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 =5;
end
% There are a total of 1 entries in each of the rate and state variable arrays.
% There are a total of 5 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_ALGEBRAIC(:,1) = strpad('V in component environment (millivolt)');
    LEGEND_VOI = strpad('t in component environment (millisec)');
    LEGEND_STATES(:,1) = strpad('n in component potassium_channel_n_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,4) = strpad('i_K in component potassium_channel (microA_per_cm2)');
    LEGEND_CONSTANTS(:,1) = strpad('g_K in component potassium_channel (milliS_per_cm2)');
    LEGEND_CONSTANTS(:,2) = strpad('Ki in component potassium_channel (mM)');
    LEGEND_CONSTANTS(:,3) = strpad('Ko in component potassium_channel (mM)');
    LEGEND_CONSTANTS(:,4) = strpad('RTF in component potassium_channel (millivolt)');
    LEGEND_CONSTANTS(:,5) = strpad('E_K in component potassium_channel (millivolt)');
    LEGEND_ALGEBRAIC(:,2) = strpad('K_conductance in component potassium_channel (milliS_per_cm2)');
    LEGEND_ALGEBRAIC(:,3) = strpad('alpha_n in component potassium_channel_n_gate (per_millisec)');
    LEGEND_ALGEBRAIC(:,5) = strpad('beta_n in component potassium_channel_n_gate (per_millisec)');
    LEGEND_RATES(:,1) = strpad('d/dt n in component potassium_channel_n_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) = 0.325;
    CONSTANTS(:,1) = 36;
    CONSTANTS(:,2) = 90;
    CONSTANTS(:,3) = 3;
    CONSTANTS(:,4) = 25;
    CONSTANTS(:,5) =  CONSTANTS(:,4).*log(CONSTANTS(:,3)./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
    ALGEBRAIC(:,1) = piecewise({VOI>5.00000&VOI<15.0000,  - 85.0000 }, 0.00000);
    ALGEBRAIC(:,3) = ( 0.0100000.*(ALGEBRAIC(:,1)+10.0000))./(exp((ALGEBRAIC(:,1)+10.0000)./10.0000) - 1.00000);
    ALGEBRAIC(:,5) =  0.125000.*exp(ALGEBRAIC(:,1)./80.0000);
    RATES(:,1) =  ALGEBRAIC(:,3).*(1.00000 - STATES(:,1)) -  ALGEBRAIC(:,5).*STATES(:,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(:,1) = piecewise({VOI>5.00000&VOI<15.0000,  - 85.0000 }, 0.00000);
    ALGEBRAIC(:,3) = ( 0.0100000.*(ALGEBRAIC(:,1)+10.0000))./(exp((ALGEBRAIC(:,1)+10.0000)./10.0000) - 1.00000);
    ALGEBRAIC(:,5) =  0.125000.*exp(ALGEBRAIC(:,1)./80.0000);
    ALGEBRAIC(:,2) =  CONSTANTS(:,1).*power(STATES(:,1), 4.00000);
    ALGEBRAIC(:,4) =  ALGEBRAIC(:,2).*(ALGEBRAIC(:,1) - CONSTANTS(:,5));
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