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 =8;
end
% There are a total of 3 entries in each of the rate and state variable arrays.
% There are a total of 22 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 (ms)');
    LEGEND_ALGEBRAIC(:,2) = strpad('Istim in component stimulus_protocol (per_ms)');
    LEGEND_CONSTANTS(:,1) = strpad('IstimStart in component stimulus_protocol (ms)');
    LEGEND_CONSTANTS(:,2) = strpad('IstimEnd in component stimulus_protocol (ms)');
    LEGEND_CONSTANTS(:,3) = strpad('IstimAmplitude in component stimulus_protocol (per_ms)');
    LEGEND_CONSTANTS(:,4) = strpad('IstimPeriod in component stimulus_protocol (ms)');
    LEGEND_CONSTANTS(:,5) = strpad('IstimPulseDuration in component stimulus_protocol (ms)');
    LEGEND_STATES(:,1) = strpad('u in component membrane (dimensionless)');
    LEGEND_CONSTANTS(:,6) = strpad('Cm in component membrane (uF_per_cm2)');
    LEGEND_ALGEBRAIC(:,1) = strpad('Vm in component membrane (mV)');
    LEGEND_CONSTANTS(:,7) = strpad('V_0 in component membrane (mV)');
    LEGEND_CONSTANTS(:,8) = strpad('V_fi in component membrane (mV)');
    LEGEND_ALGEBRAIC(:,4) = strpad('J_fi in component fast_inward_current (per_ms)');
    LEGEND_ALGEBRAIC(:,6) = strpad('J_so in component slow_outward_current (per_ms)');
    LEGEND_ALGEBRAIC(:,8) = strpad('J_si in component slow_inward_current (per_ms)');
    LEGEND_ALGEBRAIC(:,3) = strpad('p in component p (dimensionless)');
    LEGEND_CONSTANTS(:,9) = strpad('u_c in component p (dimensionless)');
    LEGEND_ALGEBRAIC(:,5) = strpad('q in component q (dimensionless)');
    LEGEND_CONSTANTS(:,10) = strpad('u_v in component q (dimensionless)');
    LEGEND_CONSTANTS(:,22) = strpad('tau_d in component fast_inward_current (ms)');
    LEGEND_CONSTANTS(:,11) = strpad('g_fi_max in component fast_inward_current (mS_per_cm2)');
    LEGEND_STATES(:,2) = strpad('v in component fast_inward_current_v_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,7) = strpad('tau_v_minus in component fast_inward_current_v_gate (ms)');
    LEGEND_CONSTANTS(:,12) = strpad('tau_v1_minus in component fast_inward_current_v_gate (ms)');
    LEGEND_CONSTANTS(:,13) = strpad('tau_v2_minus in component fast_inward_current_v_gate (ms)');
    LEGEND_CONSTANTS(:,14) = strpad('tau_v_plus in component fast_inward_current_v_gate (ms)');
    LEGEND_CONSTANTS(:,15) = strpad('tau_0 in component slow_outward_current (ms)');
    LEGEND_CONSTANTS(:,16) = strpad('tau_r in component slow_outward_current (ms)');
    LEGEND_CONSTANTS(:,17) = strpad('tau_si in component slow_inward_current (ms)');
    LEGEND_CONSTANTS(:,18) = strpad('u_csi in component slow_inward_current (dimensionless)');
    LEGEND_CONSTANTS(:,19) = strpad('k in component slow_inward_current (dimensionless)');
    LEGEND_STATES(:,3) = strpad('w in component slow_inward_current_w_gate (dimensionless)');
    LEGEND_CONSTANTS(:,20) = strpad('tau_w_minus in component slow_inward_current_w_gate (ms)');
    LEGEND_CONSTANTS(:,21) = strpad('tau_w_plus in component slow_inward_current_w_gate (ms)');
    LEGEND_RATES(:,1) = strpad('d/dt u in component membrane (dimensionless)');
    LEGEND_RATES(:,2) = strpad('d/dt v in component fast_inward_current_v_gate (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt w in component slow_inward_current_w_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 = [];
    CONSTANTS(:,1) = 100;
    CONSTANTS(:,2) = 50000;
    CONSTANTS(:,3) = -0.2;
    CONSTANTS(:,4) = 1000;
    CONSTANTS(:,5) = 1;
    STATES(:,1) = 0;
    CONSTANTS(:,6) = 1;
    CONSTANTS(:,7) = -85;
    CONSTANTS(:,8) = 15;
    CONSTANTS(:,9) = 0.13;
    CONSTANTS(:,10) = 0;
    CONSTANTS(:,11) = 5.8;
    STATES(:,2) = 1;
    CONSTANTS(:,12) = 18.2;
    CONSTANTS(:,13) = 18.2;
    CONSTANTS(:,14) = 10;
    CONSTANTS(:,15) = 12.5;
    CONSTANTS(:,16) = 130;
    CONSTANTS(:,17) = 127;
    CONSTANTS(:,18) = 0.85;
    CONSTANTS(:,19) = 10;
    STATES(:,3) = 1;
    CONSTANTS(:,20) = 80;
    CONSTANTS(:,21) = 1020;
    CONSTANTS(:,22) = CONSTANTS(:,6)./CONSTANTS(:,11);
    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(:,3) = piecewise({STATES(:,1)<CONSTANTS(:,9), 0.00000 }, 1.00000);
    RATES(:,3) = ( (1.00000 - ALGEBRAIC(:,3)).*(1.00000 - STATES(:,3)))./CONSTANTS(:,20) - ( ALGEBRAIC(:,3).*STATES(:,3))./CONSTANTS(:,21);
    ALGEBRAIC(:,5) = piecewise({STATES(:,1)<CONSTANTS(:,10), 0.00000 }, 1.00000);
    ALGEBRAIC(:,7) =  ALGEBRAIC(:,5).*CONSTANTS(:,12)+ (1.00000 - ALGEBRAIC(:,5)).*CONSTANTS(:,13);
    RATES(:,2) = ( (1.00000 - ALGEBRAIC(:,3)).*(1.00000 - STATES(:,2)))./ALGEBRAIC(:,7) - ( ALGEBRAIC(:,3).*STATES(:,2))./CONSTANTS(:,14);
    ALGEBRAIC(:,2) = piecewise({VOI>=CONSTANTS(:,1)&VOI<=CONSTANTS(:,2)&(VOI - CONSTANTS(:,1)) -  floor((VOI - CONSTANTS(:,1))./CONSTANTS(:,4)).*CONSTANTS(:,4)<=CONSTANTS(:,5), CONSTANTS(:,3) }, 0.00000);
    ALGEBRAIC(:,4) = (  - STATES(:,2).*ALGEBRAIC(:,3).*(1.00000 - STATES(:,1)).*(STATES(:,1) - CONSTANTS(:,9)))./CONSTANTS(:,22);
    ALGEBRAIC(:,6) = ( STATES(:,1).*(1.00000 - ALGEBRAIC(:,3)))./CONSTANTS(:,15)+ALGEBRAIC(:,3)./CONSTANTS(:,16);
    ALGEBRAIC(:,8) = (  - STATES(:,3).*(1.00000+ tanh( CONSTANTS(:,19).*(STATES(:,1) - CONSTANTS(:,18)))))./( 2.00000.*CONSTANTS(:,17));
    RATES(:,1) =  - (ALGEBRAIC(:,4)+ALGEBRAIC(:,6)+ALGEBRAIC(:,8)+ALGEBRAIC(:,2));
   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(:,3) = piecewise({STATES(:,1)<CONSTANTS(:,9), 0.00000 }, 1.00000);
    ALGEBRAIC(:,5) = piecewise({STATES(:,1)<CONSTANTS(:,10), 0.00000 }, 1.00000);
    ALGEBRAIC(:,7) =  ALGEBRAIC(:,5).*CONSTANTS(:,12)+ (1.00000 - ALGEBRAIC(:,5)).*CONSTANTS(:,13);
    ALGEBRAIC(:,2) = piecewise({VOI>=CONSTANTS(:,1)&VOI<=CONSTANTS(:,2)&(VOI - CONSTANTS(:,1)) -  floor((VOI - CONSTANTS(:,1))./CONSTANTS(:,4)).*CONSTANTS(:,4)<=CONSTANTS(:,5), CONSTANTS(:,3) }, 0.00000);
    ALGEBRAIC(:,4) = (  - STATES(:,2).*ALGEBRAIC(:,3).*(1.00000 - STATES(:,1)).*(STATES(:,1) - CONSTANTS(:,9)))./CONSTANTS(:,22);
    ALGEBRAIC(:,6) = ( STATES(:,1).*(1.00000 - ALGEBRAIC(:,3)))./CONSTANTS(:,15)+ALGEBRAIC(:,3)./CONSTANTS(:,16);
    ALGEBRAIC(:,8) = (  - STATES(:,3).*(1.00000+ tanh( CONSTANTS(:,19).*(STATES(:,1) - CONSTANTS(:,18)))))./( 2.00000.*CONSTANTS(:,17));
    ALGEBRAIC(:,1) = CONSTANTS(:,7)+ STATES(:,1).*(CONSTANTS(:,8) - CONSTANTS(:,7));
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