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 =20;
end
% There are a total of 10 entries in each of the rate and state variable arrays.
% There are a total of 21 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_OH_i in component environment (fmol)');
    LEGEND_STATES(:,2) = strpad('q_OH_o in component environment (fmol)');
    LEGEND_STATES(:,3) = strpad('q_Cl_i in component environment (fmol)');
    LEGEND_STATES(:,4) = strpad('q_Cl_o in component environment (fmol)');
    LEGEND_STATES(:,5) = strpad('q_S1_CHE in component environment (fmol)');
    LEGEND_STATES(:,6) = strpad('q_S2_CHE in component environment (fmol)');
    LEGEND_STATES(:,7) = strpad('q_S3_CHE in component environment (fmol)');
    LEGEND_STATES(:,8) = strpad('q_S4_CHE in component environment (fmol)');
    LEGEND_STATES(:,9) = strpad('q_S5_CHE in component environment (fmol)');
    LEGEND_STATES(:,10) = strpad('q_S6_CHE in component environment (fmol)');
    LEGEND_ALGEBRAIC(:,15) = strpad('v_R61_CHE in component CHE (fmol_per_sec)');
    LEGEND_ALGEBRAIC(:,16) = strpad('v_R12_CHE in component CHE (fmol_per_sec)');
    LEGEND_ALGEBRAIC(:,17) = strpad('v_R23_CHE in component CHE (fmol_per_sec)');
    LEGEND_ALGEBRAIC(:,18) = strpad('v_R34_CHE in component CHE (fmol_per_sec)');
    LEGEND_ALGEBRAIC(:,19) = strpad('v_R45_CHE in component CHE (fmol_per_sec)');
    LEGEND_ALGEBRAIC(:,20) = strpad('v_R56_CHE in component CHE (fmol_per_sec)');
    LEGEND_ALGEBRAIC(:,4) = strpad('pH_i in component environment (dimensionless)');
    LEGEND_ALGEBRAIC(:,5) = strpad('pH_o in component environment (dimensionless)');
    LEGEND_ALGEBRAIC(:,1) = strpad('cOH_i in component environment (mM)');
    LEGEND_ALGEBRAIC(:,2) = strpad('cOH_o in component environment (mM)');
    LEGEND_CONSTANTS(:,1) = strpad('w_i in component environment (pL)');
    LEGEND_CONSTANTS(:,2) = strpad('w_o in component environment (pL)');
    LEGEND_CONSTANTS(:,3) = strpad('kappa_R61_CHE in component CHE_parameters (fmol_per_sec)');
    LEGEND_CONSTANTS(:,4) = strpad('kappa_R12_CHE in component CHE_parameters (fmol_per_sec)');
    LEGEND_CONSTANTS(:,5) = strpad('kappa_R23_CHE in component CHE_parameters (fmol_per_sec)');
    LEGEND_CONSTANTS(:,6) = strpad('kappa_R34_CHE in component CHE_parameters (fmol_per_sec)');
    LEGEND_CONSTANTS(:,7) = strpad('kappa_R45_CHE in component CHE_parameters (fmol_per_sec)');
    LEGEND_CONSTANTS(:,8) = strpad('kappa_R56_CHE in component CHE_parameters (fmol_per_sec)');
    LEGEND_CONSTANTS(:,9) = strpad('K_OH_i in component CHE_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,10) = strpad('K_OH_o in component CHE_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,11) = strpad('K_Cl_i in component CHE_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,12) = strpad('K_Cl_o in component CHE_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,13) = strpad('K_S1_CHE in component CHE_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,14) = strpad('K_S2_CHE in component CHE_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,15) = strpad('K_S3_CHE in component CHE_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,16) = strpad('K_S4_CHE in component CHE_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,17) = strpad('K_S5_CHE in component CHE_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,18) = strpad('K_S6_CHE in component CHE_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,19) = strpad('R in component constants (J_per_K_per_mol)');
    LEGEND_CONSTANTS(:,20) = strpad('T in component constants (kelvin)');
    LEGEND_ALGEBRAIC(:,3) = strpad('mu_OH_i in component CHE (J_per_mol)');
    LEGEND_ALGEBRAIC(:,6) = strpad('mu_OH_o in component CHE (J_per_mol)');
    LEGEND_ALGEBRAIC(:,7) = strpad('mu_Cl_i in component CHE (J_per_mol)');
    LEGEND_ALGEBRAIC(:,8) = strpad('mu_Cl_o in component CHE (J_per_mol)');
    LEGEND_ALGEBRAIC(:,9) = strpad('mu_S1_CHE in component CHE (J_per_mol)');
    LEGEND_ALGEBRAIC(:,10) = strpad('mu_S2_CHE in component CHE (J_per_mol)');
    LEGEND_ALGEBRAIC(:,11) = strpad('mu_S3_CHE in component CHE (J_per_mol)');
    LEGEND_ALGEBRAIC(:,12) = strpad('mu_S4_CHE in component CHE (J_per_mol)');
    LEGEND_ALGEBRAIC(:,13) = strpad('mu_S5_CHE in component CHE (J_per_mol)');
    LEGEND_ALGEBRAIC(:,14) = strpad('mu_S6_CHE in component CHE (J_per_mol)');
    LEGEND_CONSTANTS(:,21) = strpad('F in component constants (C_per_mol)');
    LEGEND_RATES(:,1) = strpad('d/dt q_OH_i in component environment (fmol)');
    LEGEND_RATES(:,2) = strpad('d/dt q_OH_o in component environment (fmol)');
    LEGEND_RATES(:,3) = strpad('d/dt q_Cl_i in component environment (fmol)');
    LEGEND_RATES(:,4) = strpad('d/dt q_Cl_o in component environment (fmol)');
    LEGEND_RATES(:,5) = strpad('d/dt q_S1_CHE in component environment (fmol)');
    LEGEND_RATES(:,6) = strpad('d/dt q_S2_CHE in component environment (fmol)');
    LEGEND_RATES(:,7) = strpad('d/dt q_S3_CHE in component environment (fmol)');
    LEGEND_RATES(:,8) = strpad('d/dt q_S4_CHE in component environment (fmol)');
    LEGEND_RATES(:,9) = strpad('d/dt q_S5_CHE in component environment (fmol)');
    LEGEND_RATES(:,10) = strpad('d/dt q_S6_CHE 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) = 5.36764E-06;
    STATES(:,2) = 1.30166E-06;
    STATES(:,3) = 824.6;
    STATES(:,4) = 725.48;
    STATES(:,5) = 1.666e-7;
    STATES(:,6) = 1.666e-7;
    STATES(:,7) = 1.666e-7;
    STATES(:,8) = 1.666e-7;
    STATES(:,9) = 1.666e-7;
    STATES(:,10) = 1.666e-7;
    CONSTANTS(:,1) = 38;
    CONSTANTS(:,2) = 5.182;
    CONSTANTS(:,3) = 8.77838;
    CONSTANTS(:,4) = 0.031295;
    CONSTANTS(:,5) = 50940.7;
    CONSTANTS(:,6) = 0.000192726;
    CONSTANTS(:,7) = 2.96501e+06;
    CONSTANTS(:,8) = 1.82153e+06;
    CONSTANTS(:,9) = 0.0253475;
    CONSTANTS(:,10) = 7203.46;
    CONSTANTS(:,11) = 0.015572;
    CONSTANTS(:,12) = 0.00442538;
    CONSTANTS(:,13) = 28.479;
    CONSTANTS(:,14) = 856.026;
    CONSTANTS(:,15) = 353352;
    CONSTANTS(:,16) = 6070.81;
    CONSTANTS(:,17) = 0.569962;
    CONSTANTS(:,18) = 0.4887;
    CONSTANTS(:,19) = 8.31;
    CONSTANTS(:,20) = 310;
    CONSTANTS(:,21) = 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(:,6) =  CONSTANTS(:,19).*CONSTANTS(:,20).*log( CONSTANTS(:,10).*STATES(:,2));
    ALGEBRAIC(:,9) =  CONSTANTS(:,19).*CONSTANTS(:,20).*log( CONSTANTS(:,13).*STATES(:,5));
    ALGEBRAIC(:,10) =  CONSTANTS(:,19).*CONSTANTS(:,20).*log( CONSTANTS(:,14).*STATES(:,6));
    ALGEBRAIC(:,16) =  CONSTANTS(:,4).*(exp(ALGEBRAIC(:,9)./( CONSTANTS(:,19).*CONSTANTS(:,20))) - exp((ALGEBRAIC(:,10)+ALGEBRAIC(:,6))./( CONSTANTS(:,19).*CONSTANTS(:,20))));
    RATES(:,2) = ALGEBRAIC(:,16);
    ALGEBRAIC(:,14) =  CONSTANTS(:,19).*CONSTANTS(:,20).*log( CONSTANTS(:,18).*STATES(:,10));
    ALGEBRAIC(:,15) =  CONSTANTS(:,3).*(exp(ALGEBRAIC(:,14)./( CONSTANTS(:,19).*CONSTANTS(:,20))) - exp(ALGEBRAIC(:,9)./( CONSTANTS(:,19).*CONSTANTS(:,20))));
    RATES(:,5) = ALGEBRAIC(:,15) - ALGEBRAIC(:,16);
    ALGEBRAIC(:,8) =  CONSTANTS(:,19).*CONSTANTS(:,20).*log( CONSTANTS(:,12).*STATES(:,4));
    ALGEBRAIC(:,11) =  CONSTANTS(:,19).*CONSTANTS(:,20).*log( CONSTANTS(:,15).*STATES(:,7));
    ALGEBRAIC(:,17) =  CONSTANTS(:,5).*(exp((ALGEBRAIC(:,10)+ALGEBRAIC(:,8))./( CONSTANTS(:,19).*CONSTANTS(:,20))) - exp(ALGEBRAIC(:,11)./( CONSTANTS(:,19).*CONSTANTS(:,20))));
    RATES(:,4) =  - ALGEBRAIC(:,17);
    RATES(:,6) = ALGEBRAIC(:,16) - ALGEBRAIC(:,17);
    ALGEBRAIC(:,12) =  CONSTANTS(:,19).*CONSTANTS(:,20).*log( CONSTANTS(:,16).*STATES(:,8));
    ALGEBRAIC(:,18) =  CONSTANTS(:,6).*(exp(ALGEBRAIC(:,11)./( CONSTANTS(:,19).*CONSTANTS(:,20))) - exp(ALGEBRAIC(:,12)./( CONSTANTS(:,19).*CONSTANTS(:,20))));
    RATES(:,7) = ALGEBRAIC(:,17) - ALGEBRAIC(:,18);
    ALGEBRAIC(:,7) =  CONSTANTS(:,19).*CONSTANTS(:,20).*log( CONSTANTS(:,11).*STATES(:,3));
    ALGEBRAIC(:,13) =  CONSTANTS(:,19).*CONSTANTS(:,20).*log( CONSTANTS(:,17).*STATES(:,9));
    ALGEBRAIC(:,19) =  CONSTANTS(:,7).*(exp(ALGEBRAIC(:,12)./( CONSTANTS(:,19).*CONSTANTS(:,20))) - exp((ALGEBRAIC(:,13)+ALGEBRAIC(:,7))./( CONSTANTS(:,19).*CONSTANTS(:,20))));
    RATES(:,3) = ALGEBRAIC(:,19);
    RATES(:,8) = ALGEBRAIC(:,18) - ALGEBRAIC(:,19);
    ALGEBRAIC(:,3) =  CONSTANTS(:,19).*CONSTANTS(:,20).*log( CONSTANTS(:,9).*STATES(:,1));
    ALGEBRAIC(:,20) =  CONSTANTS(:,8).*(exp((ALGEBRAIC(:,13)+ALGEBRAIC(:,3))./( CONSTANTS(:,19).*CONSTANTS(:,20))) - exp(ALGEBRAIC(:,14)./( CONSTANTS(:,19).*CONSTANTS(:,20))));
    RATES(:,1) =  - ALGEBRAIC(:,20);
    RATES(:,9) = ALGEBRAIC(:,19) - ALGEBRAIC(:,20);
    RATES(:,10) = ALGEBRAIC(:,20) - ALGEBRAIC(:,15);
   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(:,6) =  CONSTANTS(:,19).*CONSTANTS(:,20).*log( CONSTANTS(:,10).*STATES(:,2));
    ALGEBRAIC(:,9) =  CONSTANTS(:,19).*CONSTANTS(:,20).*log( CONSTANTS(:,13).*STATES(:,5));
    ALGEBRAIC(:,10) =  CONSTANTS(:,19).*CONSTANTS(:,20).*log( CONSTANTS(:,14).*STATES(:,6));
    ALGEBRAIC(:,16) =  CONSTANTS(:,4).*(exp(ALGEBRAIC(:,9)./( CONSTANTS(:,19).*CONSTANTS(:,20))) - exp((ALGEBRAIC(:,10)+ALGEBRAIC(:,6))./( CONSTANTS(:,19).*CONSTANTS(:,20))));
    ALGEBRAIC(:,14) =  CONSTANTS(:,19).*CONSTANTS(:,20).*log( CONSTANTS(:,18).*STATES(:,10));
    ALGEBRAIC(:,15) =  CONSTANTS(:,3).*(exp(ALGEBRAIC(:,14)./( CONSTANTS(:,19).*CONSTANTS(:,20))) - exp(ALGEBRAIC(:,9)./( CONSTANTS(:,19).*CONSTANTS(:,20))));
    ALGEBRAIC(:,8) =  CONSTANTS(:,19).*CONSTANTS(:,20).*log( CONSTANTS(:,12).*STATES(:,4));
    ALGEBRAIC(:,11) =  CONSTANTS(:,19).*CONSTANTS(:,20).*log( CONSTANTS(:,15).*STATES(:,7));
    ALGEBRAIC(:,17) =  CONSTANTS(:,5).*(exp((ALGEBRAIC(:,10)+ALGEBRAIC(:,8))./( CONSTANTS(:,19).*CONSTANTS(:,20))) - exp(ALGEBRAIC(:,11)./( CONSTANTS(:,19).*CONSTANTS(:,20))));
    ALGEBRAIC(:,12) =  CONSTANTS(:,19).*CONSTANTS(:,20).*log( CONSTANTS(:,16).*STATES(:,8));
    ALGEBRAIC(:,18) =  CONSTANTS(:,6).*(exp(ALGEBRAIC(:,11)./( CONSTANTS(:,19).*CONSTANTS(:,20))) - exp(ALGEBRAIC(:,12)./( CONSTANTS(:,19).*CONSTANTS(:,20))));
    ALGEBRAIC(:,7) =  CONSTANTS(:,19).*CONSTANTS(:,20).*log( CONSTANTS(:,11).*STATES(:,3));
    ALGEBRAIC(:,13) =  CONSTANTS(:,19).*CONSTANTS(:,20).*log( CONSTANTS(:,17).*STATES(:,9));
    ALGEBRAIC(:,19) =  CONSTANTS(:,7).*(exp(ALGEBRAIC(:,12)./( CONSTANTS(:,19).*CONSTANTS(:,20))) - exp((ALGEBRAIC(:,13)+ALGEBRAIC(:,7))./( CONSTANTS(:,19).*CONSTANTS(:,20))));
    ALGEBRAIC(:,3) =  CONSTANTS(:,19).*CONSTANTS(:,20).*log( CONSTANTS(:,9).*STATES(:,1));
    ALGEBRAIC(:,20) =  CONSTANTS(:,8).*(exp((ALGEBRAIC(:,13)+ALGEBRAIC(:,3))./( CONSTANTS(:,19).*CONSTANTS(:,20))) - exp(ALGEBRAIC(:,14)./( CONSTANTS(:,19).*CONSTANTS(:,20))));
    ALGEBRAIC(:,1) = STATES(:,1)./CONSTANTS(:,1);
    ALGEBRAIC(:,2) = STATES(:,2)./CONSTANTS(:,2);
    ALGEBRAIC(:,4) = 14.0000+arbitrary_log(ALGEBRAIC(:,1), 10);
    ALGEBRAIC(:,5) = 14.0000+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