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 =12;
end
% There are a total of 5 entries in each of the rate and state variable arrays.
% There are a total of 31 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 interface (ms)');
    LEGEND_CONSTANTS(:,1) = strpad('Cm in component interface (uFpmmsq)');
    LEGEND_CONSTANTS(:,2) = strpad('Am in component interface (pmm)');
    LEGEND_ALGEBRAIC(:,1) = strpad('Istim in component interface (uApmmcu)');
    LEGEND_STATES(:,1) = strpad('Vm in component membrane (mV)');
    LEGEND_STATES(:,2) = strpad('Vt in component Ttubular_current_Vt_var (mV)');
    LEGEND_STATES(:,3) = strpad('m in component sodium_current_m_gate (dimensionless)');
    LEGEND_STATES(:,4) = strpad('h in component sodium_current_h_gate (dimensionless)');
    LEGEND_STATES(:,5) = strpad('n in component potassium_current_n_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,5) = strpad('INa in component sodium_current (uApmmsq)');
    LEGEND_ALGEBRAIC(:,10) = strpad('IK in component potassium_current (uApmmsq)');
    LEGEND_ALGEBRAIC(:,11) = strpad('IL in component leak_current (uApmmsq)');
    LEGEND_ALGEBRAIC(:,12) = strpad('IT in component Ttubular_current (uApmmsq)');
    LEGEND_ALGEBRAIC(:,6) = strpad('IStimC in component interface (uApmmcu)');
    LEGEND_CONSTANTS(:,31) = strpad('AmC in component interface (pmm)');
    LEGEND_CONSTANTS(:,3) = strpad('IstimStart in component interface (ms)');
    LEGEND_CONSTANTS(:,4) = strpad('IstimEnd in component interface (ms)');
    LEGEND_CONSTANTS(:,5) = strpad('IstimAmplitude in component interface (uApmmcu)');
    LEGEND_CONSTANTS(:,6) = strpad('IstimPeriod in component interface (ms)');
    LEGEND_CONSTANTS(:,7) = strpad('IstimPulseDuration in component interface (ms)');
    LEGEND_CONSTANTS(:,8) = strpad('gNa_max in component sodium_current (mSpmmsq)');
    LEGEND_CONSTANTS(:,9) = strpad('ENa in component sodium_current (mV)');
    LEGEND_ALGEBRAIC(:,2) = strpad('alpha_m in component sodium_current_m_gate (pms)');
    LEGEND_ALGEBRAIC(:,7) = strpad('beta_m in component sodium_current_m_gate (pms)');
    LEGEND_CONSTANTS(:,10) = strpad('alpha_m_max in component sodium_current_m_gate (pms)');
    LEGEND_CONSTANTS(:,11) = strpad('beta_m_max in component sodium_current_m_gate (pms)');
    LEGEND_CONSTANTS(:,12) = strpad('Em in component sodium_current_m_gate (mV)');
    LEGEND_CONSTANTS(:,13) = strpad('v_alpha_m in component sodium_current_m_gate (dimensionless)');
    LEGEND_CONSTANTS(:,14) = strpad('v_beta_m in component sodium_current_m_gate (mV)');
    LEGEND_ALGEBRAIC(:,3) = strpad('alpha_h in component sodium_current_h_gate (pms)');
    LEGEND_ALGEBRAIC(:,8) = strpad('beta_h in component sodium_current_h_gate (pms)');
    LEGEND_CONSTANTS(:,15) = strpad('alpha_h_max in component sodium_current_h_gate (pms)');
    LEGEND_CONSTANTS(:,16) = strpad('beta_h_max in component sodium_current_h_gate (pms)');
    LEGEND_CONSTANTS(:,17) = strpad('Eh in component sodium_current_h_gate (mV)');
    LEGEND_CONSTANTS(:,18) = strpad('v_alpha_h in component sodium_current_h_gate (mV)');
    LEGEND_CONSTANTS(:,19) = strpad('v_beta_h in component sodium_current_h_gate (mV)');
    LEGEND_CONSTANTS(:,20) = strpad('gK_max in component potassium_current (mSpmmsq)');
    LEGEND_CONSTANTS(:,21) = strpad('EK in component potassium_current (mV)');
    LEGEND_ALGEBRAIC(:,4) = strpad('alpha_n in component potassium_current_n_gate (pms)');
    LEGEND_ALGEBRAIC(:,9) = strpad('beta_n in component potassium_current_n_gate (pms)');
    LEGEND_CONSTANTS(:,22) = strpad('alpha_n_max in component potassium_current_n_gate (pms)');
    LEGEND_CONSTANTS(:,23) = strpad('beta_n_max in component potassium_current_n_gate (pms)');
    LEGEND_CONSTANTS(:,24) = strpad('En in component potassium_current_n_gate (mV)');
    LEGEND_CONSTANTS(:,25) = strpad('v_alpha_n in component potassium_current_n_gate (dimensionless)');
    LEGEND_CONSTANTS(:,26) = strpad('v_beta_n in component potassium_current_n_gate (mV)');
    LEGEND_CONSTANTS(:,27) = strpad('EL in component leak_current (mV)');
    LEGEND_CONSTANTS(:,28) = strpad('gL_max in component leak_current (mSpmmsq)');
    LEGEND_CONSTANTS(:,29) = strpad('Rs in component Ttubular_current (mmsqpmS)');
    LEGEND_CONSTANTS(:,30) = strpad('Ct in component Ttubular_current_Vt_var (uFpmmsq)');
    LEGEND_RATES(:,1) = strpad('d/dt Vm in component membrane (mV)');
    LEGEND_RATES(:,3) = strpad('d/dt m in component sodium_current_m_gate (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt h in component sodium_current_h_gate (dimensionless)');
    LEGEND_RATES(:,5) = strpad('d/dt n in component potassium_current_n_gate (dimensionless)');
    LEGEND_RATES(:,2) = strpad('d/dt Vt in component Ttubular_current_Vt_var (mV)');
    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) = 0.009;
    CONSTANTS(:,2) = 200.0;
    STATES(:,1) = -95.0;
    STATES(:,2) = -95.0;
    STATES(:,3) = 0.0;
    STATES(:,4) = 1.0;
    STATES(:,5) = 0.0;
    CONSTANTS(:,3) = 10;
    CONSTANTS(:,4) = 50000;
    CONSTANTS(:,5) = 0.5;
    CONSTANTS(:,6) = 1000;
    CONSTANTS(:,7) = 1;
    CONSTANTS(:,8) = 1.8;
    CONSTANTS(:,9) = 50.0;
    CONSTANTS(:,10) = 0.208;
    CONSTANTS(:,11) = 2.081;
    CONSTANTS(:,12) = -42.0;
    CONSTANTS(:,13) = 10.0;
    CONSTANTS(:,14) = 18.0;
    CONSTANTS(:,15) = 0.0156;
    CONSTANTS(:,16) = 3.382;
    CONSTANTS(:,17) = -41.0;
    CONSTANTS(:,18) = 14.7;
    CONSTANTS(:,19) = 7.6;
    CONSTANTS(:,20) = 0.415;
    CONSTANTS(:,21) = -70.0;
    CONSTANTS(:,22) = 0.0229;
    CONSTANTS(:,23) = 0.09616;
    CONSTANTS(:,24) = -40.0;
    CONSTANTS(:,25) = 7.0;
    CONSTANTS(:,26) = 40.0;
    CONSTANTS(:,27) = -95.0;
    CONSTANTS(:,28) = 0.0024;
    CONSTANTS(:,29) = 15.0;
    CONSTANTS(:,30) = 0.04;
    CONSTANTS(:,31) = CONSTANTS(:,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);
        utilOnes = 1;
    else
        statesRowCount = statesSize(1);
        ALGEBRAIC = zeros(statesRowCount, algebraicVariableCount);
        RATES = zeros(statesRowCount, statesColumnCount);
        utilOnes = ones(statesRowCount, 1);
    end
    RATES(:,2) = (STATES(:,1) - STATES(:,2))./( CONSTANTS(:,29).*CONSTANTS(:,30));
    ALGEBRAIC(:,2) = ( CONSTANTS(:,10).*(STATES(:,1) - CONSTANTS(:,12)))./(1.00000 - exp((CONSTANTS(:,12) - STATES(:,1))./CONSTANTS(:,13)));
    ALGEBRAIC(:,7) =  CONSTANTS(:,11).*exp((CONSTANTS(:,12) - STATES(:,1))./CONSTANTS(:,14));
    RATES(:,3) =  ALGEBRAIC(:,2).*(1.00000 - STATES(:,3)) -  ALGEBRAIC(:,7).*STATES(:,3);
    ALGEBRAIC(:,3) =  CONSTANTS(:,15).*exp((CONSTANTS(:,17) - STATES(:,1))./CONSTANTS(:,18));
    ALGEBRAIC(:,8) = CONSTANTS(:,16)./(1.00000+exp((CONSTANTS(:,17) - STATES(:,1))./CONSTANTS(:,19)));
    RATES(:,4) =  ALGEBRAIC(:,3).*(1.00000 - STATES(:,4)) -  ALGEBRAIC(:,8).*STATES(:,4);
    ALGEBRAIC(:,4) = ( CONSTANTS(:,22).*(STATES(:,1) - CONSTANTS(:,24)))./(1.00000 - exp((CONSTANTS(:,24) - STATES(:,1))./CONSTANTS(:,25)));
    ALGEBRAIC(:,9) =  CONSTANTS(:,23).*exp((CONSTANTS(:,24) - STATES(:,1))./CONSTANTS(:,26));
    RATES(:,5) =  ALGEBRAIC(:,4).*(1.00000 - STATES(:,5)) -  ALGEBRAIC(:,9).*STATES(:,5);
    ALGEBRAIC(:,1) = piecewise({VOI>=CONSTANTS(:,3)&VOI<=CONSTANTS(:,4)&(VOI - CONSTANTS(:,3)) -  floor((VOI - CONSTANTS(:,3))./CONSTANTS(:,6)).*CONSTANTS(:,6)<=CONSTANTS(:,7), CONSTANTS(:,5) }, 0.00000);
    ALGEBRAIC(:,5) =  CONSTANTS(:,8).*STATES(:,3).*STATES(:,3).*STATES(:,3).*STATES(:,4).*(STATES(:,1) - CONSTANTS(:,9));
    ALGEBRAIC(:,10) =  CONSTANTS(:,20).*STATES(:,5).*STATES(:,5).*STATES(:,5).*STATES(:,5).*(STATES(:,1) - CONSTANTS(:,21));
    ALGEBRAIC(:,11) =  CONSTANTS(:,28).*(STATES(:,1) - CONSTANTS(:,27));
    ALGEBRAIC(:,12) = (STATES(:,1) - STATES(:,2))./CONSTANTS(:,29);
    RATES(:,1) = (ALGEBRAIC(:,1) - (ALGEBRAIC(:,5)+ALGEBRAIC(:,10)+ALGEBRAIC(:,11)+ALGEBRAIC(:,12)))./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) = ( CONSTANTS(:,10).*(STATES(:,1) - CONSTANTS(:,12)))./(1.00000 - exp((CONSTANTS(:,12) - STATES(:,1))./CONSTANTS(:,13)));
    ALGEBRAIC(:,7) =  CONSTANTS(:,11).*exp((CONSTANTS(:,12) - STATES(:,1))./CONSTANTS(:,14));
    ALGEBRAIC(:,3) =  CONSTANTS(:,15).*exp((CONSTANTS(:,17) - STATES(:,1))./CONSTANTS(:,18));
    ALGEBRAIC(:,8) = CONSTANTS(:,16)./(1.00000+exp((CONSTANTS(:,17) - STATES(:,1))./CONSTANTS(:,19)));
    ALGEBRAIC(:,4) = ( CONSTANTS(:,22).*(STATES(:,1) - CONSTANTS(:,24)))./(1.00000 - exp((CONSTANTS(:,24) - STATES(:,1))./CONSTANTS(:,25)));
    ALGEBRAIC(:,9) =  CONSTANTS(:,23).*exp((CONSTANTS(:,24) - STATES(:,1))./CONSTANTS(:,26));
    ALGEBRAIC(:,1) = piecewise({VOI>=CONSTANTS(:,3)&VOI<=CONSTANTS(:,4)&(VOI - CONSTANTS(:,3)) -  floor((VOI - CONSTANTS(:,3))./CONSTANTS(:,6)).*CONSTANTS(:,6)<=CONSTANTS(:,7), CONSTANTS(:,5) }, 0.00000);
    ALGEBRAIC(:,5) =  CONSTANTS(:,8).*STATES(:,3).*STATES(:,3).*STATES(:,3).*STATES(:,4).*(STATES(:,1) - CONSTANTS(:,9));
    ALGEBRAIC(:,10) =  CONSTANTS(:,20).*STATES(:,5).*STATES(:,5).*STATES(:,5).*STATES(:,5).*(STATES(:,1) - CONSTANTS(:,21));
    ALGEBRAIC(:,11) =  CONSTANTS(:,28).*(STATES(:,1) - CONSTANTS(:,27));
    ALGEBRAIC(:,12) = (STATES(:,1) - STATES(:,2))./CONSTANTS(:,29);
    ALGEBRAIC(:,6) = ALGEBRAIC(:,1);
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