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 =13;
end
% There are a total of 4 entries in each of the rate and state variable arrays.
% There are a total of 24 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('C in component membrane (picoF)');
    LEGEND_CONSTANTS(:,2) = strpad('i_app in component membrane (picoA)');
    LEGEND_ALGEBRAIC(:,11) = strpad('i_NaP in component persistent_sodium_current (picoA)');
    LEGEND_ALGEBRAIC(:,5) = strpad('i_Na in component fast_sodium_current (picoA)');
    LEGEND_ALGEBRAIC(:,9) = strpad('i_K in component potassium_current (picoA)');
    LEGEND_ALGEBRAIC(:,12) = strpad('i_L in component leakage_current (picoA)');
    LEGEND_ALGEBRAIC(:,13) = strpad('i_tonic_e in component tonic_current (picoA)');
    LEGEND_CONSTANTS(:,3) = strpad('E_Na in component fast_sodium_current (millivolt)');
    LEGEND_CONSTANTS(:,4) = strpad('g_Na in component fast_sodium_current (nanoS)');
    LEGEND_ALGEBRAIC(:,1) = strpad('m_infinity in component fast_sodium_current_m_gate (dimensionless)');
    LEGEND_STATES(:,2) = strpad('n in component fast_sodium_current_n_gate (dimensionless)');
    LEGEND_CONSTANTS(:,5) = strpad('theta_m in component fast_sodium_current_m_gate (millivolt)');
    LEGEND_CONSTANTS(:,6) = strpad('sigma_m in component fast_sodium_current_m_gate (millivolt)');
    LEGEND_ALGEBRAIC(:,2) = strpad('n_infinity in component fast_sodium_current_n_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,6) = strpad('tau_n in component fast_sodium_current_n_gate (millisecond)');
    LEGEND_CONSTANTS(:,7) = strpad('tau_n_max in component fast_sodium_current_n_gate (millisecond)');
    LEGEND_CONSTANTS(:,8) = strpad('theta_n in component fast_sodium_current_n_gate (millivolt)');
    LEGEND_CONSTANTS(:,9) = strpad('sigma_n in component fast_sodium_current_n_gate (millivolt)');
    LEGEND_CONSTANTS(:,10) = strpad('g_K in component potassium_current (nanoS)');
    LEGEND_CONSTANTS(:,11) = strpad('E_K in component potassium_current (millivolt)');
    LEGEND_STATES(:,3) = strpad('n in component potassium_current_n_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,3) = strpad('n_infinity in component potassium_current_n_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,7) = strpad('tau_n in component potassium_current_n_gate (millisecond)');
    LEGEND_CONSTANTS(:,12) = strpad('tau_n_max in component potassium_current_n_gate (millisecond)');
    LEGEND_CONSTANTS(:,13) = strpad('theta_n in component potassium_current_n_gate (millivolt)');
    LEGEND_CONSTANTS(:,14) = strpad('sigma_n in component potassium_current_n_gate (millivolt)');
    LEGEND_CONSTANTS(:,15) = strpad('g_NaP in component persistent_sodium_current (nanoS)');
    LEGEND_ALGEBRAIC(:,10) = strpad('m_infinity in component persistent_sodium_current_m_gate (dimensionless)');
    LEGEND_STATES(:,4) = strpad('h in component persistent_sodium_current_h_gate (dimensionless)');
    LEGEND_CONSTANTS(:,16) = strpad('theta_m in component persistent_sodium_current_m_gate (millivolt)');
    LEGEND_CONSTANTS(:,17) = strpad('sigma_m in component persistent_sodium_current_m_gate (millivolt)');
    LEGEND_ALGEBRAIC(:,4) = strpad('h_infinity in component persistent_sodium_current_h_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,8) = strpad('tau_h in component persistent_sodium_current_h_gate (millisecond)');
    LEGEND_CONSTANTS(:,18) = strpad('tau_h_max in component persistent_sodium_current_h_gate (millisecond)');
    LEGEND_CONSTANTS(:,19) = strpad('theta_h in component persistent_sodium_current_h_gate (millivolt)');
    LEGEND_CONSTANTS(:,20) = strpad('sigma_h in component persistent_sodium_current_h_gate (millivolt)');
    LEGEND_CONSTANTS(:,21) = strpad('g_L in component leakage_current (nanoS)');
    LEGEND_CONSTANTS(:,22) = strpad('E_L in component leakage_current (millivolt)');
    LEGEND_CONSTANTS(:,23) = strpad('g_tonic_e in component tonic_current (nanoS)');
    LEGEND_CONSTANTS(:,24) = strpad('E_syn_e in component tonic_current (millivolt)');
    LEGEND_RATES(:,1) = strpad('d/dt V in component membrane (millivolt)');
    LEGEND_RATES(:,2) = strpad('d/dt n in component fast_sodium_current_n_gate (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt n in component potassium_current_n_gate (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt h in component persistent_sodium_current_h_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) = -50.0;
    CONSTANTS(:,1) = 21.0;
    CONSTANTS(:,2) = 0.0;
    CONSTANTS(:,3) = 50.0;
    CONSTANTS(:,4) = 28.0;
    STATES(:,2) = 0.01;
    CONSTANTS(:,5) = -34.0;
    CONSTANTS(:,6) = -5.0;
    CONSTANTS(:,7) = 10.0;
    CONSTANTS(:,8) = -29.0;
    CONSTANTS(:,9) = -4.0;
    CONSTANTS(:,10) = 11.2;
    CONSTANTS(:,11) = -85.0;
    STATES(:,3) = 0.01;
    CONSTANTS(:,12) = 10.0;
    CONSTANTS(:,13) = -29.0;
    CONSTANTS(:,14) = -4.0;
    CONSTANTS(:,15) = 2.8;
    STATES(:,4) = 0.46;
    CONSTANTS(:,16) = -40.0;
    CONSTANTS(:,17) = -6.0;
    CONSTANTS(:,18) = 10000.0;
    CONSTANTS(:,19) = -48.0;
    CONSTANTS(:,20) = 6.0;
    CONSTANTS(:,21) = 2.8;
    CONSTANTS(:,22) = -57.5;
    CONSTANTS(:,23) = 0.0;
    CONSTANTS(:,24) = 0.0;
    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(:,2) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,8))./CONSTANTS(:,9)));
    ALGEBRAIC(:,6) = CONSTANTS(:,7)./cosh((STATES(:,1) - CONSTANTS(:,8))./( 2.00000.*CONSTANTS(:,9)));
    RATES(:,2) = (ALGEBRAIC(:,2) - STATES(:,2))./ALGEBRAIC(:,6);
    ALGEBRAIC(:,3) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,13))./CONSTANTS(:,14)));
    ALGEBRAIC(:,7) = CONSTANTS(:,12)./cosh((STATES(:,1) - CONSTANTS(:,13))./( 2.00000.*CONSTANTS(:,14)));
    RATES(:,3) = (ALGEBRAIC(:,3) - STATES(:,3))./ALGEBRAIC(:,7);
    ALGEBRAIC(:,4) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,19))./CONSTANTS(:,20)));
    ALGEBRAIC(:,8) = CONSTANTS(:,18)./cosh((STATES(:,1) - CONSTANTS(:,19))./( 2.00000.*CONSTANTS(:,20)));
    RATES(:,4) = (ALGEBRAIC(:,4) - STATES(:,4))./ALGEBRAIC(:,8);
    ALGEBRAIC(:,10) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,16))./CONSTANTS(:,17)));
    ALGEBRAIC(:,11) =  CONSTANTS(:,15).*ALGEBRAIC(:,10).*STATES(:,4).*(STATES(:,1) - CONSTANTS(:,3));
    ALGEBRAIC(:,1) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,5))./CONSTANTS(:,6)));
    ALGEBRAIC(:,5) =  CONSTANTS(:,4).*power(ALGEBRAIC(:,1), 3.00000).*(1.00000 - STATES(:,2)).*(STATES(:,1) - CONSTANTS(:,3));
    ALGEBRAIC(:,9) =  CONSTANTS(:,10).*power(STATES(:,3), 4.00000).*(STATES(:,1) - CONSTANTS(:,11));
    ALGEBRAIC(:,12) =  CONSTANTS(:,21).*(STATES(:,1) - CONSTANTS(:,22));
    ALGEBRAIC(:,13) =  CONSTANTS(:,23).*(STATES(:,1) - CONSTANTS(:,24));
    RATES(:,1) = ( - (ALGEBRAIC(:,11)+ALGEBRAIC(:,5)+ALGEBRAIC(:,9)+ALGEBRAIC(:,12)+ALGEBRAIC(:,13))+CONSTANTS(:,2))./CONSTANTS(:,1);
   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(:,2) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,8))./CONSTANTS(:,9)));
    ALGEBRAIC(:,6) = CONSTANTS(:,7)./cosh((STATES(:,1) - CONSTANTS(:,8))./( 2.00000.*CONSTANTS(:,9)));
    ALGEBRAIC(:,3) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,13))./CONSTANTS(:,14)));
    ALGEBRAIC(:,7) = CONSTANTS(:,12)./cosh((STATES(:,1) - CONSTANTS(:,13))./( 2.00000.*CONSTANTS(:,14)));
    ALGEBRAIC(:,4) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,19))./CONSTANTS(:,20)));
    ALGEBRAIC(:,8) = CONSTANTS(:,18)./cosh((STATES(:,1) - CONSTANTS(:,19))./( 2.00000.*CONSTANTS(:,20)));
    ALGEBRAIC(:,10) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,16))./CONSTANTS(:,17)));
    ALGEBRAIC(:,11) =  CONSTANTS(:,15).*ALGEBRAIC(:,10).*STATES(:,4).*(STATES(:,1) - CONSTANTS(:,3));
    ALGEBRAIC(:,1) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,5))./CONSTANTS(:,6)));
    ALGEBRAIC(:,5) =  CONSTANTS(:,4).*power(ALGEBRAIC(:,1), 3.00000).*(1.00000 - STATES(:,2)).*(STATES(:,1) - CONSTANTS(:,3));
    ALGEBRAIC(:,9) =  CONSTANTS(:,10).*power(STATES(:,3), 4.00000).*(STATES(:,1) - CONSTANTS(:,11));
    ALGEBRAIC(:,12) =  CONSTANTS(:,21).*(STATES(:,1) - CONSTANTS(:,22));
    ALGEBRAIC(:,13) =  CONSTANTS(:,23).*(STATES(:,1) - CONSTANTS(:,24));
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