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 =10;
end
% There are a total of 4 entries in each of the rate and state variable arrays.
% There are a total of 8 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('E_R in component membrane (millivolt)');
    LEGEND_CONSTANTS(:,2) = strpad('Cm in component membrane (microF_per_cm2)');
    LEGEND_ALGEBRAIC(:,5) = strpad('i_Na in component sodium_channel (microA_per_cm2)');
    LEGEND_ALGEBRAIC(:,9) = strpad('i_K in component potassium_channel (microA_per_cm2)');
    LEGEND_ALGEBRAIC(:,10) = strpad('i_L in component leakage_current (microA_per_cm2)');
    LEGEND_ALGEBRAIC(:,1) = strpad('i_Stim in component membrane (microA_per_cm2)');
    LEGEND_CONSTANTS(:,3) = strpad('g_Na in component sodium_channel (milliS_per_cm2)');
    LEGEND_CONSTANTS(:,6) = strpad('E_Na in component sodium_channel (millivolt)');
    LEGEND_STATES(:,2) = strpad('m in component sodium_channel_m_gate (dimensionless)');
    LEGEND_STATES(:,3) = strpad('h in component sodium_channel_h_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('alpha_m in component sodium_channel_m_gate (per_millisecond)');
    LEGEND_ALGEBRAIC(:,6) = strpad('beta_m in component sodium_channel_m_gate (per_millisecond)');
    LEGEND_ALGEBRAIC(:,3) = strpad('alpha_h in component sodium_channel_h_gate (per_millisecond)');
    LEGEND_ALGEBRAIC(:,7) = strpad('beta_h in component sodium_channel_h_gate (per_millisecond)');
    LEGEND_CONSTANTS(:,4) = strpad('g_K in component potassium_channel (milliS_per_cm2)');
    LEGEND_CONSTANTS(:,7) = strpad('E_K in component potassium_channel (millivolt)');
    LEGEND_STATES(:,4) = strpad('n in component potassium_channel_n_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,4) = strpad('alpha_n in component potassium_channel_n_gate (per_millisecond)');
    LEGEND_ALGEBRAIC(:,8) = strpad('beta_n in component potassium_channel_n_gate (per_millisecond)');
    LEGEND_CONSTANTS(:,5) = strpad('g_L in component leakage_current (milliS_per_cm2)');
    LEGEND_CONSTANTS(:,8) = strpad('E_L in component leakage_current (millivolt)');
    LEGEND_RATES(:,1) = strpad('d/dt V in component membrane (millivolt)');
    LEGEND_RATES(:,2) = strpad('d/dt m in component sodium_channel_m_gate (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt h in component sodium_channel_h_gate (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt n in component 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) = -75;
    CONSTANTS(:,1) = -75;
    CONSTANTS(:,2) = 1;
    CONSTANTS(:,3) = 120;
    STATES(:,2) = 0.05;
    STATES(:,3) = 0.6;
    CONSTANTS(:,4) = 36;
    STATES(:,4) = 0.325;
    CONSTANTS(:,5) = 0.3;
    CONSTANTS(:,6) = CONSTANTS(:,1)+115.000;
    CONSTANTS(:,7) = CONSTANTS(:,1) - 12.0000;
    CONSTANTS(:,8) = CONSTANTS(:,1)+10.6130;
    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) = (  - 0.100000.*(STATES(:,1)+50.0000))./(exp( - (STATES(:,1)+50.0000)./10.0000) - 1.00000);
    ALGEBRAIC(:,6) =  4.00000.*exp( - (STATES(:,1)+75.0000)./18.0000);
    RATES(:,2) =  ALGEBRAIC(:,2).*(1.00000 - STATES(:,2)) -  ALGEBRAIC(:,6).*STATES(:,2);
    ALGEBRAIC(:,3) =  0.0700000.*exp( - (STATES(:,1)+75.0000)./20.0000);
    ALGEBRAIC(:,7) = 1.00000./(exp( - (STATES(:,1)+45.0000)./10.0000)+1.00000);
    RATES(:,3) =  ALGEBRAIC(:,3).*(1.00000 - STATES(:,3)) -  ALGEBRAIC(:,7).*STATES(:,3);
    ALGEBRAIC(:,4) = (  - 0.0100000.*(STATES(:,1)+65.0000))./(exp( - (STATES(:,1)+65.0000)./10.0000) - 1.00000);
    ALGEBRAIC(:,8) =  0.125000.*exp((STATES(:,1)+75.0000)./80.0000);
    RATES(:,4) =  ALGEBRAIC(:,4).*(1.00000 - STATES(:,4)) -  ALGEBRAIC(:,8).*STATES(:,4);
    ALGEBRAIC(:,5) =  CONSTANTS(:,3).*power(STATES(:,2), 3.00000).*STATES(:,3).*(STATES(:,1) - CONSTANTS(:,6));
    ALGEBRAIC(:,9) =  CONSTANTS(:,4).*power(STATES(:,4), 4.00000).*(STATES(:,1) - CONSTANTS(:,7));
    ALGEBRAIC(:,10) =  CONSTANTS(:,5).*(STATES(:,1) - CONSTANTS(:,8));
    ALGEBRAIC(:,1) = piecewise({VOI>=10.0000&VOI<=10.5000, 20.0000 }, 0.00000);
    RATES(:,1) =  - ( - ALGEBRAIC(:,1)+ALGEBRAIC(:,5)+ALGEBRAIC(:,9)+ALGEBRAIC(:,10))./CONSTANTS(:,2);
   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) = (  - 0.100000.*(STATES(:,1)+50.0000))./(exp( - (STATES(:,1)+50.0000)./10.0000) - 1.00000);
    ALGEBRAIC(:,6) =  4.00000.*exp( - (STATES(:,1)+75.0000)./18.0000);
    ALGEBRAIC(:,3) =  0.0700000.*exp( - (STATES(:,1)+75.0000)./20.0000);
    ALGEBRAIC(:,7) = 1.00000./(exp( - (STATES(:,1)+45.0000)./10.0000)+1.00000);
    ALGEBRAIC(:,4) = (  - 0.0100000.*(STATES(:,1)+65.0000))./(exp( - (STATES(:,1)+65.0000)./10.0000) - 1.00000);
    ALGEBRAIC(:,8) =  0.125000.*exp((STATES(:,1)+75.0000)./80.0000);
    ALGEBRAIC(:,5) =  CONSTANTS(:,3).*power(STATES(:,2), 3.00000).*STATES(:,3).*(STATES(:,1) - CONSTANTS(:,6));
    ALGEBRAIC(:,9) =  CONSTANTS(:,4).*power(STATES(:,4), 4.00000).*(STATES(:,1) - CONSTANTS(:,7));
    ALGEBRAIC(:,10) =  CONSTANTS(:,5).*(STATES(:,1) - CONSTANTS(:,8));
    ALGEBRAIC(:,1) = piecewise({VOI>=10.0000&VOI<=10.5000, 20.0000 }, 0.00000);
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