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 2 entries in each of the rate and state variable arrays.
% There are a total of 13 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('t in component main (second)');
    LEGEND_CONSTANTS(:,1) = strpad('V_m in component main (J_per_C)');
    LEGEND_CONSTANTS(:,2) = strpad('RTF in component main (J_per_C)');
    LEGEND_CONSTANTS(:,11) = strpad('epsilon in component main (dimensionless)');
    LEGEND_STATES(:,1) = strpad('TA_i in component main (mol_per_m3)');
    LEGEND_ALGEBRAIC(:,1) = strpad('CO2_o in component main (mol_per_m3)');
    LEGEND_ALGEBRAIC(:,6) = strpad('CO2_i in component main (mol_per_m3)');
    LEGEND_ALGEBRAIC(:,8) = strpad('HCO3_i in component main (mol_per_m3)');
    LEGEND_ALGEBRAIC(:,2) = strpad('HCO3_o in component main (mol_per_m3)');
    LEGEND_STATES(:,2) = strpad('H_i in component main (mol_per_m3)');
    LEGEND_CONSTANTS(:,3) = strpad('H_o in component main (mol_per_m3)');
    LEGEND_CONSTANTS(:,4) = strpad('H_Lim in component main (mol_per_m3)');
    LEGEND_ALGEBRAIC(:,7) = strpad('M_CO2 in component main (mol_per_m2_s)');
    LEGEND_ALGEBRAIC(:,9) = strpad('M_HCO3 in component main (mol_per_m2_s)');
    LEGEND_ALGEBRAIC(:,4) = strpad('M_H in component main (mol_per_m2_s)');
    LEGEND_ALGEBRAIC(:,3) = strpad('pH_i in component main (dimensionless)');
    LEGEND_CONSTANTS(:,12) = strpad('pH_o in component main (dimensionless)');
    LEGEND_CONSTANTS(:,13) = strpad('pH_Lim in component main (dimensionless)');
    LEGEND_CONSTANTS(:,5) = strpad('P_CO2 in component main (m_per_s)');
    LEGEND_CONSTANTS(:,6) = strpad('P_HCO3 in component main (m_per_s)');
    LEGEND_CONSTANTS(:,7) = strpad('k in component main (m_per_s)');
    LEGEND_CONSTANTS(:,8) = strpad('K_A in component main (mol_per_m3)');
    LEGEND_CONSTANTS(:,9) = strpad('rho in component main (per_m)');
    LEGEND_ALGEBRAIC(:,5) = strpad('alpha_i in component main (dimensionless)');
    LEGEND_CONSTANTS(:,10) = strpad('beta in component main (mol_per_m3)');
    LEGEND_RATES(:,1) = strpad('d/dt TA_i in component main (mol_per_m3)');
    LEGEND_RATES(:,2) = strpad('d/dt H_i in component main (mol_per_m3)');
    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 = [];
    CONSTANTS(:,1) = -0.057;
    CONSTANTS(:,2) = 0.0256796;
    STATES(:,1) = 0.0;
    STATES(:,2) = 3.981071705534970e-05;
    CONSTANTS(:,3) = 1.995262314968879e-05;
    CONSTANTS(:,4) = 3.981071705534970e-05;
    CONSTANTS(:,5) = 6e-5;
    CONSTANTS(:,6) = 5e-9;
    CONSTANTS(:,7) = 0.0375;
    CONSTANTS(:,8) = 1e-3;
    CONSTANTS(:,9) = 8000;
    CONSTANTS(:,10) = -26;
    CONSTANTS(:,11) = exp( - CONSTANTS(:,1)./CONSTANTS(:,2));
    CONSTANTS(:,12) =  - arbitrary_log( 0.00100000.*CONSTANTS(:,3), 10);
    CONSTANTS(:,13) =  - arbitrary_log( 0.00100000.*CONSTANTS(:,4), 10);
    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) = piecewise({VOI<100.000, 0.00000 , VOI<2800.00, 1.18770 }, 0.00000);
    ALGEBRAIC(:,5) = STATES(:,2)./(STATES(:,2)+CONSTANTS(:,8));
    ALGEBRAIC(:,6) =  ALGEBRAIC(:,5).*STATES(:,1);
    ALGEBRAIC(:,7) =  CONSTANTS(:,5).*(ALGEBRAIC(:,1) - ALGEBRAIC(:,6));
    ALGEBRAIC(:,8) =  (1.00000 - ALGEBRAIC(:,5)).*STATES(:,1);
    ALGEBRAIC(:,2) = ( CONSTANTS(:,8).*ALGEBRAIC(:,1))./CONSTANTS(:,3);
    ALGEBRAIC(:,9) = ( (( CONSTANTS(:,6).*CONSTANTS(:,1))./CONSTANTS(:,2)).*(ALGEBRAIC(:,2) -  ALGEBRAIC(:,8).*CONSTANTS(:,11)))./(1.00000 - CONSTANTS(:,11));
    RATES(:,1) =  CONSTANTS(:,9).*(ALGEBRAIC(:,7)+ALGEBRAIC(:,9));
    ALGEBRAIC(:,3) =  - arbitrary_log( 0.00100000.*STATES(:,2), 10);
    ALGEBRAIC(:,4) = piecewise({ALGEBRAIC(:,3)<CONSTANTS(:,13),  CONSTANTS(:,7).*(STATES(:,2) - CONSTANTS(:,4)) }, 0.00000);
    RATES(:,2) =  ((  - 2.30300.*STATES(:,2))./CONSTANTS(:,10)).*CONSTANTS(:,9).*(( (1.00000 - ALGEBRAIC(:,5)).*ALGEBRAIC(:,7) -  ALGEBRAIC(:,5).*ALGEBRAIC(:,9)) - ALGEBRAIC(:,4));
   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) = piecewise({VOI<100.000, 0.00000 , VOI<2800.00, 1.18770 }, 0.00000);
    ALGEBRAIC(:,5) = STATES(:,2)./(STATES(:,2)+CONSTANTS(:,8));
    ALGEBRAIC(:,6) =  ALGEBRAIC(:,5).*STATES(:,1);
    ALGEBRAIC(:,7) =  CONSTANTS(:,5).*(ALGEBRAIC(:,1) - ALGEBRAIC(:,6));
    ALGEBRAIC(:,8) =  (1.00000 - ALGEBRAIC(:,5)).*STATES(:,1);
    ALGEBRAIC(:,2) = ( CONSTANTS(:,8).*ALGEBRAIC(:,1))./CONSTANTS(:,3);
    ALGEBRAIC(:,9) = ( (( CONSTANTS(:,6).*CONSTANTS(:,1))./CONSTANTS(:,2)).*(ALGEBRAIC(:,2) -  ALGEBRAIC(:,8).*CONSTANTS(:,11)))./(1.00000 - CONSTANTS(:,11));
    ALGEBRAIC(:,3) =  - arbitrary_log( 0.00100000.*STATES(:,2), 10);
    ALGEBRAIC(:,4) = piecewise({ALGEBRAIC(:,3)<CONSTANTS(:,13),  CONSTANTS(:,7).*(STATES(:,2) - CONSTANTS(:,4)) }, 0.00000);
end

% Compute result of a piecewise function
function x = piecewise(cases, default)
    set = [0];
    for i = 1:2:length(cases)
        if (length(cases{i+1}) == 1)
            x(cases{i} & ~set,:) = cases{i+1};
        else
            x(cases{i} & ~set,:) = cases{i+1}(cases{i} & ~set);
        end
        set = set | cases{i};
        if(set), break, end
    end
    if (length(default) == 1)
        x(~set,:) = default;
    else
        x(~set,:) = default(~set);
    end
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