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 =13;
end
% There are a total of 8 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('Pyr in component Pyr (micromolar)');
    LEGEND_CONSTANTS(:,25) = strpad('v1 in component v1 (micromolar_per_second)');
    LEGEND_ALGEBRAIC(:,1) = strpad('v2 in component v2 (micromolar_per_second)');
    LEGEND_ALGEBRAIC(:,6) = strpad('v7 in component v7 (micromolar_per_second)');
    LEGEND_STATES(:,2) = strpad('AcCoA in component AcCoA (micromolar)');
    LEGEND_ALGEBRAIC(:,2) = strpad('v3 in component v3 (micromolar_per_second)');
    LEGEND_STATES(:,3) = strpad('Cit in component Cit (micromolar)');
    LEGEND_ALGEBRAIC(:,3) = strpad('v4 in component v4 (micromolar_per_second)');
    LEGEND_STATES(:,4) = strpad('KG in component KG (micromolar)');
    LEGEND_ALGEBRAIC(:,4) = strpad('v5 in component v5 (micromolar_per_second)');
    LEGEND_ALGEBRAIC(:,5) = strpad('v6 in component v6 (micromolar_per_second)');
    LEGEND_STATES(:,5) = strpad('OAA in component OAA (micromolar)');
    LEGEND_ALGEBRAIC(:,7) = strpad('v8 in component v8 (micromolar_per_second)');
    LEGEND_STATES(:,6) = strpad('NAD in component NAD (micromolar)');
    LEGEND_ALGEBRAIC(:,10) = strpad('vresp in component vresp (micromolar_per_second)');
    LEGEND_STATES(:,7) = strpad('ATP in component ATP (micromolar)');
    LEGEND_ALGEBRAIC(:,13) = strpad('vATP in component vATP (micromolar_per_second)');
    LEGEND_ALGEBRAIC(:,8) = strpad('vANT in component vANT (micromolar_per_second)');
    LEGEND_STATES(:,8) = strpad('delta_psi in component delta_psi (millivolt)');
    LEGEND_CONSTANTS(:,1) = strpad('C in component delta_psi (millimolar_per_millivolt)');
    LEGEND_ALGEBRAIC(:,9) = strpad('vleak in component vleak (micromolar_per_second)');
    LEGEND_CONSTANTS(:,2) = strpad('k1 in component v1 (micromolar_per_second)');
    LEGEND_CONSTANTS(:,3) = strpad('k2 in component v2 (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,4) = strpad('k3 in component v3 (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,5) = strpad('k4 in component v4 (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,6) = strpad('k5 in component v5 (third_order_rate_constant)');
    LEGEND_CONSTANTS(:,7) = strpad('At in component model_parameters (millimolar)');
    LEGEND_CONSTANTS(:,8) = strpad('k6 in component v6 (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,9) = strpad('k7 in component v7 (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,10) = strpad('k8 in component v8 (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,11) = strpad('kANT in component vANT (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,12) = strpad('kleak in component vleak (molar_per_millivolt_per_second)');
    LEGEND_CONSTANTS(:,13) = strpad('kresp in component vresp (millimolar_per_second)');
    LEGEND_CONSTANTS(:,14) = strpad('K in component vresp (millimolar)');
    LEGEND_CONSTANTS(:,15) = strpad('a in component vresp (per_millivolt)');
    LEGEND_CONSTANTS(:,16) = strpad('delta_psi_m in component vresp (millivolt)');
    LEGEND_CONSTANTS(:,17) = strpad('Nt in component model_parameters (millimolar)');
    LEGEND_CONSTANTS(:,18) = strpad('kATP in component vATP (millimolar_per_second)');
    LEGEND_CONSTANTS(:,19) = strpad('b in component vATP (per_micromolar)');
    LEGEND_ALGEBRAIC(:,12) = strpad('ATP_crit_delta_psi in component ATP_crit_delta_psi (micromolar)');
    LEGEND_CONSTANTS(:,20) = strpad('R in component ATP_crit_delta_psi (joule_per_mole_kelvin)');
    LEGEND_CONSTANTS(:,21) = strpad('T in component ATP_crit_delta_psi (kelvin)');
    LEGEND_CONSTANTS(:,22) = strpad('F in component ATP_crit_delta_psi (coulomb_per_mole)');
    LEGEND_CONSTANTS(:,23) = strpad('Kapp in component ATP_crit_delta_psi (per_millimolar)');
    LEGEND_CONSTANTS(:,24) = strpad('Pi in component ATP_crit_delta_psi (millimolar)');
    LEGEND_ALGEBRAIC(:,11) = strpad('delta_G_transport in component ATP_crit_delta_psi (joule_per_mole)');
    LEGEND_RATES(:,1) = strpad('d/dt Pyr in component Pyr (micromolar)');
    LEGEND_RATES(:,2) = strpad('d/dt AcCoA in component AcCoA (micromolar)');
    LEGEND_RATES(:,3) = strpad('d/dt Cit in component Cit (micromolar)');
    LEGEND_RATES(:,4) = strpad('d/dt KG in component KG (micromolar)');
    LEGEND_RATES(:,5) = strpad('d/dt OAA in component OAA (micromolar)');
    LEGEND_RATES(:,6) = strpad('d/dt NAD in component NAD (micromolar)');
    LEGEND_RATES(:,7) = strpad('d/dt ATP in component ATP (micromolar)');
    LEGEND_RATES(:,8) = strpad('d/dt delta_psi in component delta_psi (millivolt)');
    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) = 0.154;
    STATES(:,2) = 0.063;
    STATES(:,3) = 0.44;
    STATES(:,4) = 0.225;
    STATES(:,5) = 0.005;
    STATES(:,6) = 0.856;
    STATES(:,7) = 3.536;
    STATES(:,8) = 150.0;
    CONSTANTS(:,1) = 6.75e-06;
    CONSTANTS(:,2) = 38.0;
    CONSTANTS(:,3) = 152.0;
    CONSTANTS(:,4) = 57142.0;
    CONSTANTS(:,5) = 53.0;
    CONSTANTS(:,6) = 82361.0;
    CONSTANTS(:,7) = 4.160;
    CONSTANTS(:,8) = 3.2e-3;
    CONSTANTS(:,9) = 40.0;
    CONSTANTS(:,10) = 3.6;
    CONSTANTS(:,11) = 0.1;
    CONSTANTS(:,12) = 0.426;
    CONSTANTS(:,13) = 2.5;
    CONSTANTS(:,14) = 2;
    CONSTANTS(:,15) = 0.1;
    CONSTANTS(:,16) = 150.0;
    CONSTANTS(:,17) = 1.070;
    CONSTANTS(:,18) = 131.9;
    CONSTANTS(:,19) = 4;
    CONSTANTS(:,20) = 8.314;
    CONSTANTS(:,21) = 298;
    CONSTANTS(:,22) = 96485;
    CONSTANTS(:,23) = 4.4e-6;
    CONSTANTS(:,24) = 2.440;
    CONSTANTS(:,25) = CONSTANTS(:,2);
    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(:,3).*STATES(:,1).*STATES(:,6);
    ALGEBRAIC(:,2) =  CONSTANTS(:,4).*STATES(:,5).*STATES(:,2);
    RATES(:,2) = ALGEBRAIC(:,1) - ALGEBRAIC(:,2);
    ALGEBRAIC(:,3) =  CONSTANTS(:,5).*STATES(:,3).*STATES(:,6);
    RATES(:,3) = ALGEBRAIC(:,2) - ALGEBRAIC(:,3);
    ALGEBRAIC(:,4) =  CONSTANTS(:,6).*STATES(:,4).*STATES(:,6).*(CONSTANTS(:,7) - STATES(:,7));
    ALGEBRAIC(:,5) =  CONSTANTS(:,8).*(STATES(:,5) - STATES(:,4));
    RATES(:,4) = (ALGEBRAIC(:,3)+ALGEBRAIC(:,5)) - ALGEBRAIC(:,4);
    ALGEBRAIC(:,6) =  CONSTANTS(:,9).*STATES(:,1).*STATES(:,7);
    RATES(:,1) = CONSTANTS(:,25) - (ALGEBRAIC(:,1)+ALGEBRAIC(:,6));
    ALGEBRAIC(:,7) =  CONSTANTS(:,10).*STATES(:,5);
    RATES(:,5) = (ALGEBRAIC(:,4)+ALGEBRAIC(:,6)) - (ALGEBRAIC(:,2)+ALGEBRAIC(:,7)+ALGEBRAIC(:,5));
    ALGEBRAIC(:,10) =  CONSTANTS(:,13).*((CONSTANTS(:,17) - STATES(:,6))./((CONSTANTS(:,14)+CONSTANTS(:,17)) - STATES(:,6))).*(1.00000./(1.00000+exp( CONSTANTS(:,15).*(STATES(:,8) - CONSTANTS(:,16)))));
    RATES(:,6) = ALGEBRAIC(:,10) - (ALGEBRAIC(:,1)+ALGEBRAIC(:,3)+ 2.00000.*ALGEBRAIC(:,4));
    ALGEBRAIC(:,11) =  0.00120000.*CONSTANTS(:,22).*STATES(:,8);
    ALGEBRAIC(:,12) = CONSTANTS(:,7)./(1.00000+exp(( -3.00000.*ALGEBRAIC(:,11))./( CONSTANTS(:,20).*CONSTANTS(:,21)))./( CONSTANTS(:,23).*CONSTANTS(:,24)));
    ALGEBRAIC(:,13) =  CONSTANTS(:,18).*(2.00000./(1.00000+exp( CONSTANTS(:,19).*(STATES(:,7) - ALGEBRAIC(:,12)))) - 1.00000);
    ALGEBRAIC(:,8) =  CONSTANTS(:,11).*STATES(:,7);
    RATES(:,7) = (ALGEBRAIC(:,13)+ALGEBRAIC(:,4)) - (ALGEBRAIC(:,8)+ALGEBRAIC(:,6));
    ALGEBRAIC(:,9) =  CONSTANTS(:,12).*STATES(:,8);
    RATES(:,8) =  (1.00000./CONSTANTS(:,1)).*( 10.0000.*ALGEBRAIC(:,10) - ( 3.00000.*ALGEBRAIC(:,13)+ALGEBRAIC(:,9)+ALGEBRAIC(:,8)));
   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(:,3).*STATES(:,1).*STATES(:,6);
    ALGEBRAIC(:,2) =  CONSTANTS(:,4).*STATES(:,5).*STATES(:,2);
    ALGEBRAIC(:,3) =  CONSTANTS(:,5).*STATES(:,3).*STATES(:,6);
    ALGEBRAIC(:,4) =  CONSTANTS(:,6).*STATES(:,4).*STATES(:,6).*(CONSTANTS(:,7) - STATES(:,7));
    ALGEBRAIC(:,5) =  CONSTANTS(:,8).*(STATES(:,5) - STATES(:,4));
    ALGEBRAIC(:,6) =  CONSTANTS(:,9).*STATES(:,1).*STATES(:,7);
    ALGEBRAIC(:,7) =  CONSTANTS(:,10).*STATES(:,5);
    ALGEBRAIC(:,10) =  CONSTANTS(:,13).*((CONSTANTS(:,17) - STATES(:,6))./((CONSTANTS(:,14)+CONSTANTS(:,17)) - STATES(:,6))).*(1.00000./(1.00000+exp( CONSTANTS(:,15).*(STATES(:,8) - CONSTANTS(:,16)))));
    ALGEBRAIC(:,11) =  0.00120000.*CONSTANTS(:,22).*STATES(:,8);
    ALGEBRAIC(:,12) = CONSTANTS(:,7)./(1.00000+exp(( -3.00000.*ALGEBRAIC(:,11))./( CONSTANTS(:,20).*CONSTANTS(:,21)))./( CONSTANTS(:,23).*CONSTANTS(:,24)));
    ALGEBRAIC(:,13) =  CONSTANTS(:,18).*(2.00000./(1.00000+exp( CONSTANTS(:,19).*(STATES(:,7) - ALGEBRAIC(:,12)))) - 1.00000);
    ALGEBRAIC(:,8) =  CONSTANTS(:,11).*STATES(:,7);
    ALGEBRAIC(:,9) =  CONSTANTS(:,12).*STATES(:,8);
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