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 =18;
end
% There are a total of 4 entries in each of the rate and state variable arrays.
% There are a total of 14 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('HCO3_int in component concentrations (mM)');
    LEGEND_STATES(:,2) = strpad('HCO3_ext in component concentrations (mM)');
    LEGEND_STATES(:,3) = strpad('Cl_int in component concentrations (mM)');
    LEGEND_STATES(:,4) = strpad('Cl_ext in component concentrations (mM)');
    LEGEND_ALGEBRAIC(:,13) = strpad('J_AE1_HCO3 in component AE1 (mM_per_s)');
    LEGEND_ALGEBRAIC(:,18) = strpad('J_AE1_Cl in component AE1 (mM_per_s)');
    LEGEND_ALGEBRAIC(:,14) = strpad('J_HCO3_influx in component AE1 (mM_per_s)');
    LEGEND_ALGEBRAIC(:,15) = strpad('J_Cl_influx in component AE1 (mM_per_s)');
    LEGEND_CONSTANTS(:,1) = strpad('K_HCO3_ext in component AE1 (mM)');
    LEGEND_CONSTANTS(:,2) = strpad('K_HCO3_int in component AE1 (mM)');
    LEGEND_CONSTANTS(:,3) = strpad('K_Cl_ext in component AE1 (mM)');
    LEGEND_CONSTANTS(:,4) = strpad('K_Cl_int in component AE1 (mM)');
    LEGEND_CONSTANTS(:,5) = strpad('P_HCO3_ext in component AE1 (per_s)');
    LEGEND_CONSTANTS(:,6) = strpad('P_HCO3_int in component AE1 (per_s)');
    LEGEND_CONSTANTS(:,7) = strpad('P_Cl_ext in component AE1 (per_s)');
    LEGEND_CONSTANTS(:,8) = strpad('P_Cl_int in component AE1 (per_s)');
    LEGEND_ALGEBRAIC(:,2) = strpad('beta_ext in component AE1 (dimensionless)');
    LEGEND_ALGEBRAIC(:,9) = strpad('beta_int in component AE1 (dimensionless)');
    LEGEND_ALGEBRAIC(:,10) = strpad('gamma_ext in component AE1 (dimensionless)');
    LEGEND_ALGEBRAIC(:,11) = strpad('gamma_int in component AE1 (dimensionless)');
    LEGEND_ALGEBRAIC(:,12) = strpad('sigma in component AE1 (per_s)');
    LEGEND_CONSTANTS(:,9) = strpad('x_Tmax in component AE1 (mM)');
    LEGEND_CONSTANTS(:,10) = strpad('K_I in component AE1 (mM)');
    LEGEND_ALGEBRAIC(:,1) = strpad('x_T in component AE1 (mM)');
    LEGEND_ALGEBRAIC(:,16) = strpad('x_ext in component AE1 (mM)');
    LEGEND_ALGEBRAIC(:,17) = strpad('x_int in component AE1 (mM)');
    LEGEND_ALGEBRAIC(:,3) = strpad('Jo_bm in component AE1 (mM_per_s)');
    LEGEND_ALGEBRAIC(:,4) = strpad('Ji_bm in component AE1 (mM_per_s)');
    LEGEND_ALGEBRAIC(:,5) = strpad('Js_bm in component AE1 (mM_per_s)');
    LEGEND_ALGEBRAIC(:,6) = strpad('Jo_cm in component AE1 (mM_per_s)');
    LEGEND_ALGEBRAIC(:,7) = strpad('Ji_cm in component AE1 (mM_per_s)');
    LEGEND_ALGEBRAIC(:,8) = strpad('Js_cm in component AE1 (mM_per_s)');
    LEGEND_RATES(:,1) = strpad('d/dt HCO3_int in component concentrations (mM)');
    LEGEND_RATES(:,2) = strpad('d/dt HCO3_ext in component concentrations (mM)');
    LEGEND_RATES(:,3) = strpad('d/dt Cl_int in component concentrations (mM)');
    LEGEND_RATES(:,4) = strpad('d/dt Cl_ext in component concentrations (mM)');
    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) = 1.0;
    STATES(:,2) = 50.0;
    STATES(:,3) = 0.0;
    STATES(:,4) = 0.0;
    CONSTANTS(:,1) = 198;
    CONSTANTS(:,2) = 198;
    CONSTANTS(:,3) = 50;
    CONSTANTS(:,4) = 50;
    CONSTANTS(:,5) = 1247;
    CONSTANTS(:,6) = 135;
    CONSTANTS(:,7) = 562;
    CONSTANTS(:,8) = 61;
    CONSTANTS(:,9) = 1;
    CONSTANTS(:,10) = 172;
    CONSTANTS(:,10) = 1.00000;
    CONSTANTS(:,11) = 0.00000;
    CONSTANTS(:,12) = 0.00000;
    CONSTANTS(:,13) = 0.00000;
    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
    RATES(:,1) = CONSTANTS(:,10);
    RATES(:,2) = CONSTANTS(:,11);
    RATES(:,3) = CONSTANTS(:,12);
    RATES(:,4) = CONSTANTS(:,13);
   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) = CONSTANTS(:,9)./(1.00000+STATES(:,1)./CONSTANTS(:,10));
    ALGEBRAIC(:,2) = STATES(:,2)./CONSTANTS(:,1);
    ALGEBRAIC(:,3) = power( (1.00000./ALGEBRAIC(:,1)).*(1.00000./CONSTANTS(:,5)+1.00000./CONSTANTS(:,6)+CONSTANTS(:,2)./( CONSTANTS(:,6).*STATES(:,1))),  - 1.00000);
    ALGEBRAIC(:,4) = power( (1.00000./ALGEBRAIC(:,1)).*(1.00000./CONSTANTS(:,5)+1.00000./CONSTANTS(:,6)+CONSTANTS(:,1)./( CONSTANTS(:,5).*STATES(:,2))),  - 1.00000);
    ALGEBRAIC(:,5) = power( (1.00000./ALGEBRAIC(:,1)).*(1.00000./CONSTANTS(:,5)+1.00000./CONSTANTS(:,6)),  - 1.00000);
    ALGEBRAIC(:,6) = power( (1.00000./ALGEBRAIC(:,1)).*(1.00000./CONSTANTS(:,7)+1.00000./CONSTANTS(:,8)+CONSTANTS(:,4)./( CONSTANTS(:,8).*STATES(:,3))),  - 1.00000);
    ALGEBRAIC(:,7) = power( (1.00000./ALGEBRAIC(:,1)).*(1.00000./CONSTANTS(:,7)+1.00000./CONSTANTS(:,8)+CONSTANTS(:,3)./( CONSTANTS(:,7).*STATES(:,4))),  - 1.00000);
    ALGEBRAIC(:,8) = power( (1.00000./ALGEBRAIC(:,1)).*(1.00000./CONSTANTS(:,7)+1.00000./CONSTANTS(:,8)),  - 1.00000);
    ALGEBRAIC(:,9) = STATES(:,1)./CONSTANTS(:,2);
    ALGEBRAIC(:,10) = STATES(:,4)./CONSTANTS(:,3);
    ALGEBRAIC(:,11) = STATES(:,3)./CONSTANTS(:,4);
    ALGEBRAIC(:,12) =  (1.00000+ALGEBRAIC(:,2)+ALGEBRAIC(:,10)).*( CONSTANTS(:,6).*ALGEBRAIC(:,9)+ CONSTANTS(:,8).*ALGEBRAIC(:,11))+ (1.00000+ALGEBRAIC(:,9)+ALGEBRAIC(:,11)).*( CONSTANTS(:,5).*ALGEBRAIC(:,2)+ CONSTANTS(:,7).*ALGEBRAIC(:,10));
    ALGEBRAIC(:,13) =  (ALGEBRAIC(:,1)./ALGEBRAIC(:,12)).*( CONSTANTS(:,6).*ALGEBRAIC(:,9).*CONSTANTS(:,7).*ALGEBRAIC(:,10) -  CONSTANTS(:,5).*ALGEBRAIC(:,2).*CONSTANTS(:,8).*ALGEBRAIC(:,11));
    ALGEBRAIC(:,14) =  (ALGEBRAIC(:,1)./ALGEBRAIC(:,12)).*CONSTANTS(:,5).*ALGEBRAIC(:,2).*( CONSTANTS(:,6).*ALGEBRAIC(:,9)+ CONSTANTS(:,8).*ALGEBRAIC(:,11));
    ALGEBRAIC(:,15) =  (ALGEBRAIC(:,1)./ALGEBRAIC(:,12)).*CONSTANTS(:,7).*ALGEBRAIC(:,10).*( CONSTANTS(:,6).*ALGEBRAIC(:,9)+ CONSTANTS(:,8).*ALGEBRAIC(:,11));
    ALGEBRAIC(:,16) = ( ALGEBRAIC(:,1).*( CONSTANTS(:,6).*ALGEBRAIC(:,9)+ CONSTANTS(:,8).*ALGEBRAIC(:,11)))./ALGEBRAIC(:,12);
    ALGEBRAIC(:,17) = ( ALGEBRAIC(:,1).*( CONSTANTS(:,5).*ALGEBRAIC(:,2)+ CONSTANTS(:,7).*ALGEBRAIC(:,10)))./ALGEBRAIC(:,12);
    ALGEBRAIC(:,18) =  - ALGEBRAIC(:,13);
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