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 =6;
end
% There are a total of 3 entries in each of the rate and state variable arrays.
% There are a total of 8 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('q_CO2_i in component environment (fmol)');
    LEGEND_STATES(:,2) = strpad('q_HCO3_i in component environment (fmol)');
    LEGEND_STATES(:,3) = strpad('q_H_i in component environment (fmol)');
    LEGEND_ALGEBRAIC(:,6) = strpad('v_Re_CO2hyd in component CO2_hyd (fmol_per_sec)');
    LEGEND_ALGEBRAIC(:,4) = strpad('pH_i in component environment (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('cH_i in component environment (mM)');
    LEGEND_CONSTANTS(:,1) = strpad('w_i in component environment (pL)');
    LEGEND_CONSTANTS(:,2) = strpad('kappa_Re_CO2hyd in component CO2_hyd_parameters (fmol_per_sec)');
    LEGEND_CONSTANTS(:,3) = strpad('K_CO2_i in component CO2_hyd_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,4) = strpad('K_HCO3_i in component CO2_hyd_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,5) = strpad('K_H_i in component CO2_hyd_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,6) = strpad('R in component constants (J_per_K_per_mol)');
    LEGEND_CONSTANTS(:,7) = strpad('T in component constants (kelvin)');
    LEGEND_ALGEBRAIC(:,1) = strpad('mu_CO2_i in component CO2_hyd (J_per_mol)');
    LEGEND_ALGEBRAIC(:,3) = strpad('mu_HCO3_i in component CO2_hyd (J_per_mol)');
    LEGEND_ALGEBRAIC(:,5) = strpad('mu_H_i in component CO2_hyd (J_per_mol)');
    LEGEND_CONSTANTS(:,8) = strpad('F in component constants (C_per_mol)');
    LEGEND_RATES(:,1) = strpad('d/dt q_CO2_i in component environment (fmol)');
    LEGEND_RATES(:,2) = strpad('d/dt q_HCO3_i in component environment (fmol)');
    LEGEND_RATES(:,3) = strpad('d/dt q_H_i in component environment (fmol)');
    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) = 46.968;
    STATES(:,2) = 509.2;
    STATES(:,3) = 2.69019E-06;
    CONSTANTS(:,1) = 38;
    CONSTANTS(:,2) = 153.093;
    CONSTANTS(:,3) = 82.5092;
    CONSTANTS(:,4) = 0.00128495;
    CONSTANTS(:,5) = 0.00128495;
    CONSTANTS(:,6) = 8.31;
    CONSTANTS(:,7) = 310;
    CONSTANTS(:,8) = 96485;
    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(:,1) =  CONSTANTS(:,6).*CONSTANTS(:,7).*log( CONSTANTS(:,3).*STATES(:,1));
    ALGEBRAIC(:,3) =  CONSTANTS(:,6).*CONSTANTS(:,7).*log( CONSTANTS(:,4).*STATES(:,2));
    ALGEBRAIC(:,5) =  CONSTANTS(:,6).*CONSTANTS(:,7).*log( CONSTANTS(:,5).*STATES(:,3));
    ALGEBRAIC(:,6) =  CONSTANTS(:,2).*(exp(ALGEBRAIC(:,1)./( CONSTANTS(:,6).*CONSTANTS(:,7))) - exp((ALGEBRAIC(:,3)+ALGEBRAIC(:,5))./( CONSTANTS(:,6).*CONSTANTS(:,7))));
    RATES(:,1) =  - ALGEBRAIC(:,6);
    RATES(:,2) = ALGEBRAIC(:,6);
    RATES(:,3) = ALGEBRAIC(:,6);
   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(:,6).*CONSTANTS(:,7).*log( CONSTANTS(:,3).*STATES(:,1));
    ALGEBRAIC(:,3) =  CONSTANTS(:,6).*CONSTANTS(:,7).*log( CONSTANTS(:,4).*STATES(:,2));
    ALGEBRAIC(:,5) =  CONSTANTS(:,6).*CONSTANTS(:,7).*log( CONSTANTS(:,5).*STATES(:,3));
    ALGEBRAIC(:,6) =  CONSTANTS(:,2).*(exp(ALGEBRAIC(:,1)./( CONSTANTS(:,6).*CONSTANTS(:,7))) - exp((ALGEBRAIC(:,3)+ALGEBRAIC(:,5))./( CONSTANTS(:,6).*CONSTANTS(:,7))));
    ALGEBRAIC(:,2) = STATES(:,3)./CONSTANTS(:,1);
    ALGEBRAIC(:,4) =  - arbitrary_log(ALGEBRAIC(:,2), 10);
end

% Compute a logarithm to any base" +
function x = arbitrary_log(a, base)
    x = log(a) ./ log(base);
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