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 =7;
end
% There are a total of 3 entries in each of the rate and state variable arrays.
% There are a total of 16 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('tau in component membrane (millisecond)');
    LEGEND_ALGEBRAIC(:,5) = strpad('i_K in component potassium_current (picoA)');
    LEGEND_ALGEBRAIC(:,7) = strpad('i_K_ATP in component ATP_sensitive_potassium_current (picoA)');
    LEGEND_ALGEBRAIC(:,4) = strpad('i_Ca in component calcium_current (picoA)');
    LEGEND_ALGEBRAIC(:,6) = strpad('i_s in component slow_current (picoA)');
    LEGEND_CONSTANTS(:,2) = strpad('g_Ca in component calcium_current (nanoS)');
    LEGEND_CONSTANTS(:,3) = strpad('V_Ca in component calcium_current (millivolt)');
    LEGEND_ALGEBRAIC(:,1) = strpad('m_infinity in component calcium_current_m_gate (dimensionless)');
    LEGEND_CONSTANTS(:,4) = strpad('V_m in component calcium_current_m_gate (millivolt)');
    LEGEND_CONSTANTS(:,5) = strpad('theta_m in component calcium_current_m_gate (millivolt)');
    LEGEND_CONSTANTS(:,6) = strpad('V_K in component potassium_current (millivolt)');
    LEGEND_CONSTANTS(:,7) = strpad('g_K in component potassium_current (nanoS)');
    LEGEND_STATES(:,2) = strpad('n in component potassium_current_n_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('n_infinity in component potassium_current_n_gate (dimensionless)');
    LEGEND_CONSTANTS(:,8) = strpad('V_n in component potassium_current_n_gate (millivolt)');
    LEGEND_CONSTANTS(:,9) = strpad('theta_n in component potassium_current_n_gate (millivolt)');
    LEGEND_CONSTANTS(:,10) = strpad('lambda in component potassium_current_n_gate (dimensionless)');
    LEGEND_CONSTANTS(:,11) = strpad('g_s in component slow_current (nanoS)');
    LEGEND_STATES(:,3) = strpad('s in component slow_current_s_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,3) = strpad('s_infinity in component slow_current_s_gate (dimensionless)');
    LEGEND_CONSTANTS(:,12) = strpad('V_s in component slow_current_s_gate (millivolt)');
    LEGEND_CONSTANTS(:,13) = strpad('theta_s in component slow_current_s_gate (millivolt)');
    LEGEND_CONSTANTS(:,14) = strpad('tau_s in component slow_current_s_gate (millisecond)');
    LEGEND_CONSTANTS(:,15) = strpad('g_K_ATP in component ATP_sensitive_potassium_current (nanoS)');
    LEGEND_CONSTANTS(:,16) = strpad('p in component ATP_sensitive_potassium_current (dimensionless)');
    LEGEND_RATES(:,1) = strpad('d/dt V in component membrane (millivolt)');
    LEGEND_RATES(:,2) = strpad('d/dt n in component potassium_current_n_gate (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt s in component slow_current_s_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) = -64.0;
    CONSTANTS(:,1) = 20.0;
    CONSTANTS(:,2) = 3.6;
    CONSTANTS(:,3) = 25.0;
    CONSTANTS(:,4) = -20.0;
    CONSTANTS(:,5) = 12.0;
    CONSTANTS(:,6) = -75.0;
    CONSTANTS(:,7) = 10.0;
    STATES(:,2) = 0.01;
    CONSTANTS(:,8) = -17.0;
    CONSTANTS(:,9) = 5.6;
    CONSTANTS(:,10) = 0.9;
    CONSTANTS(:,11) = 4.0;
    STATES(:,3) = 0.01;
    CONSTANTS(:,12) = -22.0;
    CONSTANTS(:,13) = 8.0;
    CONSTANTS(:,14) = 20000.0;
    CONSTANTS(:,15) = 1.2;
    CONSTANTS(:,16) = 0.5;
    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(:,8) - STATES(:,1))./CONSTANTS(:,9)));
    RATES(:,2) = ( CONSTANTS(:,10).*(ALGEBRAIC(:,2) - STATES(:,2)))./CONSTANTS(:,1);
    ALGEBRAIC(:,3) = 1.00000./(1.00000+exp((CONSTANTS(:,12) - STATES(:,1))./CONSTANTS(:,13)));
    RATES(:,3) = (ALGEBRAIC(:,3) - STATES(:,3))./CONSTANTS(:,14);
    ALGEBRAIC(:,5) =  CONSTANTS(:,7).*STATES(:,2).*(STATES(:,1) - CONSTANTS(:,6));
    ALGEBRAIC(:,7) =  CONSTANTS(:,15).*CONSTANTS(:,16).*(STATES(:,1) - CONSTANTS(:,6));
    ALGEBRAIC(:,1) = 1.00000./(1.00000+exp((CONSTANTS(:,4) - STATES(:,1))./CONSTANTS(:,5)));
    ALGEBRAIC(:,4) =  CONSTANTS(:,2).*ALGEBRAIC(:,1).*(STATES(:,1) - CONSTANTS(:,3));
    ALGEBRAIC(:,6) =  CONSTANTS(:,11).*STATES(:,3).*(STATES(:,1) - CONSTANTS(:,6));
    RATES(:,1) =  - (ALGEBRAIC(:,4)+ALGEBRAIC(:,5)+ALGEBRAIC(:,7)+ALGEBRAIC(:,6))./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(:,8) - STATES(:,1))./CONSTANTS(:,9)));
    ALGEBRAIC(:,3) = 1.00000./(1.00000+exp((CONSTANTS(:,12) - STATES(:,1))./CONSTANTS(:,13)));
    ALGEBRAIC(:,5) =  CONSTANTS(:,7).*STATES(:,2).*(STATES(:,1) - CONSTANTS(:,6));
    ALGEBRAIC(:,7) =  CONSTANTS(:,15).*CONSTANTS(:,16).*(STATES(:,1) - CONSTANTS(:,6));
    ALGEBRAIC(:,1) = 1.00000./(1.00000+exp((CONSTANTS(:,4) - STATES(:,1))./CONSTANTS(:,5)));
    ALGEBRAIC(:,4) =  CONSTANTS(:,2).*ALGEBRAIC(:,1).*(STATES(:,1) - CONSTANTS(:,3));
    ALGEBRAIC(:,6) =  CONSTANTS(:,11).*STATES(:,3).*(STATES(:,1) - CONSTANTS(:,6));
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