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 18 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_CONSTANTS(:,1) = strpad('C_ext_Na in component Concentrations (mM)');
    LEGEND_CONSTANTS(:,2) = strpad('C_ext_H in component Concentrations (mM)');
    LEGEND_CONSTANTS(:,3) = strpad('C_ext_NH4 in component Concentrations (mM)');
    LEGEND_CONSTANTS(:,4) = strpad('C_int_Na in component Concentrations (mM)');
    LEGEND_ALGEBRAIC(:,1) = strpad('C_int_H in component Concentrations (mM)');
    LEGEND_CONSTANTS(:,5) = strpad('C_int_NH4 in component Concentrations (mM)');
    LEGEND_STATES(:,1) = strpad('pH_int in component Concentrations (dimensionless)');
    LEGEND_CONSTANTS(:,6) = strpad('XTxP0_NHE3_Na in component NHE3_Parameters (nmol_per_s_per_cm2)');
    LEGEND_CONSTANTS(:,7) = strpad('XTxP0_NHE3_H in component NHE3_Parameters (nmol_per_s_per_cm2)');
    LEGEND_CONSTANTS(:,8) = strpad('XTxP0_NHE3_NH4 in component NHE3_Parameters (nmol_per_s_per_cm2)');
    LEGEND_CONSTANTS(:,9) = strpad('K_NHE3_Na in component NHE3_Parameters (mM)');
    LEGEND_CONSTANTS(:,10) = strpad('K_NHE3_H in component NHE3_Parameters (mM)');
    LEGEND_CONSTANTS(:,11) = strpad('K_NHE3_NH4 in component NHE3_Parameters (mM)');
    LEGEND_ALGEBRAIC(:,3) = strpad('XTxP_NHE3_Na in component NHE3 (nmol_per_s_per_cm2)');
    LEGEND_ALGEBRAIC(:,4) = strpad('XTxP_NHE3_H in component NHE3 (nmol_per_s_per_cm2)');
    LEGEND_ALGEBRAIC(:,5) = strpad('XTxP_NHE3_NH4 in component NHE3 (nmol_per_s_per_cm2)');
    LEGEND_CONSTANTS(:,12) = strpad('alpha_ext_Na in component NHE3 (dimensionless)');
    LEGEND_CONSTANTS(:,13) = strpad('beta_ext_H in component NHE3 (dimensionless)');
    LEGEND_CONSTANTS(:,14) = strpad('gamma_ext_NH4 in component NHE3 (dimensionless)');
    LEGEND_CONSTANTS(:,15) = strpad('alpha_int_Na in component NHE3 (dimensionless)');
    LEGEND_ALGEBRAIC(:,2) = strpad('beta_int_H in component NHE3 (dimensionless)');
    LEGEND_CONSTANTS(:,16) = strpad('gamma_int_NH4 in component NHE3 (dimensionless)');
    LEGEND_ALGEBRAIC(:,6) = strpad('sum_NHE3 in component NHE3 (nmol_per_s_per_cm2)');
    LEGEND_ALGEBRAIC(:,7) = strpad('J_NHE3_Na in component NHE3 (nmol_per_s_per_cm2)');
    LEGEND_ALGEBRAIC(:,8) = strpad('J_NHE3_H in component NHE3 (nmol_per_s_per_cm2)');
    LEGEND_ALGEBRAIC(:,9) = strpad('J_NHE3_NH4 in component NHE3 (nmol_per_s_per_cm2)');
    LEGEND_CONSTANTS(:,17) = strpad('J_NHE3_Na_Max in component NHE3 (nmol_per_s_per_cm2)');
    LEGEND_ALGEBRAIC(:,11) = strpad('plot in component NHE3 (dimensionless)');
    LEGEND_ALGEBRAIC(:,12) = strpad('J_NHE3_Na2 in component NHE3 (nmol_per_s_per_cm2)');
    LEGEND_ALGEBRAIC(:,13) = strpad('J_NHE3_H2 in component NHE3 (nmol_per_s_per_cm2)');
    LEGEND_ALGEBRAIC(:,14) = strpad('J_NHE3_NH42 in component NHE3 (nmol_per_s_per_cm2)');
    LEGEND_ALGEBRAIC(:,10) = strpad('sum0_NHE3 in component NHE3 (nmol_per_s_per_cm2)');
    LEGEND_ALGEBRAIC(:,15) = strpad('plot2 in component NHE3 (dimensionless)');
    LEGEND_RATES(:,1) = strpad('d/dt pH_int in component Concentrations (dimensionless)');
    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) = 1;
    CONSTANTS(:,2) = 5.4954e-5;
    CONSTANTS(:,3) = 0;
    CONSTANTS(:,4) = 0;
    CONSTANTS(:,5) = 0;
    STATES(:,1) = 4;
    CONSTANTS(:,6) = 1.6e-3;
    CONSTANTS(:,7) = 0.48e-3;
    CONSTANTS(:,8) = 1.6e-3;
    CONSTANTS(:,9) = 30;
    CONSTANTS(:,10) = 72e-6;
    CONSTANTS(:,11) = 0.027e3;
    CONSTANTS(:,12) = CONSTANTS(:,1)./CONSTANTS(:,9);
    CONSTANTS(:,17) = 5.00000;
    CONSTANTS(:,13) = CONSTANTS(:,2)./CONSTANTS(:,10);
    CONSTANTS(:,14) = CONSTANTS(:,3)./CONSTANTS(:,11);
    CONSTANTS(:,15) = CONSTANTS(:,4)./CONSTANTS(:,9);
    CONSTANTS(:,16) = CONSTANTS(:,5)./CONSTANTS(:,11);
    CONSTANTS(:,17) = ( CONSTANTS(:,6).*CONSTANTS(:,7))./(CONSTANTS(:,6)+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(:,17);
   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) =  1000.00.*power(10.0000,  - STATES(:,1));
    ALGEBRAIC(:,2) = ALGEBRAIC(:,1)./CONSTANTS(:,10);
    ALGEBRAIC(:,3) = ( CONSTANTS(:,6).*2.00000.*ALGEBRAIC(:,1))./(ALGEBRAIC(:,1)+0.00100000);
    ALGEBRAIC(:,4) = ( CONSTANTS(:,7).*2.00000.*ALGEBRAIC(:,1))./(ALGEBRAIC(:,1)+0.00100000);
    ALGEBRAIC(:,5) = ( CONSTANTS(:,8).*2.00000.*ALGEBRAIC(:,1))./(ALGEBRAIC(:,1)+0.00100000);
    ALGEBRAIC(:,6) =  (1.00000+CONSTANTS(:,12)+CONSTANTS(:,13)+CONSTANTS(:,14)).*( ALGEBRAIC(:,3).*CONSTANTS(:,15)+ ALGEBRAIC(:,4).*ALGEBRAIC(:,2)+ ALGEBRAIC(:,5).*CONSTANTS(:,16))+ (1.00000+CONSTANTS(:,15)+ALGEBRAIC(:,2)+CONSTANTS(:,16)).*( ALGEBRAIC(:,3).*CONSTANTS(:,12)+ ALGEBRAIC(:,4).*CONSTANTS(:,13)+ ALGEBRAIC(:,5).*CONSTANTS(:,14));
    ALGEBRAIC(:,7) =  (( ALGEBRAIC(:,3).*ALGEBRAIC(:,4))./ALGEBRAIC(:,6)).*( CONSTANTS(:,12).*ALGEBRAIC(:,2) -  CONSTANTS(:,15).*CONSTANTS(:,13))+ (( ALGEBRAIC(:,3).*ALGEBRAIC(:,5))./ALGEBRAIC(:,6)).*( CONSTANTS(:,12).*CONSTANTS(:,16) -  CONSTANTS(:,15).*CONSTANTS(:,14));
    ALGEBRAIC(:,8) =  (( ALGEBRAIC(:,3).*ALGEBRAIC(:,4))./ALGEBRAIC(:,6)).*( CONSTANTS(:,15).*CONSTANTS(:,13) -  CONSTANTS(:,12).*ALGEBRAIC(:,2))+ (( ALGEBRAIC(:,4).*ALGEBRAIC(:,5))./ALGEBRAIC(:,6)).*( CONSTANTS(:,13).*CONSTANTS(:,16) -  ALGEBRAIC(:,2).*CONSTANTS(:,14));
    ALGEBRAIC(:,9) =  (( ALGEBRAIC(:,3).*ALGEBRAIC(:,5))./ALGEBRAIC(:,6)).*( CONSTANTS(:,15).*CONSTANTS(:,14) -  CONSTANTS(:,12).*CONSTANTS(:,16))+ (( ALGEBRAIC(:,4).*ALGEBRAIC(:,5))./ALGEBRAIC(:,6)).*( CONSTANTS(:,14).*ALGEBRAIC(:,2) -  CONSTANTS(:,13).*CONSTANTS(:,16));
    ALGEBRAIC(:,10) =  (1.00000+CONSTANTS(:,12)+CONSTANTS(:,13)+CONSTANTS(:,14)).*( CONSTANTS(:,6).*CONSTANTS(:,15)+ CONSTANTS(:,7).*ALGEBRAIC(:,2)+ CONSTANTS(:,8).*CONSTANTS(:,16))+ (1.00000+CONSTANTS(:,15)+ALGEBRAIC(:,2)+CONSTANTS(:,16)).*( CONSTANTS(:,6).*CONSTANTS(:,12)+ CONSTANTS(:,7).*CONSTANTS(:,13)+ CONSTANTS(:,8).*CONSTANTS(:,14));
    ALGEBRAIC(:,11) = ALGEBRAIC(:,7)./CONSTANTS(:,17);
    ALGEBRAIC(:,12) =  (( CONSTANTS(:,6).*CONSTANTS(:,7))./ALGEBRAIC(:,10)).*( CONSTANTS(:,12).*ALGEBRAIC(:,2) -  CONSTANTS(:,15).*CONSTANTS(:,13))+ (( CONSTANTS(:,6).*CONSTANTS(:,8))./ALGEBRAIC(:,6)).*( CONSTANTS(:,12).*CONSTANTS(:,16) -  CONSTANTS(:,15).*CONSTANTS(:,14));
    ALGEBRAIC(:,13) =  (( CONSTANTS(:,6).*CONSTANTS(:,7))./ALGEBRAIC(:,10)).*( CONSTANTS(:,15).*CONSTANTS(:,13) -  CONSTANTS(:,12).*ALGEBRAIC(:,2))+ (( CONSTANTS(:,7).*CONSTANTS(:,8))./ALGEBRAIC(:,6)).*( CONSTANTS(:,13).*CONSTANTS(:,16) -  ALGEBRAIC(:,2).*CONSTANTS(:,14));
    ALGEBRAIC(:,14) =  (( CONSTANTS(:,6).*CONSTANTS(:,8))./ALGEBRAIC(:,10)).*( CONSTANTS(:,15).*CONSTANTS(:,14) -  CONSTANTS(:,12).*CONSTANTS(:,16))+ (( CONSTANTS(:,7).*CONSTANTS(:,8))./ALGEBRAIC(:,6)).*( CONSTANTS(:,14).*ALGEBRAIC(:,2) -  CONSTANTS(:,13).*CONSTANTS(:,16));
    ALGEBRAIC(:,15) = ALGEBRAIC(:,12)./CONSTANTS(:,17);
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