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 =21;
end
% There are a total of 11 entries in each of the rate and state variable arrays.
% There are a total of 20 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 (millisecond)');
    LEGEND_STATES(:,1) = strpad('V in component membrane (millivolt)');
    LEGEND_CONSTANTS(:,1) = strpad('Cm in component membrane (picoF)');
    LEGEND_CONSTANTS(:,2) = strpad('i_app in component membrane (picoA)');
    LEGEND_ALGEBRAIC(:,9) = strpad('i_Na in component sodium_current (picoA)');
    LEGEND_ALGEBRAIC(:,15) = strpad('i_Ca_L in component L_type_calcium_current (picoA)');
    LEGEND_ALGEBRAIC(:,16) = strpad('i_Ca_T in component T_type_calcium_current (picoA)');
    LEGEND_ALGEBRAIC(:,17) = strpad('i_K_dr in component delayed_rectifier_K_channel_current (picoA)');
    LEGEND_ALGEBRAIC(:,18) = strpad('i_M in component M_like_K_current (picoA)');
    LEGEND_ALGEBRAIC(:,20) = strpad('i_ir in component inward_rectifier_K_current (picoA)');
    LEGEND_ALGEBRAIC(:,21) = strpad('i_d in component inward_leak_current (picoA)');
    LEGEND_CONSTANTS(:,3) = strpad('g_Na in component sodium_current (nanoS)');
    LEGEND_CONSTANTS(:,4) = strpad('V_Na in component sodium_current (millivolt)');
    LEGEND_ALGEBRAIC(:,1) = strpad('O in component sodium_current (dimensionless)');
    LEGEND_STATES(:,2) = strpad('A in component A (dimensionless)');
    LEGEND_CONSTANTS(:,5) = strpad('k1 in component reaction_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,6) = strpad('k1_ in component reaction_constants (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,2) = strpad('alpha in component reaction_constants (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,10) = strpad('beta in component reaction_constants (first_order_rate_constant)');
    LEGEND_STATES(:,3) = strpad('D in component D (dimensionless)');
    LEGEND_STATES(:,4) = strpad('A_ in component A_ (dimensionless)');
    LEGEND_CONSTANTS(:,20) = strpad('a in component reaction_constants (dimensionless)');
    LEGEND_STATES(:,5) = strpad('D_ in component D_ (dimensionless)');
    LEGEND_CONSTANTS(:,7) = strpad('k2 in component reaction_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,8) = strpad('k2_ in component reaction_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,9) = strpad('V_Ca in component L_type_calcium_current (millivolt)');
    LEGEND_CONSTANTS(:,10) = strpad('g_Ca_L in component L_type_calcium_current (nanoS)');
    LEGEND_STATES(:,6) = strpad('m in component L_type_calcium_current_m_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,3) = strpad('m_infinity in component L_type_calcium_current_m_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,11) = strpad('tau_m in component L_type_calcium_current_m_gate (millisecond)');
    LEGEND_CONSTANTS(:,11) = strpad('Vh in component L_type_calcium_current_m_gate (millivolt)');
    LEGEND_CONSTANTS(:,12) = strpad('g_Ca_T in component T_type_calcium_current (nanoS)');
    LEGEND_STATES(:,7) = strpad('m in component T_type_calcium_current_m_gate (dimensionless)');
    LEGEND_STATES(:,8) = strpad('h in component T_type_calcium_current_h_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,4) = strpad('m_infinity in component T_type_calcium_current_m_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,12) = strpad('tau_m in component T_type_calcium_current_m_gate (millisecond)');
    LEGEND_ALGEBRAIC(:,5) = strpad('h_infinity in component T_type_calcium_current_h_gate (dimensionless)');
    LEGEND_CONSTANTS(:,13) = strpad('tau_h in component T_type_calcium_current_h_gate (millisecond)');
    LEGEND_CONSTANTS(:,14) = strpad('V_K in component delayed_rectifier_K_channel_current (millivolt)');
    LEGEND_CONSTANTS(:,15) = strpad('g_K_dr in component delayed_rectifier_K_channel_current (nanoS)');
    LEGEND_STATES(:,9) = strpad('n in component delayed_rectifier_K_channel_current_n_gate (dimensionless)');
    LEGEND_STATES(:,10) = strpad('h in component delayed_rectifier_K_channel_current_h_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,6) = strpad('n_infinity in component delayed_rectifier_K_channel_current_n_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,13) = strpad('tau_n in component delayed_rectifier_K_channel_current_n_gate (millisecond)');
    LEGEND_ALGEBRAIC(:,7) = strpad('h_infinity in component delayed_rectifier_K_channel_current_h_gate (dimensionless)');
    LEGEND_CONSTANTS(:,16) = strpad('tau_h in component delayed_rectifier_K_channel_current_h_gate (millisecond)');
    LEGEND_CONSTANTS(:,17) = strpad('g_M in component M_like_K_current (nanoS)');
    LEGEND_STATES(:,11) = strpad('n in component M_like_K_current_n_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,8) = strpad('n_infinity in component M_like_K_current_n_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,14) = strpad('tau_n in component M_like_K_current_n_gate (millisecond)');
    LEGEND_CONSTANTS(:,18) = strpad('g_ir in component inward_rectifier_K_current (nanoS)');
    LEGEND_ALGEBRAIC(:,19) = strpad('n_infinity in component inward_rectifier_K_current_n_gate (dimensionless)');
    LEGEND_CONSTANTS(:,19) = strpad('g_d in component inward_leak_current (nanoS)');
    LEGEND_RATES(:,1) = strpad('d/dt V in component membrane (millivolt)');
    LEGEND_RATES(:,2) = strpad('d/dt A in component A (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt A_ in component A_ (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt D in component D (dimensionless)');
    LEGEND_RATES(:,5) = strpad('d/dt D_ in component D_ (dimensionless)');
    LEGEND_RATES(:,6) = strpad('d/dt m in component L_type_calcium_current_m_gate (dimensionless)');
    LEGEND_RATES(:,7) = strpad('d/dt m in component T_type_calcium_current_m_gate (dimensionless)');
    LEGEND_RATES(:,8) = strpad('d/dt h in component T_type_calcium_current_h_gate (dimensionless)');
    LEGEND_RATES(:,9) = strpad('d/dt n in component delayed_rectifier_K_channel_current_n_gate (dimensionless)');
    LEGEND_RATES(:,10) = strpad('d/dt h in component delayed_rectifier_K_channel_current_h_gate (dimensionless)');
    LEGEND_RATES(:,11) = strpad('d/dt n in component M_like_K_current_n_gate (dimensionless)');
    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) = -60;
    CONSTANTS(:,1) = 14;
    CONSTANTS(:,2) = 15;
    CONSTANTS(:,3) = 60;
    CONSTANTS(:,4) = 60;
    STATES(:,2) = 1;
    CONSTANTS(:,5) = 0.3;
    CONSTANTS(:,6) = 0.03;
    STATES(:,3) = 0;
    STATES(:,4) = 0;
    STATES(:,5) = 0;
    CONSTANTS(:,7) = 0.001;
    CONSTANTS(:,8) = 0.01;
    CONSTANTS(:,9) = 100;
    CONSTANTS(:,10) = 1.3;
    STATES(:,6) = 0;
    CONSTANTS(:,11) = 40;
    CONSTANTS(:,12) = 0.94;
    STATES(:,7) = 0;
    STATES(:,8) = 0;
    CONSTANTS(:,13) = 22;
    CONSTANTS(:,14) = -80;
    CONSTANTS(:,15) = 20;
    STATES(:,9) = 0;
    STATES(:,10) = 0;
    CONSTANTS(:,16) = 1000;
    CONSTANTS(:,17) = 4;
    STATES(:,11) = 0;
    CONSTANTS(:,18) = 1.71;
    CONSTANTS(:,19) = 0.044;
    CONSTANTS(:,20) = power((( CONSTANTS(:,5).*CONSTANTS(:,8))./( CONSTANTS(:,6).*CONSTANTS(:,7))), 1.0 ./ 2);
    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);
    else
        statesRowCount = statesSize(1);
        ALGEBRAIC = zeros(statesRowCount, algebraicVariableCount);
        RATES = zeros(statesRowCount, statesColumnCount);
    end
    ALGEBRAIC(:,5) = 1.00000./(1.00000+exp((STATES(:,1)+86.4000)./4.70000));
    RATES(:,8) = (ALGEBRAIC(:,5) - STATES(:,8))./CONSTANTS(:,13);
    ALGEBRAIC(:,7) = 0.700000./(1.00000+exp( - (STATES(:,1)+35.0000)./10.0000))+0.300000;
    RATES(:,10) = (ALGEBRAIC(:,7) - STATES(:,10))./CONSTANTS(:,16);
    ALGEBRAIC(:,2) = 10.0000./(1.00000+exp( - (STATES(:,1)+6.00000)./10.0000));
    ALGEBRAIC(:,10) = 10.0000./(1.00000+exp((STATES(:,1)+54.4000)./4.60000));
    RATES(:,2) = ( ALGEBRAIC(:,2).*STATES(:,3)+ CONSTANTS(:,6).*STATES(:,4)) - ( ALGEBRAIC(:,10).*STATES(:,2)+ CONSTANTS(:,5).*STATES(:,2));
    RATES(:,4) = ( ALGEBRAIC(:,2).*CONSTANTS(:,20).*STATES(:,5)+ CONSTANTS(:,5).*STATES(:,2)) - ( (ALGEBRAIC(:,10)./CONSTANTS(:,20)).*STATES(:,4)+ CONSTANTS(:,6).*STATES(:,4));
    RATES(:,3) = ( ALGEBRAIC(:,10).*STATES(:,2)+ CONSTANTS(:,8).*STATES(:,5)) - ( ALGEBRAIC(:,2).*STATES(:,3)+ CONSTANTS(:,7).*STATES(:,3));
    RATES(:,5) = ( (ALGEBRAIC(:,10)./CONSTANTS(:,20)).*STATES(:,4)+ CONSTANTS(:,7).*STATES(:,3)) - ( ALGEBRAIC(:,2).*CONSTANTS(:,20).*STATES(:,5)+ CONSTANTS(:,8).*STATES(:,5));
    ALGEBRAIC(:,3) = 1.00000./(1.00000+exp( - (STATES(:,1) - CONSTANTS(:,11))./12.0000));
    ALGEBRAIC(:,11) = 5.00000./(exp((STATES(:,1)+15.0000)./25.0000)+exp( - (STATES(:,1)+15.0000)./25.0000));
    RATES(:,6) = (ALGEBRAIC(:,3) - STATES(:,6))./ALGEBRAIC(:,11);
    ALGEBRAIC(:,4) = 1.00000./(1.00000+exp( - (STATES(:,1) - 56.1000)./10.0000));
    ALGEBRAIC(:,12) = 7.00000./(exp((STATES(:,1)+50.0000)./9.00000)+exp( - (STATES(:,1)+50.0000)./9.00000))+0.800000;
    RATES(:,7) = (ALGEBRAIC(:,4) - STATES(:,7))./ALGEBRAIC(:,12);
    ALGEBRAIC(:,6) = 1.00000./(1.00000+exp( - (STATES(:,1)+25.0000)./15.0000));
    ALGEBRAIC(:,13) = 15.0000./(exp((STATES(:,1)+30.0000)./15.0000)+exp( - (STATES(:,1)+30.0000)./15.0000))+1.00000;
    RATES(:,9) = (ALGEBRAIC(:,6) - STATES(:,9))./ALGEBRAIC(:,13);
    ALGEBRAIC(:,8) = 1.00000./(1.00000+exp( - (STATES(:,1)+37.0000)./4.00000));
    ALGEBRAIC(:,14) = 80.0000./(exp((STATES(:,1)+30.0000)./15.0000)+exp( - (STATES(:,1)+30.0000)./15.0000));
    RATES(:,11) = (ALGEBRAIC(:,8) - STATES(:,11))./ALGEBRAIC(:,14);
    ALGEBRAIC(:,1) = power(STATES(:,2), 3.00000);
    ALGEBRAIC(:,9) =  CONSTANTS(:,3).*ALGEBRAIC(:,1).*(STATES(:,1) - CONSTANTS(:,4));
    ALGEBRAIC(:,15) =  CONSTANTS(:,10).*power(STATES(:,6), 2.00000).*(STATES(:,1) - CONSTANTS(:,9));
    ALGEBRAIC(:,16) =  CONSTANTS(:,12).*power(STATES(:,7), 2.00000).*STATES(:,8).*(STATES(:,1) - CONSTANTS(:,9));
    ALGEBRAIC(:,17) =  CONSTANTS(:,15).*power(STATES(:,9), 4.00000).*STATES(:,10).*(STATES(:,1) - CONSTANTS(:,14));
    ALGEBRAIC(:,18) =  CONSTANTS(:,17).*STATES(:,11).*(STATES(:,1) - CONSTANTS(:,14));
    ALGEBRAIC(:,19) = ( 0.800000.*1.00000)./(1.00000+exp((STATES(:,1)+80.0000)./12.0000))+0.200000;
    ALGEBRAIC(:,20) =  CONSTANTS(:,18).*ALGEBRAIC(:,19).*(STATES(:,1) - CONSTANTS(:,14));
    ALGEBRAIC(:,21) =  CONSTANTS(:,19).*(STATES(:,1) - CONSTANTS(:,9));
    RATES(:,1) = (CONSTANTS(:,2) - (ALGEBRAIC(:,9)+ALGEBRAIC(:,15)+ALGEBRAIC(:,16)+ALGEBRAIC(:,17)+ALGEBRAIC(:,18)+ALGEBRAIC(:,20)+ALGEBRAIC(:,21)))./CONSTANTS(:,1);
   RATES = RATES';
end

% Calculate algebraic variables
function ALGEBRAIC = computeAlgebraic(ALGEBRAIC, CONSTANTS, STATES, VOI)
    ALGEBRAIC(:,5) = 1.00000./(1.00000+exp((STATES(:,1)+86.4000)./4.70000));
    ALGEBRAIC(:,7) = 0.700000./(1.00000+exp( - (STATES(:,1)+35.0000)./10.0000))+0.300000;
    ALGEBRAIC(:,2) = 10.0000./(1.00000+exp( - (STATES(:,1)+6.00000)./10.0000));
    ALGEBRAIC(:,10) = 10.0000./(1.00000+exp((STATES(:,1)+54.4000)./4.60000));
    ALGEBRAIC(:,3) = 1.00000./(1.00000+exp( - (STATES(:,1) - CONSTANTS(:,11))./12.0000));
    ALGEBRAIC(:,11) = 5.00000./(exp((STATES(:,1)+15.0000)./25.0000)+exp( - (STATES(:,1)+15.0000)./25.0000));
    ALGEBRAIC(:,4) = 1.00000./(1.00000+exp( - (STATES(:,1) - 56.1000)./10.0000));
    ALGEBRAIC(:,12) = 7.00000./(exp((STATES(:,1)+50.0000)./9.00000)+exp( - (STATES(:,1)+50.0000)./9.00000))+0.800000;
    ALGEBRAIC(:,6) = 1.00000./(1.00000+exp( - (STATES(:,1)+25.0000)./15.0000));
    ALGEBRAIC(:,13) = 15.0000./(exp((STATES(:,1)+30.0000)./15.0000)+exp( - (STATES(:,1)+30.0000)./15.0000))+1.00000;
    ALGEBRAIC(:,8) = 1.00000./(1.00000+exp( - (STATES(:,1)+37.0000)./4.00000));
    ALGEBRAIC(:,14) = 80.0000./(exp((STATES(:,1)+30.0000)./15.0000)+exp( - (STATES(:,1)+30.0000)./15.0000));
    ALGEBRAIC(:,1) = power(STATES(:,2), 3.00000);
    ALGEBRAIC(:,9) =  CONSTANTS(:,3).*ALGEBRAIC(:,1).*(STATES(:,1) - CONSTANTS(:,4));
    ALGEBRAIC(:,15) =  CONSTANTS(:,10).*power(STATES(:,6), 2.00000).*(STATES(:,1) - CONSTANTS(:,9));
    ALGEBRAIC(:,16) =  CONSTANTS(:,12).*power(STATES(:,7), 2.00000).*STATES(:,8).*(STATES(:,1) - CONSTANTS(:,9));
    ALGEBRAIC(:,17) =  CONSTANTS(:,15).*power(STATES(:,9), 4.00000).*STATES(:,10).*(STATES(:,1) - CONSTANTS(:,14));
    ALGEBRAIC(:,18) =  CONSTANTS(:,17).*STATES(:,11).*(STATES(:,1) - CONSTANTS(:,14));
    ALGEBRAIC(:,19) = ( 0.800000.*1.00000)./(1.00000+exp((STATES(:,1)+80.0000)./12.0000))+0.200000;
    ALGEBRAIC(:,20) =  CONSTANTS(:,18).*ALGEBRAIC(:,19).*(STATES(:,1) - CONSTANTS(:,14));
    ALGEBRAIC(:,21) =  CONSTANTS(:,19).*(STATES(:,1) - CONSTANTS(:,9));
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