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 =16;
end
% There are a total of 6 entries in each of the rate and state variable arrays.
% There are a total of 19 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('q_PKACI_init in component environment (fmol)');
    LEGEND_CONSTANTS(:,2) = strpad('q_Ip_init in component environment (fmol)');
    LEGEND_CONSTANTS(:,3) = strpad('q_Ip_PKACI_init in component environment (fmol)');
    LEGEND_CONSTANTS(:,4) = strpad('q_PP2a_init in component environment (fmol)');
    LEGEND_CONSTANTS(:,5) = strpad('q_Ip_PP2a_init in component environment (fmol)');
    LEGEND_CONSTANTS(:,6) = strpad('q_I_init in component environment (fmol)');
    LEGEND_ALGEBRAIC(:,1) = strpad('q_PKACI in component environment (fmol)');
    LEGEND_ALGEBRAIC(:,2) = strpad('q_Ip in component environment (fmol)');
    LEGEND_ALGEBRAIC(:,3) = strpad('q_Ip_PKACI in component environment (fmol)');
    LEGEND_ALGEBRAIC(:,4) = strpad('q_PP2a in component environment (fmol)');
    LEGEND_ALGEBRAIC(:,5) = strpad('q_Ip_PP2a in component environment (fmol)');
    LEGEND_ALGEBRAIC(:,6) = strpad('q_I in component environment (fmol)');
    LEGEND_STATES(:,1) = strpad('q_PKACI in component Inhib1 (fmol)');
    LEGEND_STATES(:,2) = strpad('q_Ip in component Inhib1 (fmol)');
    LEGEND_STATES(:,3) = strpad('q_Ip_PKACI in component Inhib1 (fmol)');
    LEGEND_STATES(:,4) = strpad('q_PP2a in component Inhib1 (fmol)');
    LEGEND_STATES(:,5) = strpad('q_Ip_PP2a in component Inhib1 (fmol)');
    LEGEND_STATES(:,6) = strpad('q_I in component Inhib1 (fmol)');
    LEGEND_CONSTANTS(:,7) = strpad('kappa_PKAi1 in component Inhib1_parameters (fmol_per_sec)');
    LEGEND_CONSTANTS(:,8) = strpad('kappa_PKAi2 in component Inhib1_parameters (fmol_per_sec)');
    LEGEND_CONSTANTS(:,9) = strpad('kappa_PP2ai1 in component Inhib1_parameters (fmol_per_sec)');
    LEGEND_CONSTANTS(:,10) = strpad('kappa_PP2ai2 in component Inhib1_parameters (fmol_per_sec)');
    LEGEND_CONSTANTS(:,11) = strpad('K_PKACI in component Inhib1_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,12) = strpad('K_Ip in component Inhib1_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,13) = strpad('K_Ip_PKACI in component Inhib1_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,14) = strpad('K_PP2a in component Inhib1_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,15) = strpad('K_Ip_PP2a in component Inhib1_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,16) = strpad('K_I in component Inhib1_parameters (per_fmol)');
    LEGEND_CONSTANTS(:,17) = strpad('R in component constants (J_per_K_per_mol)');
    LEGEND_CONSTANTS(:,18) = strpad('T in component constants (kelvin)');
    LEGEND_ALGEBRAIC(:,13) = strpad('vPKAi1 in component Inhib1 (fmol_per_sec)');
    LEGEND_ALGEBRAIC(:,14) = strpad('vPKAi2 in component Inhib1 (fmol_per_sec)');
    LEGEND_ALGEBRAIC(:,15) = strpad('vPP2ai1 in component Inhib1 (fmol_per_sec)');
    LEGEND_ALGEBRAIC(:,16) = strpad('vPP2ai2 in component Inhib1 (fmol_per_sec)');
    LEGEND_ALGEBRAIC(:,7) = strpad('mu_PKACI in component Inhib1 (J_per_mol)');
    LEGEND_ALGEBRAIC(:,8) = strpad('mu_Ip in component Inhib1 (J_per_mol)');
    LEGEND_ALGEBRAIC(:,9) = strpad('mu_Ip_PKACI in component Inhib1 (J_per_mol)');
    LEGEND_ALGEBRAIC(:,10) = strpad('mu_PP2a in component Inhib1 (J_per_mol)');
    LEGEND_ALGEBRAIC(:,11) = strpad('mu_Ip_PP2a in component Inhib1 (J_per_mol)');
    LEGEND_ALGEBRAIC(:,12) = strpad('mu_I in component Inhib1 (J_per_mol)');
    LEGEND_CONSTANTS(:,19) = strpad('F in component constants (C_per_mol)');
    LEGEND_RATES(:,1) = strpad('d/dt q_PKACI in component Inhib1 (fmol)');
    LEGEND_RATES(:,2) = strpad('d/dt q_Ip in component Inhib1 (fmol)');
    LEGEND_RATES(:,3) = strpad('d/dt q_Ip_PKACI in component Inhib1 (fmol)');
    LEGEND_RATES(:,4) = strpad('d/dt q_PP2a in component Inhib1 (fmol)');
    LEGEND_RATES(:,5) = strpad('d/dt q_Ip_PP2a in component Inhib1 (fmol)');
    LEGEND_RATES(:,6) = strpad('d/dt q_I in component Inhib1 (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 = [];
    CONSTANTS(:,1) = 1.117E-03;
    CONSTANTS(:,2) = 9.994E-04;
    CONSTANTS(:,3) = 1e-13;
    CONSTANTS(:,4) = 8.512E-03;
    CONSTANTS(:,5) = 1e-13;
    CONSTANTS(:,6) = 1.140E-02;
    STATES(:,1) = 1e-16;
    STATES(:,2) = 1e-16;
    STATES(:,3) = 1e-16;
    STATES(:,4) = 1e-16;
    STATES(:,5) = 1e-16;
    STATES(:,6) = 1e-16;
    CONSTANTS(:,7) = 20.9606;
    CONSTANTS(:,8) = 22.2706;
    CONSTANTS(:,9) = 5.39341;
    CONSTANTS(:,10) = 5.30013;
    CONSTANTS(:,11) = 0.284433;
    CONSTANTS(:,12) = 0.133405;
    CONSTANTS(:,13) = 1.38688;
    CONSTANTS(:,14) = 0.0704691;
    CONSTANTS(:,15) = 0.342795;
    CONSTANTS(:,16) = 0.150247;
    CONSTANTS(:,17) = 8.31;
    CONSTANTS(:,18) = 310;
    CONSTANTS(:,19) = 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(:,1) = STATES(:,1)+CONSTANTS(:,1);
    ALGEBRAIC(:,7) =  CONSTANTS(:,17).*CONSTANTS(:,18).*log( CONSTANTS(:,11).*ALGEBRAIC(:,1));
    ALGEBRAIC(:,3) = STATES(:,3)+CONSTANTS(:,3);
    ALGEBRAIC(:,9) =  CONSTANTS(:,17).*CONSTANTS(:,18).*log( CONSTANTS(:,13).*ALGEBRAIC(:,3));
    ALGEBRAIC(:,6) = STATES(:,6)+CONSTANTS(:,6);
    ALGEBRAIC(:,12) =  CONSTANTS(:,17).*CONSTANTS(:,18).*log( CONSTANTS(:,16).*ALGEBRAIC(:,6));
    ALGEBRAIC(:,13) =  CONSTANTS(:,7).*(exp((ALGEBRAIC(:,7)+ALGEBRAIC(:,12))./( CONSTANTS(:,17).*CONSTANTS(:,18))) - exp(ALGEBRAIC(:,9)./( CONSTANTS(:,17).*CONSTANTS(:,18))));
    ALGEBRAIC(:,2) = STATES(:,2)+CONSTANTS(:,2);
    ALGEBRAIC(:,8) =  CONSTANTS(:,17).*CONSTANTS(:,18).*log( CONSTANTS(:,12).*ALGEBRAIC(:,2));
    ALGEBRAIC(:,14) =  CONSTANTS(:,8).*(exp(ALGEBRAIC(:,9)./( CONSTANTS(:,17).*CONSTANTS(:,18))) - exp((ALGEBRAIC(:,7)+ALGEBRAIC(:,8))./( CONSTANTS(:,17).*CONSTANTS(:,18))));
    RATES(:,1) = ALGEBRAIC(:,14) - ALGEBRAIC(:,13);
    RATES(:,3) = ALGEBRAIC(:,13) - ALGEBRAIC(:,14);
    ALGEBRAIC(:,4) = STATES(:,4)+CONSTANTS(:,4);
    ALGEBRAIC(:,10) =  CONSTANTS(:,17).*CONSTANTS(:,18).*log( CONSTANTS(:,14).*ALGEBRAIC(:,4));
    ALGEBRAIC(:,5) = STATES(:,5)+CONSTANTS(:,5);
    ALGEBRAIC(:,11) =  CONSTANTS(:,17).*CONSTANTS(:,18).*log( CONSTANTS(:,15).*ALGEBRAIC(:,5));
    ALGEBRAIC(:,15) =  CONSTANTS(:,9).*(exp((ALGEBRAIC(:,10)+ALGEBRAIC(:,8))./( CONSTANTS(:,17).*CONSTANTS(:,18))) - exp(ALGEBRAIC(:,11)./( CONSTANTS(:,17).*CONSTANTS(:,18))));
    RATES(:,2) = ALGEBRAIC(:,14) - ALGEBRAIC(:,15);
    ALGEBRAIC(:,16) =  CONSTANTS(:,10).*(exp(ALGEBRAIC(:,11)./( CONSTANTS(:,17).*CONSTANTS(:,18))) - exp((ALGEBRAIC(:,10)+ALGEBRAIC(:,12))./( CONSTANTS(:,17).*CONSTANTS(:,18))));
    RATES(:,4) = ALGEBRAIC(:,16) - ALGEBRAIC(:,15);
    RATES(:,5) = ALGEBRAIC(:,15) - ALGEBRAIC(:,16);
    RATES(:,6) = ALGEBRAIC(:,16) - ALGEBRAIC(:,13);
   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(:,1);
    ALGEBRAIC(:,7) =  CONSTANTS(:,17).*CONSTANTS(:,18).*log( CONSTANTS(:,11).*ALGEBRAIC(:,1));
    ALGEBRAIC(:,3) = STATES(:,3)+CONSTANTS(:,3);
    ALGEBRAIC(:,9) =  CONSTANTS(:,17).*CONSTANTS(:,18).*log( CONSTANTS(:,13).*ALGEBRAIC(:,3));
    ALGEBRAIC(:,6) = STATES(:,6)+CONSTANTS(:,6);
    ALGEBRAIC(:,12) =  CONSTANTS(:,17).*CONSTANTS(:,18).*log( CONSTANTS(:,16).*ALGEBRAIC(:,6));
    ALGEBRAIC(:,13) =  CONSTANTS(:,7).*(exp((ALGEBRAIC(:,7)+ALGEBRAIC(:,12))./( CONSTANTS(:,17).*CONSTANTS(:,18))) - exp(ALGEBRAIC(:,9)./( CONSTANTS(:,17).*CONSTANTS(:,18))));
    ALGEBRAIC(:,2) = STATES(:,2)+CONSTANTS(:,2);
    ALGEBRAIC(:,8) =  CONSTANTS(:,17).*CONSTANTS(:,18).*log( CONSTANTS(:,12).*ALGEBRAIC(:,2));
    ALGEBRAIC(:,14) =  CONSTANTS(:,8).*(exp(ALGEBRAIC(:,9)./( CONSTANTS(:,17).*CONSTANTS(:,18))) - exp((ALGEBRAIC(:,7)+ALGEBRAIC(:,8))./( CONSTANTS(:,17).*CONSTANTS(:,18))));
    ALGEBRAIC(:,4) = STATES(:,4)+CONSTANTS(:,4);
    ALGEBRAIC(:,10) =  CONSTANTS(:,17).*CONSTANTS(:,18).*log( CONSTANTS(:,14).*ALGEBRAIC(:,4));
    ALGEBRAIC(:,5) = STATES(:,5)+CONSTANTS(:,5);
    ALGEBRAIC(:,11) =  CONSTANTS(:,17).*CONSTANTS(:,18).*log( CONSTANTS(:,15).*ALGEBRAIC(:,5));
    ALGEBRAIC(:,15) =  CONSTANTS(:,9).*(exp((ALGEBRAIC(:,10)+ALGEBRAIC(:,8))./( CONSTANTS(:,17).*CONSTANTS(:,18))) - exp(ALGEBRAIC(:,11)./( CONSTANTS(:,17).*CONSTANTS(:,18))));
    ALGEBRAIC(:,16) =  CONSTANTS(:,10).*(exp(ALGEBRAIC(:,11)./( CONSTANTS(:,17).*CONSTANTS(:,18))) - exp((ALGEBRAIC(:,10)+ALGEBRAIC(:,12))./( CONSTANTS(:,17).*CONSTANTS(:,18))));
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