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 1 entries in each of the rate and state variable arrays.
% There are a total of 25 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('Na_ext in component concentrations (mM)');
    LEGEND_CONSTANTS(:,1) = strpad('Na_int in component concentrations (mM)');
    LEGEND_CONSTANTS(:,2) = strpad('H_ext in component concentrations (mM)');
    LEGEND_CONSTANTS(:,3) = strpad('H_int in component concentrations (mM)');
    LEGEND_CONSTANTS(:,4) = strpad('NH4_ext in component concentrations (mM)');
    LEGEND_CONSTANTS(:,5) = strpad('NH4_int in component concentrations (mM)');
    LEGEND_ALGEBRAIC(:,3) = strpad('J_NHE3_Na in component NHE3 (mM_per_s)');
    LEGEND_ALGEBRAIC(:,4) = strpad('J_NHE3_H in component NHE3 (mM_per_s)');
    LEGEND_ALGEBRAIC(:,5) = strpad('J_NHE3_NH4 in component NHE3 (mM_per_s)');
    LEGEND_CONSTANTS(:,23) = strpad('J_NHE3_Na_Max in component NHE3 (mM_per_s)');
    LEGEND_ALGEBRAIC(:,6) = strpad('plot in component fluxes (dimensionless)');
    LEGEND_CONSTANTS(:,6) = strpad('x_T in component NHE3 (mM)');
    LEGEND_ALGEBRAIC(:,2) = strpad('sigma in component NHE3 (per_s)');
    LEGEND_CONSTANTS(:,21) = strpad('P_Na in component NHE3 (per_s)');
    LEGEND_CONSTANTS(:,22) = strpad('P_H in component NHE3 (per_s)');
    LEGEND_CONSTANTS(:,24) = strpad('P_NH4 in component NHE3 (per_s)');
    LEGEND_CONSTANTS(:,7) = strpad('P0_Na in component NHE3 (per_s)');
    LEGEND_CONSTANTS(:,8) = strpad('P0_H in component NHE3 (per_s)');
    LEGEND_CONSTANTS(:,9) = strpad('P0_NH4 in component NHE3 (per_s)');
    LEGEND_CONSTANTS(:,10) = strpad('K_Na in component NHE3 (mM)');
    LEGEND_CONSTANTS(:,11) = strpad('K_H in component NHE3 (mM)');
    LEGEND_CONSTANTS(:,12) = strpad('K_NH4 in component NHE3 (mM)');
    LEGEND_CONSTANTS(:,13) = strpad('K_I in component NHE3 (mM)');
    LEGEND_CONSTANTS(:,14) = strpad('f_m in component NHE3 (dimensionless)');
    LEGEND_CONSTANTS(:,15) = strpad('f_M in component NHE3 (dimensionless)');
    LEGEND_ALGEBRAIC(:,1) = strpad('alpha_ext_Na in component NHE3 (dimensionless)');
    LEGEND_CONSTANTS(:,16) = strpad('alpha_int_Na in component NHE3 (dimensionless)');
    LEGEND_CONSTANTS(:,17) = strpad('beta_ext_H in component NHE3 (dimensionless)');
    LEGEND_CONSTANTS(:,18) = strpad('beta_int_H in component NHE3 (dimensionless)');
    LEGEND_CONSTANTS(:,19) = strpad('gamma_ext_NH4 in component NHE3 (dimensionless)');
    LEGEND_CONSTANTS(:,20) = strpad('gamma_int_NH4 in component NHE3 (dimensionless)');
    LEGEND_RATES(:,1) = strpad('d/dt Na_ext 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) = 1.0;
    CONSTANTS(:,1) = 0.0;
    CONSTANTS(:,2) = 3.1623e-5;
    CONSTANTS(:,3) = 1.0e-3;
    CONSTANTS(:,4) = 0.0;
    CONSTANTS(:,5) = 0.0;
    CONSTANTS(:,6) = 1.0;
    CONSTANTS(:,7) = 1.6e-3;
    CONSTANTS(:,8) = 0.48e-3;
    CONSTANTS(:,9) = 1.6e-3;
    CONSTANTS(:,10) = 30.0;
    CONSTANTS(:,11) = 72e-6;
    CONSTANTS(:,12) = 27.0;
    CONSTANTS(:,13) = 1.0e-6;
    CONSTANTS(:,14) = 0.0;
    CONSTANTS(:,15) = 2.0;
    CONSTANTS(:,16) = CONSTANTS(:,1)./CONSTANTS(:,10);
    CONSTANTS(:,24) = 100.000;
    CONSTANTS(:,17) = CONSTANTS(:,2)./CONSTANTS(:,11);
    CONSTANTS(:,18) = CONSTANTS(:,3)./CONSTANTS(:,11);
    CONSTANTS(:,19) = CONSTANTS(:,4)./CONSTANTS(:,12);
    CONSTANTS(:,20) = CONSTANTS(:,5)./CONSTANTS(:,12);
    CONSTANTS(:,21) = ( CONSTANTS(:,7).*( CONSTANTS(:,15).*CONSTANTS(:,3)+ CONSTANTS(:,14).*CONSTANTS(:,13)))./(CONSTANTS(:,3)+CONSTANTS(:,13));
    CONSTANTS(:,22) = ( CONSTANTS(:,8).*( CONSTANTS(:,15).*CONSTANTS(:,3)+ CONSTANTS(:,14).*CONSTANTS(:,13)))./(CONSTANTS(:,3)+CONSTANTS(:,13));
    CONSTANTS(:,23) = ( CONSTANTS(:,6).*CONSTANTS(:,21).*CONSTANTS(:,22))./(CONSTANTS(:,21)+CONSTANTS(:,22));
    CONSTANTS(:,24) = ( CONSTANTS(:,9).*( CONSTANTS(:,15).*CONSTANTS(:,3)+ CONSTANTS(:,14).*CONSTANTS(:,13)))./(CONSTANTS(:,3)+CONSTANTS(:,13));
    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(:,24);
   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) = STATES(:,1)./CONSTANTS(:,10);
    ALGEBRAIC(:,2) =  (1.00000+ALGEBRAIC(:,1)+CONSTANTS(:,17)+CONSTANTS(:,19)).*( CONSTANTS(:,21).*CONSTANTS(:,16)+ CONSTANTS(:,22).*CONSTANTS(:,18)+ CONSTANTS(:,24).*CONSTANTS(:,20))+ (1.00000+CONSTANTS(:,16)+CONSTANTS(:,18)+CONSTANTS(:,20)).*( CONSTANTS(:,21).*ALGEBRAIC(:,1)+ CONSTANTS(:,22).*CONSTANTS(:,17)+ CONSTANTS(:,24).*CONSTANTS(:,19));
    ALGEBRAIC(:,3) =  (CONSTANTS(:,6)./ALGEBRAIC(:,2)).*( CONSTANTS(:,21).*CONSTANTS(:,22).*( CONSTANTS(:,16).*CONSTANTS(:,17) -  ALGEBRAIC(:,1).*CONSTANTS(:,18))+ CONSTANTS(:,21).*CONSTANTS(:,24).*( CONSTANTS(:,16).*CONSTANTS(:,19) -  ALGEBRAIC(:,1).*CONSTANTS(:,20)));
    ALGEBRAIC(:,4) =  (CONSTANTS(:,6)./ALGEBRAIC(:,2)).*( CONSTANTS(:,21).*CONSTANTS(:,22).*( ALGEBRAIC(:,1).*CONSTANTS(:,18) -  CONSTANTS(:,16).*CONSTANTS(:,17))+ CONSTANTS(:,22).*CONSTANTS(:,24).*( CONSTANTS(:,18).*CONSTANTS(:,19) -  CONSTANTS(:,17).*CONSTANTS(:,20)));
    ALGEBRAIC(:,5) =  (CONSTANTS(:,6)./ALGEBRAIC(:,2)).*( CONSTANTS(:,21).*CONSTANTS(:,24).*( ALGEBRAIC(:,1).*CONSTANTS(:,20) -  CONSTANTS(:,16).*CONSTANTS(:,19))+ CONSTANTS(:,22).*CONSTANTS(:,24).*( CONSTANTS(:,17).*CONSTANTS(:,20) -  CONSTANTS(:,19).*CONSTANTS(:,18)));
    ALGEBRAIC(:,6) =  - STATES(:,1)./(ALGEBRAIC(:,3)./CONSTANTS(:,23));
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