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 =11;
end
% There are a total of 4 entries in each of the rate and state variable arrays.
% There are a total of 23 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('C in component membrane (picofarad)');
    LEGEND_ALGEBRAIC(:,6) = strpad('I_Ca in component I_Ca (picoampere)');
    LEGEND_ALGEBRAIC(:,1) = strpad('I_K in component I_K (picoampere)');
    LEGEND_ALGEBRAIC(:,8) = strpad('I_SK in component I_SK (picoampere)');
    LEGEND_ALGEBRAIC(:,11) = strpad('I_DA in component I_DA (picoampere)');
    LEGEND_CONSTANTS(:,2) = strpad('gK in component I_K (nanosiemens)');
    LEGEND_CONSTANTS(:,3) = strpad('VK in component model_parameters (millivolt)');
    LEGEND_STATES(:,2) = strpad('n in component n (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('n_infinity in component n (dimensionless)');
    LEGEND_CONSTANTS(:,4) = strpad('lambda in component n (dimensionless)');
    LEGEND_CONSTANTS(:,5) = strpad('tau_n in component n (millisecond)');
    LEGEND_CONSTANTS(:,6) = strpad('vn in component n (millivolt)');
    LEGEND_CONSTANTS(:,7) = strpad('sn in component n (millivolt)');
    LEGEND_CONSTANTS(:,8) = strpad('gCa in component I_Ca (nanosiemens)');
    LEGEND_CONSTANTS(:,9) = strpad('VCa in component model_parameters (millivolt)');
    LEGEND_ALGEBRAIC(:,5) = strpad('m_infinity in component m (dimensionless)');
    LEGEND_CONSTANTS(:,10) = strpad('vm in component m (millivolt)');
    LEGEND_CONSTANTS(:,11) = strpad('sm in component m (millivolt)');
    LEGEND_CONSTANTS(:,12) = strpad('gSK in component I_SK (nanosiemens)');
    LEGEND_ALGEBRAIC(:,7) = strpad('s_infinity in component I_SK (dimensionless)');
    LEGEND_CONSTANTS(:,13) = strpad('ks in component I_SK (micromolar)');
    LEGEND_STATES(:,3) = strpad('Ca in component Ca (micromolar)');
    LEGEND_ALGEBRAIC(:,10) = strpad('I_BK in component I_DA (picoampere)');
    LEGEND_CONSTANTS(:,14) = strpad('gBK in component I_DA (nanosiemens)');
    LEGEND_ALGEBRAIC(:,9) = strpad('f_infinity in component f (dimensionless)');
    LEGEND_CONSTANTS(:,15) = strpad('vf in component f (millivolt)');
    LEGEND_CONSTANTS(:,16) = strpad('sf in component f (millivolt)');
    LEGEND_STATES(:,4) = strpad('h in component h (dimensionless)');
    LEGEND_ALGEBRAIC(:,3) = strpad('h_infinity in component h (dimensionless)');
    LEGEND_CONSTANTS(:,17) = strpad('tau_h in component h (millisecond)');
    LEGEND_CONSTANTS(:,18) = strpad('vh in component h (millivolt)');
    LEGEND_CONSTANTS(:,19) = strpad('sh in component h (millivolt)');
    LEGEND_CONSTANTS(:,20) = strpad('fc in component Ca (dimensionless)');
    LEGEND_CONSTANTS(:,21) = strpad('alpha in component Ca (micromolar_femtocoulomb)');
    LEGEND_CONSTANTS(:,22) = strpad('kc in component Ca (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,4) = strpad('PRL in component PRL (dimensionless)');
    LEGEND_CONSTANTS(:,23) = strpad('kPRL in component PRL (micromolar_4)');
    LEGEND_RATES(:,1) = strpad('d/dt V in component membrane (millivolt)');
    LEGEND_RATES(:,2) = strpad('d/dt n in component n (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt h in component h (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt Ca in component Ca (micromolar)');
    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) = -60;
    CONSTANTS(:,1) = 10;
    CONSTANTS(:,2) = 4;
    CONSTANTS(:,3) = -75;
    STATES(:,2) = 0.1;
    CONSTANTS(:,4) = 0.7;
    CONSTANTS(:,5) = 30;
    CONSTANTS(:,6) = -5;
    CONSTANTS(:,7) = 10;
    CONSTANTS(:,8) = 2;
    CONSTANTS(:,9) = 50;
    CONSTANTS(:,10) = -20;
    CONSTANTS(:,11) = 12;
    CONSTANTS(:,12) = 1.7;
    CONSTANTS(:,13) = 0.5;
    STATES(:,3) = 0.1;
    CONSTANTS(:,14) = 0.2;
    CONSTANTS(:,15) = -20;
    CONSTANTS(:,16) = 5.6;
    STATES(:,4) = 0.1;
    CONSTANTS(:,17) = 20;
    CONSTANTS(:,18) = -60;
    CONSTANTS(:,19) = 5;
    CONSTANTS(:,20) = 0.01;
    CONSTANTS(:,21) = 0.0015;
    CONSTANTS(:,22) = 0.16;
    CONSTANTS(:,23) = 1;
    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(:,6) - STATES(:,1))./CONSTANTS(:,7)));
    RATES(:,2) = ( CONSTANTS(:,4).*(ALGEBRAIC(:,2) - STATES(:,2)))./CONSTANTS(:,5);
    ALGEBRAIC(:,3) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,18))./CONSTANTS(:,19)));
    RATES(:,4) = (ALGEBRAIC(:,3) - STATES(:,4))./CONSTANTS(:,17);
    ALGEBRAIC(:,5) = 1.00000./(1.00000+exp((CONSTANTS(:,10) - STATES(:,1))./CONSTANTS(:,11)));
    ALGEBRAIC(:,6) =  CONSTANTS(:,8).*ALGEBRAIC(:,5).*(STATES(:,1) - CONSTANTS(:,9));
    RATES(:,3) =   - CONSTANTS(:,20).*( CONSTANTS(:,21).*ALGEBRAIC(:,6)+ CONSTANTS(:,22).*STATES(:,3));
    ALGEBRAIC(:,1) =  CONSTANTS(:,2).*STATES(:,2).*(STATES(:,1) - CONSTANTS(:,3));
    ALGEBRAIC(:,7) = power(STATES(:,3), 2.00000)./(power(STATES(:,3), 2.00000)+power(CONSTANTS(:,13), 2.00000));
    ALGEBRAIC(:,8) =  CONSTANTS(:,12).*ALGEBRAIC(:,7).*(STATES(:,1) - CONSTANTS(:,3));
    ALGEBRAIC(:,9) = 1.00000./(1.00000+exp((CONSTANTS(:,15) - STATES(:,1))./CONSTANTS(:,16)));
    ALGEBRAIC(:,10) =  CONSTANTS(:,14).*ALGEBRAIC(:,9).*(STATES(:,1) - CONSTANTS(:,3));
    ALGEBRAIC(:,11) = ALGEBRAIC(:,10);
    RATES(:,1) =  - (ALGEBRAIC(:,6)+ALGEBRAIC(:,1)+ALGEBRAIC(:,8)+ALGEBRAIC(:,11))./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(:,6) - STATES(:,1))./CONSTANTS(:,7)));
    ALGEBRAIC(:,3) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,18))./CONSTANTS(:,19)));
    ALGEBRAIC(:,5) = 1.00000./(1.00000+exp((CONSTANTS(:,10) - STATES(:,1))./CONSTANTS(:,11)));
    ALGEBRAIC(:,6) =  CONSTANTS(:,8).*ALGEBRAIC(:,5).*(STATES(:,1) - CONSTANTS(:,9));
    ALGEBRAIC(:,1) =  CONSTANTS(:,2).*STATES(:,2).*(STATES(:,1) - CONSTANTS(:,3));
    ALGEBRAIC(:,7) = power(STATES(:,3), 2.00000)./(power(STATES(:,3), 2.00000)+power(CONSTANTS(:,13), 2.00000));
    ALGEBRAIC(:,8) =  CONSTANTS(:,12).*ALGEBRAIC(:,7).*(STATES(:,1) - CONSTANTS(:,3));
    ALGEBRAIC(:,9) = 1.00000./(1.00000+exp((CONSTANTS(:,15) - STATES(:,1))./CONSTANTS(:,16)));
    ALGEBRAIC(:,10) =  CONSTANTS(:,14).*ALGEBRAIC(:,9).*(STATES(:,1) - CONSTANTS(:,3));
    ALGEBRAIC(:,11) = ALGEBRAIC(:,10);
    ALGEBRAIC(:,4) =  CONSTANTS(:,23).*power(STATES(:,3), 4.00000);
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