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 =9;
end
% There are a total of 3 entries in each of the rate and state variable arrays.
% There are a total of 28 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 (femtoF)');
    LEGEND_ALGEBRAIC(:,6) = strpad('i_Ca in component calcium_current (picoA)');
    LEGEND_ALGEBRAIC(:,1) = strpad('i_K in component rapidly_activating_K_current (picoA)');
    LEGEND_ALGEBRAIC(:,7) = strpad('i_K_Ca in component calcium_activated_K_current (picoA)');
    LEGEND_ALGEBRAIC(:,9) = strpad('i_Na_Ca in component Na_Ca_exchanger_current (picoA)');
    LEGEND_CONSTANTS(:,2) = strpad('V_K in component rapidly_activating_K_current (millivolt)');
    LEGEND_CONSTANTS(:,3) = strpad('g_K in component rapidly_activating_K_current (picoS)');
    LEGEND_STATES(:,2) = strpad('n in component rapidly_activating_K_current_n_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('n_infinity in component rapidly_activating_K_current_n_gate (dimensionless)');
    LEGEND_CONSTANTS(:,4) = strpad('lamda in component rapidly_activating_K_current_n_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,4) = strpad('tau_n in component rapidly_activating_K_current_n_gate (millisecond)');
    LEGEND_CONSTANTS(:,5) = strpad('V_n in component rapidly_activating_K_current_n_gate (millivolt)');
    LEGEND_CONSTANTS(:,6) = strpad('S_n in component rapidly_activating_K_current_n_gate (millivolt)');
    LEGEND_CONSTANTS(:,7) = strpad('a in component rapidly_activating_K_current_n_gate (millivolt)');
    LEGEND_CONSTANTS(:,8) = strpad('b in component rapidly_activating_K_current_n_gate (millivolt)');
    LEGEND_CONSTANTS(:,9) = strpad('c in component rapidly_activating_K_current_n_gate (millisecond)');
    LEGEND_CONSTANTS(:,10) = strpad('V_ in component rapidly_activating_K_current_n_gate (millivolt)');
    LEGEND_CONSTANTS(:,11) = strpad('V_Ca in component calcium_current (millivolt)');
    LEGEND_CONSTANTS(:,12) = strpad('g_Ca in component calcium_current (picoS)');
    LEGEND_ALGEBRAIC(:,3) = strpad('m_infinity in component calcium_current_m_gate (dimensionless)');
    LEGEND_ALGEBRAIC(:,5) = strpad('h in component calcium_current_h_gate (dimensionless)');
    LEGEND_CONSTANTS(:,13) = strpad('V_m in component calcium_current_m_gate (millivolt)');
    LEGEND_CONSTANTS(:,14) = strpad('S_m in component calcium_current_m_gate (millivolt)');
    LEGEND_CONSTANTS(:,15) = strpad('V_h in component calcium_current_h_gate (millivolt)');
    LEGEND_CONSTANTS(:,16) = strpad('S_h in component calcium_current_h_gate (millivolt)');
    LEGEND_CONSTANTS(:,17) = strpad('g_K_Ca in component calcium_activated_K_current (picoS)');
    LEGEND_CONSTANTS(:,18) = strpad('K_d in component calcium_activated_K_current (micromolar)');
    LEGEND_STATES(:,3) = strpad('Ca_i in component ionic_concentrations (micromolar)');
    LEGEND_CONSTANTS(:,19) = strpad('g_Na_Ca in component Na_Ca_exchanger_current (picoS)');
    LEGEND_CONSTANTS(:,20) = strpad('K_1_2 in component Na_Ca_exchanger_current (micromolar)');
    LEGEND_ALGEBRAIC(:,8) = strpad('V_Na_Ca in component Na_Ca_exchanger_current (millivolt)');
    LEGEND_CONSTANTS(:,21) = strpad('RT_F in component Na_Ca_exchanger_current (millivolt)');
    LEGEND_CONSTANTS(:,22) = strpad('nH in component Na_Ca_exchanger_current (dimensionless)');
    LEGEND_CONSTANTS(:,23) = strpad('Ca_o in component ionic_concentrations (micromolar)');
    LEGEND_CONSTANTS(:,24) = strpad('Na_i in component ionic_concentrations (millimolar)');
    LEGEND_CONSTANTS(:,25) = strpad('Na_o in component ionic_concentrations (millimolar)');
    LEGEND_CONSTANTS(:,26) = strpad('f in component ionic_concentrations (dimensionless)');
    LEGEND_CONSTANTS(:,27) = strpad('k_Ca in component ionic_concentrations (per_millisecond)');
    LEGEND_CONSTANTS(:,28) = strpad('alpha in component ionic_concentrations (mole_per_microlitre_coulomb)');
    LEGEND_RATES(:,1) = strpad('d/dt V in component membrane (millivolt)');
    LEGEND_RATES(:,2) = strpad('d/dt n in component rapidly_activating_K_current_n_gate (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt Ca_i in component ionic_concentrations (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) = -76.0;
    CONSTANTS(:,1) = 5310.0;
    CONSTANTS(:,2) = -75.0;
    CONSTANTS(:,3) = 2500.0;
    STATES(:,2) = 0.1;
    CONSTANTS(:,4) = 1.6;
    CONSTANTS(:,5) = -15.0;
    CONSTANTS(:,6) = 5.6;
    CONSTANTS(:,7) = 65.0;
    CONSTANTS(:,8) = 20.0;
    CONSTANTS(:,9) = 6.0;
    CONSTANTS(:,10) = -75.0;
    CONSTANTS(:,11) = 110.0;
    CONSTANTS(:,12) = 1400.0;
    CONSTANTS(:,13) = 4.0;
    CONSTANTS(:,14) = 14.0;
    CONSTANTS(:,15) = -10.0;
    CONSTANTS(:,16) = -10.0;
    CONSTANTS(:,17) = 30000.0;
    CONSTANTS(:,18) = 100.0;
    STATES(:,3) = 0.52;
    CONSTANTS(:,19) = 234.0;
    CONSTANTS(:,20) = 1.5;
    CONSTANTS(:,21) = 26.54;
    CONSTANTS(:,22) = 5.0;
    CONSTANTS(:,23) = 2600.0;
    CONSTANTS(:,24) = 10.0;
    CONSTANTS(:,25) = 140.0;
    CONSTANTS(:,26) = 0.001;
    CONSTANTS(:,27) = 0.03;
    CONSTANTS(:,28) = 0.0000045055;
    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(:,5) - STATES(:,1))./CONSTANTS(:,6)));
    ALGEBRAIC(:,4) = CONSTANTS(:,9)./(exp((STATES(:,1) - CONSTANTS(:,10))./CONSTANTS(:,7))+exp((CONSTANTS(:,10) - STATES(:,1))./CONSTANTS(:,8)));
    RATES(:,2) =  CONSTANTS(:,4).*((ALGEBRAIC(:,2) - STATES(:,2))./ALGEBRAIC(:,4));
    ALGEBRAIC(:,3) = 1.00000./(1.00000+exp((CONSTANTS(:,13) - STATES(:,1))./CONSTANTS(:,14)));
    ALGEBRAIC(:,5) = 1.00000./(1.00000+exp((CONSTANTS(:,15) - STATES(:,1))./CONSTANTS(:,16)));
    ALGEBRAIC(:,6) =  CONSTANTS(:,12).*ALGEBRAIC(:,3).*ALGEBRAIC(:,5).*(STATES(:,1) - CONSTANTS(:,11));
    ALGEBRAIC(:,1) =  CONSTANTS(:,3).*STATES(:,2).*(STATES(:,1) - CONSTANTS(:,2));
    ALGEBRAIC(:,7) =  CONSTANTS(:,17).*(STATES(:,3)./(CONSTANTS(:,18)+STATES(:,3))).*(STATES(:,1) - CONSTANTS(:,2));
    ALGEBRAIC(:,8) =  CONSTANTS(:,21).*( 3.00000.*log(CONSTANTS(:,25)./CONSTANTS(:,24) - log(CONSTANTS(:,23)./STATES(:,3))));
    ALGEBRAIC(:,9) =  CONSTANTS(:,19).*(power(STATES(:,3), CONSTANTS(:,22))./(power(CONSTANTS(:,20), CONSTANTS(:,22))+power(STATES(:,3), CONSTANTS(:,22)))).*(STATES(:,1) - ALGEBRAIC(:,8));
    RATES(:,1) =  - (ALGEBRAIC(:,1)+ALGEBRAIC(:,6)+ALGEBRAIC(:,7)+ALGEBRAIC(:,9))./CONSTANTS(:,1);
    RATES(:,3) =  CONSTANTS(:,26).*(  - CONSTANTS(:,28).*(ALGEBRAIC(:,6) -  2.00000.*ALGEBRAIC(:,9)) -  CONSTANTS(:,27).*STATES(:,3));
   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(:,5) - STATES(:,1))./CONSTANTS(:,6)));
    ALGEBRAIC(:,4) = CONSTANTS(:,9)./(exp((STATES(:,1) - CONSTANTS(:,10))./CONSTANTS(:,7))+exp((CONSTANTS(:,10) - STATES(:,1))./CONSTANTS(:,8)));
    ALGEBRAIC(:,3) = 1.00000./(1.00000+exp((CONSTANTS(:,13) - STATES(:,1))./CONSTANTS(:,14)));
    ALGEBRAIC(:,5) = 1.00000./(1.00000+exp((CONSTANTS(:,15) - STATES(:,1))./CONSTANTS(:,16)));
    ALGEBRAIC(:,6) =  CONSTANTS(:,12).*ALGEBRAIC(:,3).*ALGEBRAIC(:,5).*(STATES(:,1) - CONSTANTS(:,11));
    ALGEBRAIC(:,1) =  CONSTANTS(:,3).*STATES(:,2).*(STATES(:,1) - CONSTANTS(:,2));
    ALGEBRAIC(:,7) =  CONSTANTS(:,17).*(STATES(:,3)./(CONSTANTS(:,18)+STATES(:,3))).*(STATES(:,1) - CONSTANTS(:,2));
    ALGEBRAIC(:,8) =  CONSTANTS(:,21).*( 3.00000.*log(CONSTANTS(:,25)./CONSTANTS(:,24) - log(CONSTANTS(:,23)./STATES(:,3))));
    ALGEBRAIC(:,9) =  CONSTANTS(:,19).*(power(STATES(:,3), CONSTANTS(:,22))./(power(CONSTANTS(:,20), CONSTANTS(:,22))+power(STATES(:,3), CONSTANTS(:,22)))).*(STATES(:,1) - ALGEBRAIC(:,8));
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