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 32 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 (femtofarad)');
    LEGEND_ALGEBRAIC(:,6) = strpad('Ica in component Ica (femtoampere)');
    LEGEND_ALGEBRAIC(:,8) = strpad('Is1 in component Is1 (femtoampere)');
    LEGEND_ALGEBRAIC(:,12) = strpad('Is2 in component Is2 (femtoampere)');
    LEGEND_ALGEBRAIC(:,11) = strpad('Il in component Il (femtoampere)');
    LEGEND_ALGEBRAIC(:,9) = strpad('Ik in component Ik (femtoampere)');
    LEGEND_CONSTANTS(:,2) = strpad('gCa in component Ica (picosiemens)');
    LEGEND_CONSTANTS(:,3) = strpad('VCa in component Ica (millivolt)');
    LEGEND_ALGEBRAIC(:,1) = strpad('m_infinity in component m (dimensionless)');
    LEGEND_CONSTANTS(:,4) = strpad('vm in component m (millivolt)');
    LEGEND_CONSTANTS(:,5) = strpad('sm in component m (millivolt)');
    LEGEND_CONSTANTS(:,6) = strpad('gs1 in component Is1 (picosiemens)');
    LEGEND_CONSTANTS(:,7) = strpad('VK in component Ik (millivolt)');
    LEGEND_STATES(:,2) = strpad('s1 in component s1 (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('s1_infinity in component s1 (dimensionless)');
    LEGEND_CONSTANTS(:,8) = strpad('autos1 in component s1 (dimensionless)');
    LEGEND_CONSTANTS(:,9) = strpad('s1knot in component s1 (dimensionless)');
    LEGEND_CONSTANTS(:,10) = strpad('tau_s1 in component s1 (millisecond)');
    LEGEND_CONSTANTS(:,11) = strpad('vs1 in component s1 (millivolt)');
    LEGEND_CONSTANTS(:,12) = strpad('ss1 in component s1 (millivolt)');
    LEGEND_CONSTANTS(:,13) = strpad('gK in component Ik (picosiemens)');
    LEGEND_STATES(:,3) = strpad('n in component n (dimensionless)');
    LEGEND_ALGEBRAIC(:,3) = strpad('n_infinity in component n (dimensionless)');
    LEGEND_CONSTANTS(:,14) = strpad('tau_n_bar in component n (millisecond)');
    LEGEND_ALGEBRAIC(:,7) = strpad('tau_n in component n (millisecond)');
    LEGEND_CONSTANTS(:,15) = strpad('vn in component n (millivolt)');
    LEGEND_CONSTANTS(:,16) = strpad('sn in component n (millivolt)');
    LEGEND_CONSTANTS(:,17) = strpad('gl in component Il (picosiemens)');
    LEGEND_CONSTANTS(:,18) = strpad('Vl in component Il (millivolt)');
    LEGEND_ALGEBRAIC(:,10) = strpad('q in component Il (dimensionless)');
    LEGEND_STATES(:,4) = strpad('p in component Il (dimensionless)');
    LEGEND_CONSTANTS(:,19) = strpad('alpha_p in component Il (dimensionless)');
    LEGEND_CONSTANTS(:,20) = strpad('tau_p in component Il (millisecond)');
    LEGEND_CONSTANTS(:,31) = strpad('beta_p in component Il (dimensionless)');
    LEGEND_CONSTANTS(:,21) = strpad('p0 in component Il (dimensionless)');
    LEGEND_CONSTANTS(:,22) = strpad('noise in component Il (dimensionless)');
    LEGEND_ALGEBRAIC(:,4) = strpad('sigma in component Il (dimensionless)');
    LEGEND_CONSTANTS(:,23) = strpad('w in component Il (dimensionless)');
    LEGEND_CONSTANTS(:,32) = strpad('nstoc in component Il (dimensionless)');
    LEGEND_CONSTANTS(:,24) = strpad('delNoise in component Il (dimensionless)');
    LEGEND_CONSTANTS(:,25) = strpad('gs2 in component Is2 (picosiemens)');
    LEGEND_STATES(:,5) = strpad('s2 in component s2 (dimensionless)');
    LEGEND_ALGEBRAIC(:,5) = strpad('s2_infinity in component s2 (dimensionless)');
    LEGEND_CONSTANTS(:,26) = strpad('autos2 in component s2 (dimensionless)');
    LEGEND_CONSTANTS(:,27) = strpad('s2knot in component s2 (dimensionless)');
    LEGEND_CONSTANTS(:,28) = strpad('tau_s2 in component s2 (millisecond)');
    LEGEND_CONSTANTS(:,29) = strpad('vs2 in component s2 (millivolt)');
    LEGEND_CONSTANTS(:,30) = strpad('ss2 in component s2 (millivolt)');
    LEGEND_RATES(:,1) = strpad('d/dt V in component membrane (millivolt)');
    LEGEND_RATES(:,2) = strpad('d/dt s1 in component s1 (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt n in component n (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt p in component Il (dimensionless)');
    LEGEND_RATES(:,5) = strpad('d/dt s2 in component s2 (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) = -40.0;
    CONSTANTS(:,1) = 4525.0;
    CONSTANTS(:,2) = 280.0;
    CONSTANTS(:,3) = 100.0;
    CONSTANTS(:,4) = -22.0;
    CONSTANTS(:,5) = 7.5;
    CONSTANTS(:,6) = 22.0;
    CONSTANTS(:,7) = -80.0;
    STATES(:,2) = 0.9;
    CONSTANTS(:,8) = 1;
    CONSTANTS(:,9) = 1;
    CONSTANTS(:,10) = 1000.0;
    CONSTANTS(:,11) = -50.0;
    CONSTANTS(:,12) = 5;
    CONSTANTS(:,13) = 1300.0;
    STATES(:,3) = 0.0;
    CONSTANTS(:,14) = 8.25;
    CONSTANTS(:,15) = -9.0;
    CONSTANTS(:,16) = 10.0;
    CONSTANTS(:,17) = 41.0;
    CONSTANTS(:,18) = -40.0;
    STATES(:,4) = 0.14;
    CONSTANTS(:,19) = 1.0;
    CONSTANTS(:,20) = 100.0;
    CONSTANTS(:,21) = 0.2;
    CONSTANTS(:,22) = 1;
    CONSTANTS(:,23) = 1;
    CONSTANTS(:,24) = 3;
    CONSTANTS(:,25) = 16;
    STATES(:,5) = 0.5;
    CONSTANTS(:,26) = 1;
    CONSTANTS(:,27) = 0.47;
    CONSTANTS(:,28) = 30000.0;
    CONSTANTS(:,29) = -40.0;
    CONSTANTS(:,30) = 15;
    CONSTANTS(:,31) =  CONSTANTS(:,19).*(1.00000./CONSTANTS(:,21) - 1.00000);
    CONSTANTS(:,32) = 1000.00./power(CONSTANTS(:,24), 2.00000);
    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./(1.00000+exp((CONSTANTS(:,11) - STATES(:,1))./CONSTANTS(:,12)));
    RATES(:,2) =  CONSTANTS(:,8).*((ALGEBRAIC(:,2) - STATES(:,2))./CONSTANTS(:,10))+ (1.00000 - CONSTANTS(:,8)).*(CONSTANTS(:,9) - STATES(:,2));
    ALGEBRAIC(:,4) = power((( CONSTANTS(:,19).*(1.00000 - STATES(:,4))+ CONSTANTS(:,31).*STATES(:,4))./( CONSTANTS(:,20).*CONSTANTS(:,32))), 1.0 ./ 2);
    RATES(:,4) = ( CONSTANTS(:,19).*(1.00000 - STATES(:,4)) -  CONSTANTS(:,31).*STATES(:,4))./CONSTANTS(:,20)+ CONSTANTS(:,22).*CONSTANTS(:,23).*ALGEBRAIC(:,4);
    ALGEBRAIC(:,5) = 1.00000./(1.00000+exp((CONSTANTS(:,29) - STATES(:,1))./CONSTANTS(:,30)));
    RATES(:,5) =  CONSTANTS(:,26).*((ALGEBRAIC(:,5) - STATES(:,5))./CONSTANTS(:,28))+ (1.00000 - CONSTANTS(:,26)).*(CONSTANTS(:,27) - STATES(:,5));
    ALGEBRAIC(:,3) = 1.00000./(1.00000+exp((CONSTANTS(:,15) - STATES(:,1))./CONSTANTS(:,16)));
    ALGEBRAIC(:,7) = CONSTANTS(:,14)./(1.00000+exp((STATES(:,1) - CONSTANTS(:,15))./CONSTANTS(:,16)));
    RATES(:,3) = (ALGEBRAIC(:,3) - STATES(:,3))./ALGEBRAIC(:,7);
    ALGEBRAIC(:,1) = 1.00000./(1.00000+exp((CONSTANTS(:,4) - STATES(:,1))./CONSTANTS(:,5)));
    ALGEBRAIC(:,6) =  CONSTANTS(:,2).*ALGEBRAIC(:,1).*(STATES(:,1) - CONSTANTS(:,3));
    ALGEBRAIC(:,8) =  CONSTANTS(:,6).*STATES(:,2).*(STATES(:,1) - CONSTANTS(:,7));
    ALGEBRAIC(:,12) =  CONSTANTS(:,25).*STATES(:,5).*(STATES(:,1) - CONSTANTS(:,7));
    ALGEBRAIC(:,10) = (1.00000+STATES(:,4))./2.00000;
    ALGEBRAIC(:,11) =  CONSTANTS(:,17).*ALGEBRAIC(:,10).*(STATES(:,1) - CONSTANTS(:,18));
    ALGEBRAIC(:,9) =  CONSTANTS(:,13).*STATES(:,3).*(STATES(:,1) - CONSTANTS(:,7));
    RATES(:,1) =  - (ALGEBRAIC(:,6)+ALGEBRAIC(:,8)+ALGEBRAIC(:,12)+ALGEBRAIC(:,11)+ALGEBRAIC(:,9))./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./(1.00000+exp((CONSTANTS(:,11) - STATES(:,1))./CONSTANTS(:,12)));
    ALGEBRAIC(:,4) = power((( CONSTANTS(:,19).*(1.00000 - STATES(:,4))+ CONSTANTS(:,31).*STATES(:,4))./( CONSTANTS(:,20).*CONSTANTS(:,32))), 1.0 ./ 2);
    ALGEBRAIC(:,5) = 1.00000./(1.00000+exp((CONSTANTS(:,29) - STATES(:,1))./CONSTANTS(:,30)));
    ALGEBRAIC(:,3) = 1.00000./(1.00000+exp((CONSTANTS(:,15) - STATES(:,1))./CONSTANTS(:,16)));
    ALGEBRAIC(:,7) = CONSTANTS(:,14)./(1.00000+exp((STATES(:,1) - CONSTANTS(:,15))./CONSTANTS(:,16)));
    ALGEBRAIC(:,1) = 1.00000./(1.00000+exp((CONSTANTS(:,4) - STATES(:,1))./CONSTANTS(:,5)));
    ALGEBRAIC(:,6) =  CONSTANTS(:,2).*ALGEBRAIC(:,1).*(STATES(:,1) - CONSTANTS(:,3));
    ALGEBRAIC(:,8) =  CONSTANTS(:,6).*STATES(:,2).*(STATES(:,1) - CONSTANTS(:,7));
    ALGEBRAIC(:,12) =  CONSTANTS(:,25).*STATES(:,5).*(STATES(:,1) - CONSTANTS(:,7));
    ALGEBRAIC(:,10) = (1.00000+STATES(:,4))./2.00000;
    ALGEBRAIC(:,11) =  CONSTANTS(:,17).*ALGEBRAIC(:,10).*(STATES(:,1) - CONSTANTS(:,18));
    ALGEBRAIC(:,9) =  CONSTANTS(:,13).*STATES(:,3).*(STATES(:,1) - CONSTANTS(:,7));
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