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 =16;
end
% There are a total of 6 entries in each of the rate and state variable arrays.
% There are a total of 11 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 environment (ms)');
    LEGEND_STATES(:,1) = strpad('V_m in component membrane (mV)');
    LEGEND_ALGEBRAIC(:,1) = strpad('i_Stim in component membrane (mA_per_cm2)');
    LEGEND_CONSTANTS(:,1) = strpad('stim_amplitude in component membrane (mA_per_cm2)');
    LEGEND_CONSTANTS(:,2) = strpad('stim_duration in component membrane (ms)');
    LEGEND_ALGEBRAIC(:,7) = strpad('i_Naf in component fast_sodium_channel (mA_per_cm2)');
    LEGEND_ALGEBRAIC(:,13) = strpad('i_Nap in component persistent_sodium_channel (mA_per_cm2)');
    LEGEND_ALGEBRAIC(:,14) = strpad('i_Ks in component slow_potassium_channel (mA_per_cm2)');
    LEGEND_ALGEBRAIC(:,15) = strpad('i_Kf in component juxtaparanodal_fast_potassium_channel (mA_per_cm2)');
    LEGEND_ALGEBRAIC(:,16) = strpad('i_Lk in component leakage_channel (mA_per_cm2)');
    LEGEND_CONSTANTS(:,3) = strpad('C_n in component membrane (mF_per_cm2)');
    LEGEND_CONSTANTS(:,4) = strpad('E_Na in component membrane (mV)');
    LEGEND_CONSTANTS(:,5) = strpad('E_K in component membrane (mV)');
    LEGEND_CONSTANTS(:,6) = strpad('E_Lk in component membrane (mV)');
    LEGEND_CONSTANTS(:,7) = strpad('g_Naf in component fast_sodium_channel (S_per_cm2)');
    LEGEND_STATES(:,2) = strpad('m in component fast_sodium_channel_m_gate (dimensionless)');
    LEGEND_STATES(:,3) = strpad('h in component fast_sodium_channel_h_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('alpha_m in component fast_sodium_channel_m_gate (per_ms)');
    LEGEND_ALGEBRAIC(:,8) = strpad('beta_m in component fast_sodium_channel_m_gate (per_ms)');
    LEGEND_ALGEBRAIC(:,3) = strpad('alpha_h in component fast_sodium_channel_h_gate (per_ms)');
    LEGEND_ALGEBRAIC(:,9) = strpad('beta_h in component fast_sodium_channel_h_gate (per_ms)');
    LEGEND_CONSTANTS(:,8) = strpad('g_Nap in component persistent_sodium_channel (S_per_cm2)');
    LEGEND_STATES(:,4) = strpad('p in component persistent_sodium_channel_p_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,4) = strpad('alpha_p in component persistent_sodium_channel_p_gate (per_ms)');
    LEGEND_ALGEBRAIC(:,10) = strpad('beta_p in component persistent_sodium_channel_p_gate (per_ms)');
    LEGEND_CONSTANTS(:,9) = strpad('g_Ks in component slow_potassium_channel (S_per_cm2)');
    LEGEND_STATES(:,5) = strpad('s in component slow_potassium_channel_s_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,5) = strpad('alpha_s in component slow_potassium_channel_s_gate (per_ms)');
    LEGEND_ALGEBRAIC(:,11) = strpad('beta_s in component slow_potassium_channel_s_gate (per_ms)');
    LEGEND_CONSTANTS(:,10) = strpad('g_Kf in component juxtaparanodal_fast_potassium_channel (S_per_cm2)');
    LEGEND_STATES(:,6) = strpad('n in component juxtaparanodal_fast_potassium_channel_n_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,6) = strpad('alpha_n in component juxtaparanodal_fast_potassium_channel_n_gate (per_ms)');
    LEGEND_ALGEBRAIC(:,12) = strpad('beta_n in component juxtaparanodal_fast_potassium_channel_n_gate (per_ms)');
    LEGEND_CONSTANTS(:,11) = strpad('g_Lk in component leakage_channel (S_per_cm2)');
    LEGEND_RATES(:,1) = strpad('d/dt V_m in component membrane (mV)');
    LEGEND_RATES(:,2) = strpad('d/dt m in component fast_sodium_channel_m_gate (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt h in component fast_sodium_channel_h_gate (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt p in component persistent_sodium_channel_p_gate (dimensionless)');
    LEGEND_RATES(:,5) = strpad('d/dt s in component slow_potassium_channel_s_gate (dimensionless)');
    LEGEND_RATES(:,6) = strpad('d/dt n in component juxtaparanodal_fast_potassium_channel_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) = -88.5901439103062;
    CONSTANTS(:,1) = 0.05;
    CONSTANTS(:,2) = 0.5;
    CONSTANTS(:,3) = 0.002;
    CONSTANTS(:,4) = 50;
    CONSTANTS(:,5) = -90;
    CONSTANTS(:,6) = -90;
    CONSTANTS(:,7) = 3;
    STATES(:,2) = 0.0302964457761589;
    STATES(:,3) = 0.841520865130776;
    CONSTANTS(:,8) = 0.01;
    STATES(:,4) = 0.0969864645712442;
    CONSTANTS(:,9) = 0.08;
    STATES(:,5) = 0.00997371545602793;
    CONSTANTS(:,10) = 0;
    STATES(:,6) = 0.000886041197111556;
    CONSTANTS(:,11) = 0.007;
    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) = ( 6.57000.*(STATES(:,1)+20.4000))./(1.00000 - exp( - (STATES(:,1)+20.4000)./10.3000));
    ALGEBRAIC(:,8) = (  - 0.304000.*(STATES(:,1)+25.7000))./(1.00000 - exp((STATES(:,1)+25.7000)./9.16000));
    RATES(:,2) =  ALGEBRAIC(:,2).*(1.00000 - STATES(:,2)) -  ALGEBRAIC(:,8).*STATES(:,2);
    ALGEBRAIC(:,3) = (  - 0.340000.*(STATES(:,1)+114.000))./(1.00000 - exp((STATES(:,1)+114.000)./11.0000));
    ALGEBRAIC(:,9) = 12.6000./(1.00000+exp( - (STATES(:,1)+31.8000)./13.4000));
    RATES(:,3) =  ALGEBRAIC(:,3).*(1.00000 - STATES(:,3)) -  ALGEBRAIC(:,9).*STATES(:,3);
    ALGEBRAIC(:,4) = ( 0.0353000.*(STATES(:,1)+27.0000))./(1.00000 - exp( - (STATES(:,1)+27.0000)./10.2000));
    ALGEBRAIC(:,10) = (  - 0.000883000.*(STATES(:,1)+34.0000))./(1.00000 - exp((STATES(:,1)+34.0000)./10.0000));
    RATES(:,4) =  ALGEBRAIC(:,4).*(1.00000 - STATES(:,4)) -  ALGEBRAIC(:,10).*STATES(:,4);
    ALGEBRAIC(:,5) = 0.300000./(1.00000+exp( - (STATES(:,1)+53.0000)./5.00000));
    ALGEBRAIC(:,11) = 0.0300000./(1.00000+exp( - (STATES(:,1)+90.0000)./1.00000));
    RATES(:,5) =  ALGEBRAIC(:,5).*(1.00000 - STATES(:,5)) -  ALGEBRAIC(:,11).*STATES(:,5);
    ALGEBRAIC(:,6) = ( 0.0462000.*(STATES(:,1)+83.2000))./(1.00000 - exp( - (STATES(:,1)+83.2000)./1.10000));
    ALGEBRAIC(:,12) = (  - 0.0824000.*(STATES(:,1)+66.0000))./(1.00000 - exp((STATES(:,1)+66.0000)./10.5000));
    RATES(:,6) =  ALGEBRAIC(:,6).*(1.00000 - STATES(:,6)) -  ALGEBRAIC(:,12).*STATES(:,6);
    ALGEBRAIC(:,1) = piecewise({VOI>=10.0000&VOI<=10.0000+CONSTANTS(:,2), CONSTANTS(:,1) }, 0.00000);
    ALGEBRAIC(:,7) =  CONSTANTS(:,7).*power(STATES(:,2), 3.00000).*STATES(:,3).*(STATES(:,1) - CONSTANTS(:,4));
    ALGEBRAIC(:,13) =  CONSTANTS(:,8).*power(STATES(:,4), 3.00000).*(STATES(:,1) - CONSTANTS(:,4));
    ALGEBRAIC(:,14) =  CONSTANTS(:,9).*STATES(:,5).*(STATES(:,1) - CONSTANTS(:,5));
    ALGEBRAIC(:,15) =  CONSTANTS(:,10).*power(STATES(:,6), 4.00000).*(STATES(:,1) - CONSTANTS(:,5));
    ALGEBRAIC(:,16) =  CONSTANTS(:,11).*(STATES(:,1) - CONSTANTS(:,6));
    RATES(:,1) =  - ( - ALGEBRAIC(:,1)+ALGEBRAIC(:,7)+ALGEBRAIC(:,13)+ALGEBRAIC(:,14)+ALGEBRAIC(:,15)+ALGEBRAIC(:,16))./CONSTANTS(:,3);
   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) = ( 6.57000.*(STATES(:,1)+20.4000))./(1.00000 - exp( - (STATES(:,1)+20.4000)./10.3000));
    ALGEBRAIC(:,8) = (  - 0.304000.*(STATES(:,1)+25.7000))./(1.00000 - exp((STATES(:,1)+25.7000)./9.16000));
    ALGEBRAIC(:,3) = (  - 0.340000.*(STATES(:,1)+114.000))./(1.00000 - exp((STATES(:,1)+114.000)./11.0000));
    ALGEBRAIC(:,9) = 12.6000./(1.00000+exp( - (STATES(:,1)+31.8000)./13.4000));
    ALGEBRAIC(:,4) = ( 0.0353000.*(STATES(:,1)+27.0000))./(1.00000 - exp( - (STATES(:,1)+27.0000)./10.2000));
    ALGEBRAIC(:,10) = (  - 0.000883000.*(STATES(:,1)+34.0000))./(1.00000 - exp((STATES(:,1)+34.0000)./10.0000));
    ALGEBRAIC(:,5) = 0.300000./(1.00000+exp( - (STATES(:,1)+53.0000)./5.00000));
    ALGEBRAIC(:,11) = 0.0300000./(1.00000+exp( - (STATES(:,1)+90.0000)./1.00000));
    ALGEBRAIC(:,6) = ( 0.0462000.*(STATES(:,1)+83.2000))./(1.00000 - exp( - (STATES(:,1)+83.2000)./1.10000));
    ALGEBRAIC(:,12) = (  - 0.0824000.*(STATES(:,1)+66.0000))./(1.00000 - exp((STATES(:,1)+66.0000)./10.5000));
    ALGEBRAIC(:,1) = piecewise({VOI>=10.0000&VOI<=10.0000+CONSTANTS(:,2), CONSTANTS(:,1) }, 0.00000);
    ALGEBRAIC(:,7) =  CONSTANTS(:,7).*power(STATES(:,2), 3.00000).*STATES(:,3).*(STATES(:,1) - CONSTANTS(:,4));
    ALGEBRAIC(:,13) =  CONSTANTS(:,8).*power(STATES(:,4), 3.00000).*(STATES(:,1) - CONSTANTS(:,4));
    ALGEBRAIC(:,14) =  CONSTANTS(:,9).*STATES(:,5).*(STATES(:,1) - CONSTANTS(:,5));
    ALGEBRAIC(:,15) =  CONSTANTS(:,10).*power(STATES(:,6), 4.00000).*(STATES(:,1) - CONSTANTS(:,5));
    ALGEBRAIC(:,16) =  CONSTANTS(:,11).*(STATES(:,1) - CONSTANTS(:,6));
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