt)');
    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) = 0.004;
    CONSTANTS(:,2) = 0.88;
    CONSTANTS(:,3) = 26;
    CONSTANTS(:,4) = 13;
    CONSTANTS(:,5) = 0.9;
    CONSTANTS(:,6) = 1;
    CONSTANTS(:,7) = 1;
    CONSTANTS(:,8) = 1;
    CONSTANTS(:,9) = 13;
    CONSTANTS(:,10) = 2;
    CONSTANTS(:,11) = 6;
    CONSTANTS(:,12) = 2;
    CONSTANTS(:,13) = 3;
    CONSTANTS(:,14) = 1.9;
    CONSTANTS(:,15) = 5;
    CONSTANTS(:,16) = 0.06;
    CONSTANTS(:,17) = 20;
    CONSTANTS(:,18) = 0.7;
    CONSTANTS(:,19) = 2;
    CONSTANTS(:,20) = 1;
    CONSTANTS(:,21) = 2;
    CONSTANTS(:,22) = 2;
    CONSTANTS(:,23) = 2;
    CONSTANTS(:,24) = 1.5;
    CONSTANTS(:,25) = 1.3;
    CONSTANTS(:,26) = 20;
    CONSTANTS(:,27) = 10;
    CONSTANTS(:,28) = 5;
    CONSTANTS(:,29) = 71;
    CONSTANTS(:,30) = -50;
    CONSTANTS(:,31) = 0;
    CONSTANTS(:,32) = -70;
    CONSTANTS(:,33) = 9.649e4;
    CONSTANTS(:,34) = 1e-13;
    CONSTANTS(:,35) = 20;
    CONSTANTS(:,36) = 0.5;
    CONSTANTS(:,37) = 1.5;
    STATES(:,1) = 0;
    CONSTANTS(:,38) = 1;
    STATES(:,2) = 0;
    CONSTANTS(:,39) = 1;
    STATES(:,3) = 1.35648992164649e-88;
    STATES(:,4) = 6.60756525051462e-8;
    STATES(:,5) = 5.09073088043779e-12;
    STATES(:,6) = 1.86113118246926e-13;
    STATES(:,7) = -70;
    CONSTANTS(:,40) =  (1.00000e+12./1.00000).*(1.00000./1000.00).*CONSTANTS(:,33).*CONSTANTS(:,34);
    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(:,2).*STATES(:,5);
    RATES(:,6) = ALGEBRAIC(:,4) -  CONSTANTS(:,3).*STATES(:,6);
    ALGEBRAIC(:,5) =  CONSTANTS(:,4).*STATES(:,6);
    RATES(:,4) = ALGEBRAIC(:,5) -  CONSTANTS(:,5).*STATES(:,4);
    ALGEBRAIC(:,2) =  CONSTANTS(:,17).*STATES(:,1);
    ALGEBRAIC(:,7) =  CONSTANTS(:,28).*STATES(:,2);
    RATES(:,2) =  ALGEBRAIC(:,2).*(CONSTANTS(:,39) - STATES(:,2)) - ALGEBRAIC(:,7);
    ALGEBRAIC(:,3) = ( STATES(:,2).*CONSTANTS(:,29))./(1.00000+power(STATES(:,4)./CONSTANTS(:,19), CONSTANTS(:,24)));
    ALGEBRAIC(:,8) =  CONSTANTS(:,26).*STATES(:,3);
    RATES(:,3) = ALGEBRAIC(:,3) - ALGEBRAIC(:,8);
    ALGEBRAIC(:,1) = piecewise({VOI<CONSTANTS(:,36), 0.00000 }, 1.00000);
    ALGEBRAIC(:,6) = piecewise({VOI<CONSTANTS(:,37), 0.00000 }, 1.00000);
    ALGEBRAIC(:,10) =  CONSTANTS(:,35).*(ALGEBRAIC(:,1) - ALGEBRAIC(:,6));
    RATES(:,1) =  CONSTANTS(:,16).*ALGEBRAIC(:,10).*(CONSTANTS(:,38) - STATES(:,1)) -  CONSTANTS(:,27).*STATES(:,1);
    ALGEBRAIC(:,9) = 1.00000+( (CONSTANTS(:,15) - 1.00000).*power(STATES(:,6), CONSTANTS(:,25)))./(power(STATES(:,6), CONSTANTS(:,25))+power(CONSTANTS(:,20), CONSTANTS(:,25)));
    ALGEBRAIC(:,11) =  (( CONSTANTS(:,7).*power(STATES(:,3), CONSTANTS(:,21)))./(power(STATES(:,3), CONSTANTS(:,21))+power( ALGEBRAIC(:,9).*CONSTANTS(:,12), CONSTANTS(:,21)))).*(1.00000./1000.00).*(CONSTANTS(:,31) - STATES(:,7));
    ALGEBRAIC(:,13) =  CONSTANTS(:,10).*STATES(:,5);
    RATES(:,5) = ( (1000.00./1.00000).*CONSTANTS(:,14).*ALGEBRAIC(:,11) - ALGEBRAIC(:,13)) - (ALGEBRAIC(:,4) -  CONSTANTS(:,3).*STATES(:,6));
    ALGEBRAIC(:,12) =  (( CONSTANTS(:,6).*power(STATES(:,5), CONSTANTS(:,22)))./(power(STATES(:,5), CONSTANTS(:,22))+power(CONSTANTS(:,13), CONSTANTS(:,22)))).*(1.00000./1000.00).*(CONSTANTS(:,30) - STATES(:,7));
    ALGEBRAIC(:,14) =  (1.00000./1000.00).*CONSTANTS(:,40).*ALGEBRAIC(:,13);
    ALGEBRAIC(:,15) =  CONSTANTS(:,11).*(1.00000./1000.00).*(CONSTANTS(:,32) - STATES(:,7));
    RATES(:,7) =  (1000.00./1.00000).*(1.00000./CONSTANTS(:,1)).*(ALGEBRAIC(:,11)+ALGEBRAIC(:,12)+ALGEBRAIC(:,14)+ALGEBRAIC(:,15));
   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(:,2).*STATES(:,5);
    ALGEBRAIC(:,5) =  CONSTANTS(:,4).*STATES(:,6);
    ALGEBRAIC(:,2) =  CONSTANTS(:,17).*STATES(:,1);
    ALGEBRAIC(:,7) =  CONSTANTS(:,28).*STATES(:,2);
    ALGEBRAIC(:,3) = ( STATES(:,2).*CONSTANTS(:,29))./(1.00000+power(STATES(:,4)./CONSTANTS(:,19), CONSTANTS(:,24)));
    ALGEBRAIC(:,8) =  CONSTANTS(:,26).*STATES(:,3);
    ALGEBRAIC(:,1) = piecewise({VOI<CONSTANTS(:,36), 0.00000 }, 1.00000);
    ALGEBRAIC(:,6) = piecewise({VOI<CONSTANTS(:,37), 0.00000 }, 1.00000);
    ALGEBRAIC(:,10) =  CONSTANTS(:,35).*(ALGEBRAIC(:,1) - ALGEBRAIC(:,6));
    ALGEBRAIC(:,9) = 1.00000+( (CONSTANTS(:,15) - 1.00000).*power(STATES(:,6), CONSTANTS(:,25)))./(power(STATES(:,6), CONSTANTS(:,25))+power(CONSTANTS(:,20), CONSTANTS(:,25)));
    ALGEBRAIC(:,11) =  (( CONSTANTS(:,7).*power(STATES(:,3), CONSTANTS(:,21)))./(power(STATES(:,3), CONSTANTS(:,21))+power( ALGEBRAIC(:,9).*CONSTANTS(:,12), CONSTANTS(:,21)))).*(1.00000./1000.00).*(CONSTANTS(:,31) - STATES(:,7));
    ALGEBRAIC(:,13) =  CONSTANTS(:,10).*STATES(:,5);
    ALGEBRAIC(:,12) =  (( CONSTANTS(:,6).*power(STATES(:,5), CONSTANTS(:,22)))./(power(STATES(:,5), CONSTANTS(:,22))+power(CONSTANTS(:,13), CONSTANTS(:,22)))).*(1.00000./1000.00).*(CONSTANTS(:,30) - STATES(:,7));
    ALGEBRAIC(:,14) =  (1.00000./1000.00).*CONSTANTS(:,40).*ALGEBRAIC(:,13);
    ALGEBRAIC(:,15) =  CONSTANTS(:,11).*(1.00000./1000.00).*(CONSTANTS(:,32) - 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