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 =13;
end
% There are a total of 5 entries in each of the rate and state variable arrays.
% There are a total of 20 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 (second)');
    LEGEND_STATES(:,1) = strpad('V_s in component soma_compartment (mV)');
    LEGEND_CONSTANTS(:,1) = strpad('V_Na in component soma_compartment (mV)');
    LEGEND_CONSTANTS(:,2) = strpad('V_K in component soma_compartment (mV)');
    LEGEND_ALGEBRAIC(:,9) = strpad('I_Na in component soma_compartment (uA_per_cm2)');
    LEGEND_ALGEBRAIC(:,1) = strpad('I_K_DR in component soma_compartment (uA_per_cm2)');
    LEGEND_CONSTANTS(:,3) = strpad('g_K_DR in component soma_compartment (mS_per_cm2)');
    LEGEND_CONSTANTS(:,4) = strpad('g_Na in component soma_compartment (mS_per_cm2)');
    LEGEND_CONSTANTS(:,5) = strpad('g_c in component model_parameters (mS_per_cm2)');
    LEGEND_STATES(:,2) = strpad('V_D in component dendritic_compartment (mV)');
    LEGEND_CONSTANTS(:,6) = strpad('C_m in component model_parameters (uF_per_cm2)');
    LEGEND_CONSTANTS(:,7) = strpad('p in component model_parameters (dimensionless)');
    LEGEND_STATES(:,3) = strpad('n in component gating_variables (dimensionless)');
    LEGEND_STATES(:,4) = strpad('h in component gating_variables (dimensionless)');
    LEGEND_ALGEBRAIC(:,5) = strpad('m_infinity in component gating_variables (dimensionless)');
    LEGEND_CONSTANTS(:,8) = strpad('V_L in component dendritic_compartment (mV)');
    LEGEND_CONSTANTS(:,9) = strpad('V_NMDA in component dendritic_compartment (mV)');
    LEGEND_ALGEBRAIC(:,2) = strpad('I_L in component dendritic_compartment (uA_per_cm2)');
    LEGEND_ALGEBRAIC(:,13) = strpad('I_D in component dendritic_compartment (uA_per_cm2)');
    LEGEND_ALGEBRAIC(:,10) = strpad('I_pump in component dendritic_compartment (uA_per_cm2)');
    LEGEND_ALGEBRAIC(:,11) = strpad('I_NMDA in component dendritic_compartment (uA_per_cm2)');
    LEGEND_ALGEBRAIC(:,12) = strpad('I_Na_NMDA in component dendritic_compartment (uA_per_cm2)');
    LEGEND_CONSTANTS(:,10) = strpad('R_pump in component dendritic_compartment (uA_per_cm2)');
    LEGEND_CONSTANTS(:,11) = strpad('alpha in component dendritic_compartment (mMcm2_per_uAs)');
    LEGEND_CONSTANTS(:,12) = strpad('g_NMDA in component dendritic_compartment (mS_per_cm2)');
    LEGEND_CONSTANTS(:,13) = strpad('g_Na_NMDA in component dendritic_compartment (mS_per_cm2)');
    LEGEND_CONSTANTS(:,14) = strpad('g_L in component dendritic_compartment (mS_per_cm2)');
    LEGEND_STATES(:,5) = strpad('Na in component dendritic_compartment (mM)');
    LEGEND_CONSTANTS(:,15) = strpad('Na_eq in component dendritic_compartment (mM)');
    LEGEND_CONSTANTS(:,16) = strpad('K_p in component dendritic_compartment (mM)');
    LEGEND_CONSTANTS(:,17) = strpad('Mg_o in component dendritic_compartment (mM)');
    LEGEND_CONSTANTS(:,18) = strpad('K_Mg in component dendritic_compartment (mM)');
    LEGEND_CONSTANTS(:,19) = strpad('q in component dendritic_compartment (mV)');
    LEGEND_ALGEBRAIC(:,6) = strpad('phi_Na in component dendritic_compartment (dimensionless)');
    LEGEND_CONSTANTS(:,20) = strpad('phi_Na_eq in component dendritic_compartment (dimensionless)');
    LEGEND_ALGEBRAIC(:,3) = strpad('n_infinity in component gating_variables (dimensionless)');
    LEGEND_ALGEBRAIC(:,4) = strpad('h_infinity in component gating_variables (dimensionless)');
    LEGEND_ALGEBRAIC(:,7) = strpad('tau_h in component gating_variables (second)');
    LEGEND_ALGEBRAIC(:,8) = strpad('tau_n in component gating_variables (second)');
    LEGEND_RATES(:,1) = strpad('d/dt V_s in component soma_compartment (mV)');
    LEGEND_RATES(:,2) = strpad('d/dt V_D in component dendritic_compartment (mV)');
    LEGEND_RATES(:,5) = strpad('d/dt Na in component dendritic_compartment (mM)');
    LEGEND_RATES(:,4) = strpad('d/dt h in component gating_variables (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt n in component gating_variables (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;
    CONSTANTS(:,1) = 55;
    CONSTANTS(:,2) = -85;
    CONSTANTS(:,3) = 3.2;
    CONSTANTS(:,4) = 3.2;
    CONSTANTS(:,5) = 0.0;
    STATES(:,2) = -25.0;
    CONSTANTS(:,6) = 1;
    CONSTANTS(:,7) = 0.5;
    STATES(:,3) = 0.002;
    STATES(:,4) = 1;
    CONSTANTS(:,8) = -50;
    CONSTANTS(:,9) = 0;
    CONSTANTS(:,10) = 18.0;
    CONSTANTS(:,11) = 0.5;
    CONSTANTS(:,12) = 1.25;
    CONSTANTS(:,13) = 1.0;
    CONSTANTS(:,14) = 0.18;
    STATES(:,5) = 5.09;
    CONSTANTS(:,15) = 8;
    CONSTANTS(:,16) = 15;
    CONSTANTS(:,17) = 1.4;
    CONSTANTS(:,18) = 10.0;
    CONSTANTS(:,19) = 12.5;
    CONSTANTS(:,20) = power(CONSTANTS(:,15), 3.00000)./(power(CONSTANTS(:,15), 3.00000)+power(CONSTANTS(:,16), 3.00000));
    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(:,4) = 1.00000./(1.00000+exp((STATES(:,1)+30.0000)./8.30000));
    ALGEBRAIC(:,7) =  0.400000.*(1.00000+2.00000./(1.00000+exp((STATES(:,1)+25.0000)./5.00000)));
    RATES(:,4) = (ALGEBRAIC(:,4) - STATES(:,4))./ALGEBRAIC(:,7);
    ALGEBRAIC(:,3) = 1.00000./(1.00000+exp( - (STATES(:,1)+31.0000)./5.30000));
    ALGEBRAIC(:,8) = (0.800000+1.60000./(1.00000+exp( 0.100000.*(STATES(:,1)+25.0000))))./(1.00000+exp(  - 0.100000.*(STATES(:,1)+70.0000)));
    RATES(:,3) = (ALGEBRAIC(:,3) - STATES(:,3))./ALGEBRAIC(:,8);
    ALGEBRAIC(:,5) = 1.00000./(1.00000+exp( - (STATES(:,1)+35.0000)./6.20000));
    ALGEBRAIC(:,9) =  CONSTANTS(:,4).*STATES(:,4).*(STATES(:,1) - CONSTANTS(:,1)).*power(ALGEBRAIC(:,5), 3.00000);
    ALGEBRAIC(:,1) =  CONSTANTS(:,3).*(STATES(:,1) - CONSTANTS(:,2)).*power(STATES(:,3), 2.00000);
    RATES(:,1) =  - ( 1000.00.*(ALGEBRAIC(:,1)+ALGEBRAIC(:,9)+ (CONSTANTS(:,5)./CONSTANTS(:,7)).*(STATES(:,1) - STATES(:,2))))./CONSTANTS(:,6);
    ALGEBRAIC(:,2) =  CONSTANTS(:,14).*(STATES(:,2) - CONSTANTS(:,8));
    ALGEBRAIC(:,6) = power(STATES(:,5), 3.00000)./(power(STATES(:,5), 3.00000)+power(CONSTANTS(:,16), 3.00000));
    ALGEBRAIC(:,10) =  CONSTANTS(:,10).*(ALGEBRAIC(:,6) - CONSTANTS(:,20));
    ALGEBRAIC(:,11) =  (CONSTANTS(:,12)./(1.00000+ (CONSTANTS(:,17)./CONSTANTS(:,18)).*exp( - (STATES(:,2)./CONSTANTS(:,19))))).*(STATES(:,2) - CONSTANTS(:,9));
    RATES(:,2) =  - ( 1000.00.*(ALGEBRAIC(:,11)+ALGEBRAIC(:,10)+ALGEBRAIC(:,2)+ (CONSTANTS(:,5)./(1.00000 - CONSTANTS(:,7))).*(STATES(:,2) - STATES(:,1))))./CONSTANTS(:,6);
    ALGEBRAIC(:,12) =  (CONSTANTS(:,13)./(1.00000+ (CONSTANTS(:,17)./CONSTANTS(:,18)).*exp( - (STATES(:,2)./CONSTANTS(:,19))))).*(STATES(:,2) - CONSTANTS(:,1));
    RATES(:,5) =  CONSTANTS(:,11).*( - ALGEBRAIC(:,12) -  3.00000.*ALGEBRAIC(:,10));
   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(:,4) = 1.00000./(1.00000+exp((STATES(:,1)+30.0000)./8.30000));
    ALGEBRAIC(:,7) =  0.400000.*(1.00000+2.00000./(1.00000+exp((STATES(:,1)+25.0000)./5.00000)));
    ALGEBRAIC(:,3) = 1.00000./(1.00000+exp( - (STATES(:,1)+31.0000)./5.30000));
    ALGEBRAIC(:,8) = (0.800000+1.60000./(1.00000+exp( 0.100000.*(STATES(:,1)+25.0000))))./(1.00000+exp(  - 0.100000.*(STATES(:,1)+70.0000)));
    ALGEBRAIC(:,5) = 1.00000./(1.00000+exp( - (STATES(:,1)+35.0000)./6.20000));
    ALGEBRAIC(:,9) =  CONSTANTS(:,4).*STATES(:,4).*(STATES(:,1) - CONSTANTS(:,1)).*power(ALGEBRAIC(:,5), 3.00000);
    ALGEBRAIC(:,1) =  CONSTANTS(:,3).*(STATES(:,1) - CONSTANTS(:,2)).*power(STATES(:,3), 2.00000);
    ALGEBRAIC(:,2) =  CONSTANTS(:,14).*(STATES(:,2) - CONSTANTS(:,8));
    ALGEBRAIC(:,6) = power(STATES(:,5), 3.00000)./(power(STATES(:,5), 3.00000)+power(CONSTANTS(:,16), 3.00000));
    ALGEBRAIC(:,10) =  CONSTANTS(:,10).*(ALGEBRAIC(:,6) - CONSTANTS(:,20));
    ALGEBRAIC(:,11) =  (CONSTANTS(:,12)./(1.00000+ (CONSTANTS(:,17)./CONSTANTS(:,18)).*exp( - (STATES(:,2)./CONSTANTS(:,19))))).*(STATES(:,2) - CONSTANTS(:,9));
    ALGEBRAIC(:,12) =  (CONSTANTS(:,13)./(1.00000+ (CONSTANTS(:,17)./CONSTANTS(:,18)).*exp( - (STATES(:,2)./CONSTANTS(:,19))))).*(STATES(:,2) - CONSTANTS(:,1));
    ALGEBRAIC(:,13) = ALGEBRAIC(:,11)+ALGEBRAIC(:,10)+ALGEBRAIC(:,2);
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