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 =15;
end
% There are a total of 1 entries in each of the rate and state variable arrays.
% There are a total of 17 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_i in component Concentrations (mM)');
    LEGEND_CONSTANTS(:,1) = strpad('HCO3_e in component Concentrations (mM)');
    LEGEND_CONSTANTS(:,2) = strpad('Cl_i in component Concentrations (mM)');
    LEGEND_CONSTANTS(:,3) = strpad('Cl_e in component Concentrations (mM)');
    LEGEND_CONSTANTS(:,4) = strpad('x_Tmax in component Concentrations (nmol_per_cm2)');
    LEGEND_ALGEBRAIC(:,1) = strpad('x_T in component Concentrations (nmol_per_cm2)');
    LEGEND_CONSTANTS(:,5) = strpad('K_I in component AE1_rate_constants (mM)');
    LEGEND_CONSTANTS(:,6) = strpad('Kc_p in component AE1_rate_constants (mM)');
    LEGEND_CONSTANTS(:,7) = strpad('Kc_pp in component AE1_rate_constants (mM)');
    LEGEND_CONSTANTS(:,8) = strpad('Kb_p in component AE1_rate_constants (mM)');
    LEGEND_CONSTANTS(:,9) = strpad('Kb_pp in component AE1_rate_constants (mM)');
    LEGEND_CONSTANTS(:,10) = strpad('Pc_p in component AE1_rate_constants (per_s)');
    LEGEND_CONSTANTS(:,11) = strpad('Pc_pp in component AE1_rate_constants (per_s)');
    LEGEND_CONSTANTS(:,12) = strpad('Pb_p in component AE1_rate_constants (per_s)');
    LEGEND_CONSTANTS(:,13) = strpad('Pb_pp in component AE1_rate_constants (per_s)');
    LEGEND_CONSTANTS(:,14) = strpad('beta_p in component AE1 (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('beta_pp in component AE1 (dimensionless)');
    LEGEND_CONSTANTS(:,15) = strpad('gamma_p in component AE1 (dimensionless)');
    LEGEND_CONSTANTS(:,16) = strpad('gamma_pp in component AE1 (dimensionless)');
    LEGEND_ALGEBRAIC(:,9) = strpad('sigma in component AE1 (per_s)');
    LEGEND_ALGEBRAIC(:,10) = strpad('x_p in component AE1 (nmol_per_cm2)');
    LEGEND_ALGEBRAIC(:,11) = strpad('x_pp in component AE1 (nmol_per_cm2)');
    LEGEND_ALGEBRAIC(:,12) = strpad('J_HCO3 in component AE1 (nmol_per_s_per_cm2)');
    LEGEND_ALGEBRAIC(:,15) = strpad('J_Cl in component AE1 (nmol_per_s_per_cm2)');
    LEGEND_ALGEBRAIC(:,13) = strpad('Jb_influx in component AE1 (nmol_per_s_per_cm2)');
    LEGEND_ALGEBRAIC(:,14) = strpad('Jc_influx in component AE1 (nmol_per_s_per_cm2)');
    LEGEND_ALGEBRAIC(:,3) = strpad('Jo_bm in component AE1 (nmol_per_s_per_cm2)');
    LEGEND_ALGEBRAIC(:,4) = strpad('Ji_bm in component AE1 (nmol_per_s_per_cm2)');
    LEGEND_ALGEBRAIC(:,5) = strpad('Js_bm in component AE1 (nmol_per_s_per_cm2)');
    LEGEND_ALGEBRAIC(:,6) = strpad('Jo_cm in component AE1 (nmol_per_s_per_cm2)');
    LEGEND_ALGEBRAIC(:,7) = strpad('Ji_cm in component AE1 (nmol_per_s_per_cm2)');
    LEGEND_ALGEBRAIC(:,8) = strpad('Js_cm in component AE1 (nmol_per_s_per_cm2)');
    LEGEND_RATES(:,1) = strpad('d/dt HCO3_i 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) = 0;
    CONSTANTS(:,1) = 26;
    CONSTANTS(:,2) = 29;
    CONSTANTS(:,3) = 114;
    CONSTANTS(:,4) = 1;
    CONSTANTS(:,5) = 172;
    CONSTANTS(:,6) = 50;
    CONSTANTS(:,7) = 50;
    CONSTANTS(:,8) = 198;
    CONSTANTS(:,9) = 198;
    CONSTANTS(:,10) = 562;
    CONSTANTS(:,11) = 61;
    CONSTANTS(:,12) = 1247;
    CONSTANTS(:,13) = 135;
    CONSTANTS(:,14) = CONSTANTS(:,1)./CONSTANTS(:,8);
    CONSTANTS(:,16) = 60.0000;
    CONSTANTS(:,15) = CONSTANTS(:,3)./CONSTANTS(:,6);
    CONSTANTS(:,16) = CONSTANTS(:,2)./CONSTANTS(:,7);
    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(:,16);
   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(:,4)./(1.00000+STATES(:,1)./CONSTANTS(:,5));
    ALGEBRAIC(:,2) = STATES(:,1)./CONSTANTS(:,9);
    ALGEBRAIC(:,3) = power( (1.00000./ALGEBRAIC(:,1)).*(1.00000./CONSTANTS(:,12)+1.00000./CONSTANTS(:,13)+CONSTANTS(:,9)./( CONSTANTS(:,13).*STATES(:,1))),  - 1.00000);
    ALGEBRAIC(:,4) = power( (1.00000./ALGEBRAIC(:,1)).*(1.00000./CONSTANTS(:,12)+1.00000./CONSTANTS(:,13)+CONSTANTS(:,8)./( CONSTANTS(:,12).*CONSTANTS(:,1))),  - 1.00000);
    ALGEBRAIC(:,5) = power( (1.00000./ALGEBRAIC(:,1)).*(1.00000./CONSTANTS(:,12)+1.00000./CONSTANTS(:,13)),  - 1.00000);
    ALGEBRAIC(:,6) = power( (1.00000./ALGEBRAIC(:,1)).*(1.00000./CONSTANTS(:,10)+1.00000./CONSTANTS(:,11)+CONSTANTS(:,7)./( CONSTANTS(:,11).*CONSTANTS(:,2))),  - 1.00000);
    ALGEBRAIC(:,7) = power( (1.00000./ALGEBRAIC(:,1)).*(1.00000./CONSTANTS(:,10)+1.00000./CONSTANTS(:,11)+CONSTANTS(:,6)./( CONSTANTS(:,10).*CONSTANTS(:,3))),  - 1.00000);
    ALGEBRAIC(:,8) = power( (1.00000./ALGEBRAIC(:,1)).*(1.00000./CONSTANTS(:,10)+1.00000./CONSTANTS(:,11)),  - 1.00000);
    ALGEBRAIC(:,9) =  (1.00000+CONSTANTS(:,14)+CONSTANTS(:,15)).*( CONSTANTS(:,13).*ALGEBRAIC(:,2)+ CONSTANTS(:,11).*CONSTANTS(:,16))+ (1.00000+ALGEBRAIC(:,2)+CONSTANTS(:,16)).*( CONSTANTS(:,12).*CONSTANTS(:,14)+ CONSTANTS(:,10).*CONSTANTS(:,15));
    ALGEBRAIC(:,10) = ( ALGEBRAIC(:,1).*( CONSTANTS(:,13).*ALGEBRAIC(:,2)+ CONSTANTS(:,11).*CONSTANTS(:,16)))./ALGEBRAIC(:,9);
    ALGEBRAIC(:,11) = ( ALGEBRAIC(:,1).*( CONSTANTS(:,12).*CONSTANTS(:,14)+ CONSTANTS(:,10).*CONSTANTS(:,15)))./ALGEBRAIC(:,9);
    ALGEBRAIC(:,12) =  (ALGEBRAIC(:,1)./ALGEBRAIC(:,9)).*( CONSTANTS(:,13).*ALGEBRAIC(:,2).*CONSTANTS(:,10).*CONSTANTS(:,15) -  CONSTANTS(:,12).*CONSTANTS(:,14).*CONSTANTS(:,11).*CONSTANTS(:,16));
    ALGEBRAIC(:,13) =  (ALGEBRAIC(:,1)./ALGEBRAIC(:,9)).*CONSTANTS(:,12).*CONSTANTS(:,14).*( CONSTANTS(:,13).*ALGEBRAIC(:,2)+ CONSTANTS(:,11).*CONSTANTS(:,16));
    ALGEBRAIC(:,14) =  (ALGEBRAIC(:,1)./ALGEBRAIC(:,9)).*CONSTANTS(:,10).*CONSTANTS(:,15).*( CONSTANTS(:,13).*ALGEBRAIC(:,2)+ CONSTANTS(:,11).*CONSTANTS(:,16));
    ALGEBRAIC(:,15) =  - ALGEBRAIC(:,12);
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