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 =17;
end
% There are a total of 7 entries in each of the rate and state variable arrays.
% There are a total of 1 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 (microF_per_cm2)');
    LEGEND_ALGEBRAIC(:,1) = strpad('i_Na in component sodium_channel (microA_per_cm2)');
    LEGEND_ALGEBRAIC(:,8) = strpad('i_K in component potassium_channel (microA_per_cm2)');
    LEGEND_ALGEBRAIC(:,15) = strpad('i_Leak in component leakage_current (microA_per_cm2)');
    LEGEND_ALGEBRAIC(:,16) = strpad('i_s in component calcium_channel (microA_per_cm2)');
    LEGEND_ALGEBRAIC(:,17) = strpad('i_h in component hyperpolarization_activated_channel (microA_per_cm2)');
    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(:,9) = 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(:,10) = strpad('beta_h in component sodium_channel_h_gate (per_millisecond)');
    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(:,11) = strpad('beta_n in component potassium_channel_n_gate (per_millisecond)');
    LEGEND_STATES(:,5) = strpad('d in component calcium_channel_d_gate (dimensionless)');
    LEGEND_STATES(:,6) = strpad('f in component calcium_channel_f_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,5) = strpad('alpha_d in component calcium_channel_d_gate (per_millisecond)');
    LEGEND_ALGEBRAIC(:,12) = strpad('beta_d in component calcium_channel_d_gate (per_millisecond)');
    LEGEND_ALGEBRAIC(:,6) = strpad('alpha_f in component calcium_channel_f_gate (per_millisecond)');
    LEGEND_ALGEBRAIC(:,13) = strpad('beta_f in component calcium_channel_f_gate (per_millisecond)');
    LEGEND_STATES(:,7) = strpad('q in component hyperpolarization_activated_channel_q_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,7) = strpad('alpha_q in component hyperpolarization_activated_channel_q_gate (per_millisecond)');
    LEGEND_ALGEBRAIC(:,14) = strpad('beta_q in component hyperpolarization_activated_channel_q_gate (per_millisecond)');
    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_RATES(:,5) = strpad('d/dt d in component calcium_channel_d_gate (dimensionless)');
    LEGEND_RATES(:,6) = strpad('d/dt f in component calcium_channel_f_gate (dimensionless)');
    LEGEND_RATES(:,7) = strpad('d/dt q in component hyperpolarization_activated_channel_q_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) = -62.83;
    CONSTANTS(:,1) = 1;
    STATES(:,2) = 0.047938;
    STATES(:,3) = 0.95994;
    STATES(:,4) = 0.509494;
    STATES(:,5) = 0.000032;
    STATES(:,6) = 1;
    STATES(:,7) = 0.010759;
    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.*(STATES(:,1)+37.0000))./( - exp((STATES(:,1)+37.0000)./ - 10.0000)+1.00000);
    ALGEBRAIC(:,9) =  40.0000.*exp((STATES(:,1)+62.0000)./ - 17.8000);
    RATES(:,2) =  ALGEBRAIC(:,2).*(1.00000 - STATES(:,2)) -  ALGEBRAIC(:,9).*STATES(:,2);
    ALGEBRAIC(:,3) =  0.00120900.*exp((STATES(:,1)+20.0000)./ - 6.53400);
    ALGEBRAIC(:,10) = 1.00000./(1.00000+exp((STATES(:,1)+30.0000)./ - 10.0000));
    RATES(:,3) =  ALGEBRAIC(:,3).*(1.00000 - STATES(:,3)) -  ALGEBRAIC(:,10).*STATES(:,3);
    ALGEBRAIC(:,4) = ( 0.00900000.*1.00000)./(1.00000+exp( - (STATES(:,1)+3.80000)./9.71000))+0.000600000;
    ALGEBRAIC(:,11) = (  - 0.000225000.*(STATES(:,1)+40.0000))./(1.00000 - exp((STATES(:,1)+40.0000)./13.3000));
    RATES(:,4) =  ALGEBRAIC(:,4).*(1.00000 - STATES(:,4)) -  ALGEBRAIC(:,11).*STATES(:,4);
    ALGEBRAIC(:,5) = ( 0.0145000.*(STATES(:,1)+35.0000))./(1.00000 - exp( - (STATES(:,1)+35.0000)./2.50000))+( 0.0312500.*STATES(:,1))./(1.00000 - exp( - STATES(:,1)./4.80000));
    ALGEBRAIC(:,12) = (  - 0.00421000.*(STATES(:,1) - 5.00000))./( - exp((STATES(:,1) - 5.00000)./2.50000)+1.00000);
    RATES(:,5) =  ALGEBRAIC(:,5).*(1.00000 - STATES(:,5)) -  ALGEBRAIC(:,12).*STATES(:,5);
    ALGEBRAIC(:,6) = (  - 0.000355000.*(STATES(:,1)+20.0000))./( - exp((STATES(:,1)+20.0000)./5.63300)+1.00000);
    ALGEBRAIC(:,13) = ( 0.000944000.*(STATES(:,1)+60.0000))./(1.00000+exp( - (STATES(:,1)+29.5000)./4.16000));
    RATES(:,6) =  ALGEBRAIC(:,6).*(1.00000 - STATES(:,6)) -  ALGEBRAIC(:,13).*STATES(:,6);
    ALGEBRAIC(:,7) = ( 0.000340000.*(STATES(:,1)+100.000))./(exp((STATES(:,1)+100.000)./4.40000) - 1.00000)+4.95000e-05;
    ALGEBRAIC(:,14) = ( 0.000500000.*(STATES(:,1)+40.0000))./(1.00000 - exp( - (STATES(:,1)+40.0000)./6.00000))+8.45000e-05;
    RATES(:,7) =  ALGEBRAIC(:,7).*(1.00000 - STATES(:,7)) -  ALGEBRAIC(:,14).*STATES(:,7);
    ALGEBRAIC(:,1) =  0.500000.*power(STATES(:,2), 3.00000).*STATES(:,3).*(STATES(:,1) - 30.0000);
    ALGEBRAIC(:,8) = ( 0.700000.*STATES(:,4).*(exp( 0.0277000.*(STATES(:,1)+90.0000)) - 1.00000))./exp( 0.0277000.*(STATES(:,1)+40.0000));
    ALGEBRAIC(:,15) =  0.800000.*(1.00000 - exp( - (STATES(:,1)+60.0000)./20.0000));
    ALGEBRAIC(:,16) =  12.5000.*( 0.950000.*STATES(:,5)+0.0500000).*( 0.950000.*STATES(:,6)+0.0500000).*(exp((STATES(:,1) - 10.0000)./15.0000) - 1.00000);
    ALGEBRAIC(:,17) =  0.400000.*STATES(:,7).*(STATES(:,1)+45.0000);
    RATES(:,1) =  - (ALGEBRAIC(:,1)+ALGEBRAIC(:,8)+ALGEBRAIC(:,15)+ALGEBRAIC(:,16)+ALGEBRAIC(:,17))./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.*(STATES(:,1)+37.0000))./( - exp((STATES(:,1)+37.0000)./ - 10.0000)+1.00000);
    ALGEBRAIC(:,9) =  40.0000.*exp((STATES(:,1)+62.0000)./ - 17.8000);
    ALGEBRAIC(:,3) =  0.00120900.*exp((STATES(:,1)+20.0000)./ - 6.53400);
    ALGEBRAIC(:,10) = 1.00000./(1.00000+exp((STATES(:,1)+30.0000)./ - 10.0000));
    ALGEBRAIC(:,4) = ( 0.00900000.*1.00000)./(1.00000+exp( - (STATES(:,1)+3.80000)./9.71000))+0.000600000;
    ALGEBRAIC(:,11) = (  - 0.000225000.*(STATES(:,1)+40.0000))./(1.00000 - exp((STATES(:,1)+40.0000)./13.3000));
    ALGEBRAIC(:,5) = ( 0.0145000.*(STATES(:,1)+35.0000))./(1.00000 - exp( - (STATES(:,1)+35.0000)./2.50000))+( 0.0312500.*STATES(:,1))./(1.00000 - exp( - STATES(:,1)./4.80000));
    ALGEBRAIC(:,12) = (  - 0.00421000.*(STATES(:,1) - 5.00000))./( - exp((STATES(:,1) - 5.00000)./2.50000)+1.00000);
    ALGEBRAIC(:,6) = (  - 0.000355000.*(STATES(:,1)+20.0000))./( - exp((STATES(:,1)+20.0000)./5.63300)+1.00000);
    ALGEBRAIC(:,13) = ( 0.000944000.*(STATES(:,1)+60.0000))./(1.00000+exp( - (STATES(:,1)+29.5000)./4.16000));
    ALGEBRAIC(:,7) = ( 0.000340000.*(STATES(:,1)+100.000))./(exp((STATES(:,1)+100.000)./4.40000) - 1.00000)+4.95000e-05;
    ALGEBRAIC(:,14) = ( 0.000500000.*(STATES(:,1)+40.0000))./(1.00000 - exp( - (STATES(:,1)+40.0000)./6.00000))+8.45000e-05;
    ALGEBRAIC(:,1) =  0.500000.*power(STATES(:,2), 3.00000).*STATES(:,3).*(STATES(:,1) - 30.0000);
    ALGEBRAIC(:,8) = ( 0.700000.*STATES(:,4).*(exp( 0.0277000.*(STATES(:,1)+90.0000)) - 1.00000))./exp( 0.0277000.*(STATES(:,1)+40.0000));
    ALGEBRAIC(:,15) =  0.800000.*(1.00000 - exp( - (STATES(:,1)+60.0000)./20.0000));
    ALGEBRAIC(:,16) =  12.5000.*( 0.950000.*STATES(:,5)+0.0500000).*( 0.950000.*STATES(:,6)+0.0500000).*(exp((STATES(:,1) - 10.0000)./15.0000) - 1.00000);
    ALGEBRAIC(:,17) =  0.400000.*STATES(:,7).*(STATES(:,1)+45.0000);
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