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 4 entries in each of the rate and state variable arrays.
% There are a total of 14 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_ALGEBRAIC(:,5) = strpad('phi3_c1 in component phi (per_second)');
    LEGEND_STATES(:,1) = strpad('h1 in component h1 (dimensionless)');
    LEGEND_ALGEBRAIC(:,1) = strpad('phi1_c1 in component phi (second_order_rate)');
    LEGEND_ALGEBRAIC(:,3) = strpad('phi2_c1 in component phi (per_second)');
    LEGEND_CONSTANTS(:,1) = strpad('p in component model_parameters (micro_molar)');
    LEGEND_ALGEBRAIC(:,2) = strpad('phi_1_c1 in component phi (per_second)');
    LEGEND_ALGEBRAIC(:,9) = strpad('phi3_c2 in component phi (per_second)');
    LEGEND_STATES(:,2) = strpad('h2 in component h2 (dimensionless)');
    LEGEND_ALGEBRAIC(:,4) = strpad('phi1_c2 in component phi (second_order_rate)');
    LEGEND_ALGEBRAIC(:,7) = strpad('phi2_c2 in component phi (per_second)');
    LEGEND_ALGEBRAIC(:,6) = strpad('phi_1_c2 in component phi (per_second)');
    LEGEND_CONSTANTS(:,2) = strpad('r2 in component model_parameters (second_order_rate)');
    LEGEND_CONSTANTS(:,3) = strpad('R1 in component model_parameters (micro_molar)');
    LEGEND_CONSTANTS(:,4) = strpad('k1 in component model_parameters (micro_molar_per_second)');
    LEGEND_CONSTANTS(:,5) = strpad('R3 in component model_parameters (micro_molar)');
    LEGEND_CONSTANTS(:,6) = strpad('k2 in component model_parameters (micro_molar_per_second)');
    LEGEND_CONSTANTS(:,7) = strpad('r4 in component model_parameters (per_second)');
    LEGEND_CONSTANTS(:,8) = strpad('k3 in component model_parameters (micro_molar_per_second)');
    LEGEND_CONSTANTS(:,9) = strpad('R5 in component model_parameters (micro_molar)');
    LEGEND_STATES(:,3) = strpad('c1 in component c1 (micro_molar)');
    LEGEND_STATES(:,4) = strpad('c2 in component c2 (micro_molar)');
    LEGEND_CONSTANTS(:,10) = strpad('Vp in component model_parameters (micro_molar_per_second)');
    LEGEND_CONSTANTS(:,11) = strpad('Kp in component model_parameters (micro_molar)');
    LEGEND_ALGEBRAIC(:,8) = strpad('j_pump_c1 in component j_pump (micro_molar_per_second)');
    LEGEND_ALGEBRAIC(:,10) = strpad('j_pump_c2 in component j_pump (micro_molar_per_second)');
    LEGEND_CONSTANTS(:,12) = strpad('kf in component model_parameters (micro_molar_per_second)');
    LEGEND_ALGEBRAIC(:,11) = strpad('j_receptor_c1 in component j_receptor (micro_molar_per_second)');
    LEGEND_ALGEBRAIC(:,12) = strpad('j_receptor_c2 in component j_receptor (micro_molar_per_second)');
    LEGEND_ALGEBRAIC(:,13) = strpad('j_diffusion in component j_diffusion (micro_molar_per_second)');
    LEGEND_CONSTANTS(:,13) = strpad('D in component model_parameters (per_second)');
    LEGEND_CONSTANTS(:,14) = strpad('j_leak in component model_parameters (micro_molar_per_second)');
    LEGEND_RATES(:,1) = strpad('d/dt h1 in component h1 (dimensionless)');
    LEGEND_RATES(:,2) = strpad('d/dt h2 in component h2 (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt c1 in component c1 (micro_molar)');
    LEGEND_RATES(:,4) = strpad('d/dt c2 in component c2 (micro_molar)');
    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) = 0.8;
    CONSTANTS(:,1) = 0.2778;
    STATES(:,2) = 0.1;
    CONSTANTS(:,2) = 100;
    CONSTANTS(:,3) = 6;
    CONSTANTS(:,4) = 44;
    CONSTANTS(:,5) = 50;
    CONSTANTS(:,6) = 26.5;
    CONSTANTS(:,7) = 20;
    CONSTANTS(:,8) = 1.6;
    CONSTANTS(:,9) = 1.6;
    STATES(:,3) = 0.3;
    STATES(:,4) = 0.1;
    CONSTANTS(:,10) = 1.2;
    CONSTANTS(:,11) = 0.18;
    CONSTANTS(:,12) = 28;
    CONSTANTS(:,13) = 0.01;
    CONSTANTS(:,14) = 0.2;
    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(:,5) = CONSTANTS(:,8)./(CONSTANTS(:,9)+STATES(:,3));
    ALGEBRAIC(:,1) = ( CONSTANTS(:,2).*STATES(:,3))./(CONSTANTS(:,3)+STATES(:,3));
    ALGEBRAIC(:,3) = (CONSTANTS(:,6)+ CONSTANTS(:,7).*STATES(:,3))./(CONSTANTS(:,5)+STATES(:,3));
    ALGEBRAIC(:,2) = CONSTANTS(:,4)./(CONSTANTS(:,5)+STATES(:,3));
    RATES(:,1) =  ALGEBRAIC(:,5).*(1.00000 - STATES(:,1)) - ( ALGEBRAIC(:,1).*ALGEBRAIC(:,3).*STATES(:,1).*CONSTANTS(:,1))./( ALGEBRAIC(:,1).*CONSTANTS(:,1)+ALGEBRAIC(:,2));
    ALGEBRAIC(:,9) = CONSTANTS(:,8)./(CONSTANTS(:,9)+STATES(:,4));
    ALGEBRAIC(:,4) = ( CONSTANTS(:,2).*STATES(:,4))./(CONSTANTS(:,3)+STATES(:,4));
    ALGEBRAIC(:,7) = (CONSTANTS(:,6)+ CONSTANTS(:,7).*STATES(:,4))./(CONSTANTS(:,5)+STATES(:,4));
    ALGEBRAIC(:,6) = CONSTANTS(:,4)./(CONSTANTS(:,5)+STATES(:,4));
    RATES(:,2) =  ALGEBRAIC(:,9).*(1.00000 - STATES(:,2)) - ( ALGEBRAIC(:,4).*ALGEBRAIC(:,7).*STATES(:,2).*CONSTANTS(:,1))./( ALGEBRAIC(:,4).*CONSTANTS(:,1)+ALGEBRAIC(:,6));
    ALGEBRAIC(:,8) = ( CONSTANTS(:,10).*power(STATES(:,3), 2.00000))./(power(CONSTANTS(:,11), 2.00000)+power(STATES(:,3), 2.00000));
    ALGEBRAIC(:,11) =  CONSTANTS(:,12).*power(( CONSTANTS(:,1).*STATES(:,1).*ALGEBRAIC(:,1))./( ALGEBRAIC(:,1).*CONSTANTS(:,1)+ALGEBRAIC(:,2)), 4.00000);
    ALGEBRAIC(:,13) =  CONSTANTS(:,13).*(STATES(:,4) - STATES(:,3));
    RATES(:,3) = (ALGEBRAIC(:,11) - ALGEBRAIC(:,8))+CONSTANTS(:,14)+ALGEBRAIC(:,13);
    ALGEBRAIC(:,10) = ( CONSTANTS(:,10).*power(STATES(:,4), 2.00000))./(power(CONSTANTS(:,11), 2.00000)+power(STATES(:,4), 2.00000));
    ALGEBRAIC(:,12) =  CONSTANTS(:,12).*power(( CONSTANTS(:,1).*STATES(:,2).*ALGEBRAIC(:,4))./( ALGEBRAIC(:,4).*CONSTANTS(:,1)+ALGEBRAIC(:,6)), 4.00000);
    RATES(:,4) = (ALGEBRAIC(:,12) - ALGEBRAIC(:,10))+CONSTANTS(:,14)+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(:,5) = CONSTANTS(:,8)./(CONSTANTS(:,9)+STATES(:,3));
    ALGEBRAIC(:,1) = ( CONSTANTS(:,2).*STATES(:,3))./(CONSTANTS(:,3)+STATES(:,3));
    ALGEBRAIC(:,3) = (CONSTANTS(:,6)+ CONSTANTS(:,7).*STATES(:,3))./(CONSTANTS(:,5)+STATES(:,3));
    ALGEBRAIC(:,2) = CONSTANTS(:,4)./(CONSTANTS(:,5)+STATES(:,3));
    ALGEBRAIC(:,9) = CONSTANTS(:,8)./(CONSTANTS(:,9)+STATES(:,4));
    ALGEBRAIC(:,4) = ( CONSTANTS(:,2).*STATES(:,4))./(CONSTANTS(:,3)+STATES(:,4));
    ALGEBRAIC(:,7) = (CONSTANTS(:,6)+ CONSTANTS(:,7).*STATES(:,4))./(CONSTANTS(:,5)+STATES(:,4));
    ALGEBRAIC(:,6) = CONSTANTS(:,4)./(CONSTANTS(:,5)+STATES(:,4));
    ALGEBRAIC(:,8) = ( CONSTANTS(:,10).*power(STATES(:,3), 2.00000))./(power(CONSTANTS(:,11), 2.00000)+power(STATES(:,3), 2.00000));
    ALGEBRAIC(:,11) =  CONSTANTS(:,12).*power(( CONSTANTS(:,1).*STATES(:,1).*ALGEBRAIC(:,1))./( ALGEBRAIC(:,1).*CONSTANTS(:,1)+ALGEBRAIC(:,2)), 4.00000);
    ALGEBRAIC(:,13) =  CONSTANTS(:,13).*(STATES(:,4) - STATES(:,3));
    ALGEBRAIC(:,10) = ( CONSTANTS(:,10).*power(STATES(:,4), 2.00000))./(power(CONSTANTS(:,11), 2.00000)+power(STATES(:,4), 2.00000));
    ALGEBRAIC(:,12) =  CONSTANTS(:,12).*power(( CONSTANTS(:,1).*STATES(:,2).*ALGEBRAIC(:,4))./( ALGEBRAIC(:,4).*CONSTANTS(:,1)+ALGEBRAIC(:,6)), 4.00000);
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