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 5 entries in each of the rate and state variable arrays.
% There are a total of 15 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_ALGEBRAIC(:,1) = strpad('Vs in component membrane (millivolt)');
    LEGEND_CONSTANTS(:,1) = strpad('V_I in component membrane (millivolt)');
    LEGEND_CONSTANTS(:,2) = strpad('V_K in component membrane (millivolt)');
    LEGEND_CONSTANTS(:,3) = strpad('V_L in component membrane (millivolt)');
    LEGEND_CONSTANTS(:,4) = strpad('V_H_Na in component membrane (millivolt)');
    LEGEND_CONSTANTS(:,5) = strpad('V_H_K in component membrane (millivolt)');
    LEGEND_CONSTANTS(:,14) = strpad('g_I in component membrane (milliS_per_microF)');
    LEGEND_CONSTANTS(:,6) = strpad('g_K in component membrane (milliS_per_microF)');
    LEGEND_CONSTANTS(:,7) = strpad('g_L in component membrane (milliS_per_microF)');
    LEGEND_CONSTANTS(:,15) = strpad('g_T in component membrane (milliS_per_microF)');
    LEGEND_CONSTANTS(:,8) = strpad('g_P in component membrane (milliS_per_microF)');
    LEGEND_CONSTANTS(:,9) = strpad('Kp in component membrane (millimolar)');
    LEGEND_STATES(:,2) = strpad('c in component calcium_concentration (millimolar)');
    LEGEND_ALGEBRAIC(:,9) = strpad('sI in component sI_gate (dimensionless)');
    LEGEND_STATES(:,3) = strpad('yI in component yI_gate (dimensionless)');
    LEGEND_STATES(:,4) = strpad('xT in component xT_gate (dimensionless)');
    LEGEND_STATES(:,5) = strpad('xK in component xK_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('alpha_m in component sI_gate (per_millisecond)');
    LEGEND_ALGEBRAIC(:,6) = strpad('beta_m in component sI_gate (per_millisecond)');
    LEGEND_ALGEBRAIC(:,10) = strpad('ZI in component yI_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,3) = strpad('alpha_h in component yI_gate (per_millisecond)');
    LEGEND_ALGEBRAIC(:,7) = strpad('beta_h in component yI_gate (per_millisecond)');
    LEGEND_ALGEBRAIC(:,12) = strpad('tau_yI in component yI_gate (millisecond)');
    LEGEND_ALGEBRAIC(:,4) = strpad('sT in component xT_gate (dimensionless)');
    LEGEND_CONSTANTS(:,10) = strpad('tau_xT in component xT_gate (millisecond)');
    LEGEND_CONSTANTS(:,11) = strpad('V_Ca in component calcium_concentration (millivolt)');
    LEGEND_CONSTANTS(:,12) = strpad('rho in component calcium_concentration (per_millisecond)');
    LEGEND_CONSTANTS(:,13) = strpad('K_c in component calcium_concentration (millimolar_per_millivolt)');
    LEGEND_ALGEBRAIC(:,5) = strpad('alpha_n in component xK_gate (per_millisecond)');
    LEGEND_ALGEBRAIC(:,8) = strpad('beta_n in component xK_gate (per_millisecond)');
    LEGEND_ALGEBRAIC(:,13) = strpad('tau_xK in component xK_gate (millisecond)');
    LEGEND_ALGEBRAIC(:,11) = strpad('sK in component xK_gate (dimensionless)');
    LEGEND_RATES(:,1) = strpad('d/dt V in component membrane (millivolt)');
    LEGEND_RATES(:,3) = strpad('d/dt yI in component yI_gate (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt xT in component xT_gate (dimensionless)');
    LEGEND_RATES(:,2) = strpad('d/dt c in component calcium_concentration (millimolar)');
    LEGEND_RATES(:,5) = strpad('d/dt xK in component xK_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) = -54;
    CONSTANTS(:,1) = 30.0;
    CONSTANTS(:,2) = -75.0;
    CONSTANTS(:,3) = -40.0;
    CONSTANTS(:,4) = 115.0;
    CONSTANTS(:,5) = -12.0;
    CONSTANTS(:,6) = 0.3;
    CONSTANTS(:,7) = 0.003;
    CONSTANTS(:,8) = 0.03;
    CONSTANTS(:,9) = 0.5;
    STATES(:,2) = 0.1;
    STATES(:,3) = 0.1;
    STATES(:,4) = 0.1;
    STATES(:,5) = 0.1;
    CONSTANTS(:,10) = 235.0;
    CONSTANTS(:,11) = 140.0;
    CONSTANTS(:,12) = 0.0003;
    CONSTANTS(:,13) = 0.0085;
    CONSTANTS(:,14) =  1.00000.*((CONSTANTS(:,4) - CONSTANTS(:,5))./(CONSTANTS(:,1) - CONSTANTS(:,2)));
    CONSTANTS(:,15) =  1.00000.*(( CONSTANTS(:,4).*CONSTANTS(:,2) -  CONSTANTS(:,1).*CONSTANTS(:,5))./(CONSTANTS(:,1) - 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) =  CONSTANTS(:,12).*( CONSTANTS(:,13).*STATES(:,4).*(CONSTANTS(:,11) - STATES(:,1)) - STATES(:,2));
    ALGEBRAIC(:,1) =  1.00000.*CONSTANTS(:,14).*STATES(:,1)+ 1.00000.*CONSTANTS(:,15);
    ALGEBRAIC(:,4) = 1.00000./(exp( 0.150000.*(-50.0000 - ALGEBRAIC(:,1)))+1.00000);
    RATES(:,4) = (ALGEBRAIC(:,4) - STATES(:,4))./CONSTANTS(:,10);
    ALGEBRAIC(:,2) = ( 0.100000.*(50.0000 - ALGEBRAIC(:,1)))./ - exp((50.0000 - ALGEBRAIC(:,1))./10.0000);
    ALGEBRAIC(:,6) =  4.00000.*exp((25.0000 - ALGEBRAIC(:,1))./18.0000);
    ALGEBRAIC(:,9) = ALGEBRAIC(:,2)./(ALGEBRAIC(:,2)+ALGEBRAIC(:,6));
    RATES(:,1) =  ( CONSTANTS(:,14).*power(ALGEBRAIC(:,9), 3.00000).*STATES(:,3)+ CONSTANTS(:,15).*STATES(:,4)).*(CONSTANTS(:,1) - STATES(:,1))+ ( CONSTANTS(:,6).*power(STATES(:,5), 4.00000)+ CONSTANTS(:,8).*STATES(:,2).*power(CONSTANTS(:,9)+STATES(:,2), -1.00000)).*(CONSTANTS(:,2) - STATES(:,1))+ CONSTANTS(:,7).*(CONSTANTS(:,3) - STATES(:,1));
    ALGEBRAIC(:,3) =  0.0700000.*exp((25.0000 - ALGEBRAIC(:,1))./20.0000);
    ALGEBRAIC(:,7) = 1.00000./(exp((55.0000 - ALGEBRAIC(:,1))./10.0000)+1.00000);
    ALGEBRAIC(:,10) = ALGEBRAIC(:,3)./(ALGEBRAIC(:,3)+ALGEBRAIC(:,7));
    ALGEBRAIC(:,12) = 12.5000./(ALGEBRAIC(:,3)+ALGEBRAIC(:,7));
    RATES(:,3) = (ALGEBRAIC(:,10) - STATES(:,3))./ALGEBRAIC(:,12);
    ALGEBRAIC(:,5) = ( 0.0100000.*(55.0000 - ALGEBRAIC(:,1)))./(exp((55.0000 - ALGEBRAIC(:,1))./10.0000) - 1.00000);
    ALGEBRAIC(:,8) =  0.125000.*exp((45.0000 - ALGEBRAIC(:,1))./80.0000);
    ALGEBRAIC(:,13) = 12.5000./(ALGEBRAIC(:,5)+ALGEBRAIC(:,8));
    ALGEBRAIC(:,11) = ALGEBRAIC(:,5)./(ALGEBRAIC(:,5)+ALGEBRAIC(:,8));
    RATES(:,5) = (ALGEBRAIC(:,11) - STATES(:,5))./ALGEBRAIC(:,13);
   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(:,1) =  1.00000.*CONSTANTS(:,14).*STATES(:,1)+ 1.00000.*CONSTANTS(:,15);
    ALGEBRAIC(:,4) = 1.00000./(exp( 0.150000.*(-50.0000 - ALGEBRAIC(:,1)))+1.00000);
    ALGEBRAIC(:,2) = ( 0.100000.*(50.0000 - ALGEBRAIC(:,1)))./ - exp((50.0000 - ALGEBRAIC(:,1))./10.0000);
    ALGEBRAIC(:,6) =  4.00000.*exp((25.0000 - ALGEBRAIC(:,1))./18.0000);
    ALGEBRAIC(:,9) = ALGEBRAIC(:,2)./(ALGEBRAIC(:,2)+ALGEBRAIC(:,6));
    ALGEBRAIC(:,3) =  0.0700000.*exp((25.0000 - ALGEBRAIC(:,1))./20.0000);
    ALGEBRAIC(:,7) = 1.00000./(exp((55.0000 - ALGEBRAIC(:,1))./10.0000)+1.00000);
    ALGEBRAIC(:,10) = ALGEBRAIC(:,3)./(ALGEBRAIC(:,3)+ALGEBRAIC(:,7));
    ALGEBRAIC(:,12) = 12.5000./(ALGEBRAIC(:,3)+ALGEBRAIC(:,7));
    ALGEBRAIC(:,5) = ( 0.0100000.*(55.0000 - ALGEBRAIC(:,1)))./(exp((55.0000 - ALGEBRAIC(:,1))./10.0000) - 1.00000);
    ALGEBRAIC(:,8) =  0.125000.*exp((45.0000 - ALGEBRAIC(:,1))./80.0000);
    ALGEBRAIC(:,13) = 12.5000./(ALGEBRAIC(:,5)+ALGEBRAIC(:,8));
    ALGEBRAIC(:,11) = ALGEBRAIC(:,5)./(ALGEBRAIC(:,5)+ALGEBRAIC(:,8));
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