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 9 entries in each of the rate and state variable arrays.
% There are a total of 51 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 (day)');
    LEGEND_ALGEBRAIC(:,1) = strpad('A_B in component A_B (mm2)');
    LEGEND_STATES(:,1) = strpad('r_B in component r_B (mm)');
    LEGEND_CONSTANTS(:,1) = strpad('X_c in component r_B (pM)');
    LEGEND_CONSTANTS(:,2) = strpad('X_b in component r_B (pM)');
    LEGEND_CONSTANTS(:,3) = strpad('X_y in component r_B (pM)');
    LEGEND_CONSTANTS(:,4) = strpad('k_rB in component r_B (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,5) = strpad('k_for in component r_B (mm_per_day)');
    LEGEND_CONSTANTS(:,6) = strpad('k_res in component r_B (mm_per_day)');
    LEGEND_STATES(:,2) = strpad('xc in component xc (pM)');
    LEGEND_STATES(:,3) = strpad('xb in component xb (pM)');
    LEGEND_STATES(:,4) = strpad('xy in component xy (pM)');
    LEGEND_CONSTANTS(:,7) = strpad('X_bss in component xy (pM)');
    LEGEND_CONSTANTS(:,8) = strpad('X_yss in component xy (pM)');
    LEGEND_CONSTANTS(:,9) = strpad('k_byp in component xy (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,10) = strpad('k_yd in component xy (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,6) = strpad('F_sti in component F_sti (pM_N_per_mm2)');
    LEGEND_CONSTANTS(:,11) = strpad('k_Fs in component F_sti (mm2_per_N)');
    LEGEND_CONSTANTS(:,12) = strpad('k_y in component F_sti (per_pM)');
    LEGEND_ALGEBRAIC(:,5) = strpad('F_s in component F_s (N_per_mm2)');
    LEGEND_ALGEBRAIC(:,3) = strpad('F_a in component F_s (newton)');
    LEGEND_STATES(:,5) = strpad('x_no in component x_no (pM)');
    LEGEND_CONSTANTS(:,13) = strpad('X_noe in component x_no (flux)');
    LEGEND_CONSTANTS(:,14) = strpad('k_yno in component x_no (mm2_day_per_dyn)');
    LEGEND_CONSTANTS(:,15) = strpad('k_nod in component x_no (first_order_rate_constant)');
    LEGEND_STATES(:,6) = strpad('x_pge in component x_pge (pM)');
    LEGEND_CONSTANTS(:,16) = strpad('X_pgex in component x_pge (flux)');
    LEGEND_CONSTANTS(:,17) = strpad('k_pged in component x_pge (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,18) = strpad('k_nopge in component x_pge (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,19) = strpad('k_ypge in component x_pge (mm2_day_per_dyn)');
    LEGEND_STATES(:,7) = strpad('x_opg in component x_opg (pM)');
    LEGEND_CONSTANTS(:,20) = strpad('k_opgd in component x_opg (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,21) = strpad('k_nopg in component x_opg (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,22) = strpad('Io in component model_parameters (flux)');
    LEGEND_CONSTANTS(:,23) = strpad('K_o_p in component model_parameters (picomole_per_day_picomole_cells)');
    LEGEND_STATES(:,8) = strpad('xr in component xr (pM)');
    LEGEND_ALGEBRAIC(:,4) = strpad('pi_c in component model_parameters (dimensionless)');
    LEGEND_STATES(:,9) = strpad('x_kl in component x_kl (pM)');
    LEGEND_ALGEBRAIC(:,2) = strpad('pi_L in component x_kl (dimensionless)');
    LEGEND_CONSTANTS(:,24) = strpad('K_l_p in component x_kl (dimensionless)');
    LEGEND_CONSTANTS(:,25) = strpad('K in component x_kl (pM)');
    LEGEND_CONSTANTS(:,26) = strpad('k_nokl in component x_kl (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,27) = strpad('Il in component x_kl (flux)');
    LEGEND_CONSTANTS(:,28) = strpad('rl in component x_kl (flux)');
    LEGEND_CONSTANTS(:,29) = strpad('k1 in component x_kl (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,30) = strpad('k2 in component x_kl (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,31) = strpad('k3 in component x_kl (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,32) = strpad('k4 in component x_kl (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,33) = strpad('ko in component x_kl (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,51) = strpad('pi_p in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,34) = strpad('D_R in component xr (flux)');
    LEGEND_CONSTANTS(:,35) = strpad('k_pger in component xr (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,47) = strpad('D_B in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,36) = strpad('k_B in component xb (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,37) = strpad('D_C in component xc (flux)');
    LEGEND_CONSTANTS(:,38) = strpad('D_A in component xc (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,39) = strpad('f0 in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,40) = strpad('dB in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,41) = strpad('C_s in component model_parameters (pM)');
    LEGEND_CONSTANTS(:,48) = strpad('P in component model_parameters (pM)');
    LEGEND_CONSTANTS(:,49) = strpad('P_0 in component model_parameters (pM)');
    LEGEND_CONSTANTS(:,50) = strpad('P_s in component model_parameters (pM)');
    LEGEND_CONSTANTS(:,42) = strpad('SP in component model_parameters (flux)');
    LEGEND_CONSTANTS(:,43) = strpad('k5 in component model_parameters (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,44) = strpad('k6 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,45) = strpad('IP in component model_parameters (flux)');
    LEGEND_CONSTANTS(:,46) = strpad('kP in component model_parameters (first_order_rate_constant)');
    LEGEND_RATES(:,1) = strpad('d/dt r_B in component r_B (mm)');
    LEGEND_RATES(:,4) = strpad('d/dt xy in component xy (pM)');
    LEGEND_RATES(:,5) = strpad('d/dt x_no in component x_no (pM)');
    LEGEND_RATES(:,6) = strpad('d/dt x_pge in component x_pge (pM)');
    LEGEND_RATES(:,7) = strpad('d/dt x_opg in component x_opg (pM)');
    LEGEND_RATES(:,9) = strpad('d/dt x_kl in component x_kl (pM)');
    LEGEND_RATES(:,8) = strpad('d/dt xr in component xr (pM)');
    LEGEND_RATES(:,3) = strpad('d/dt xb in component xb (pM)');
    LEGEND_RATES(:,2) = strpad('d/dt xc in component xc (pM)');
    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) = 0.9912;
    CONSTANTS(:,1) = 9.127e-4;
    CONSTANTS(:,2) = 7.282e-4;
    CONSTANTS(:,3) = 7.300e-3;
    CONSTANTS(:,4) = 1.0e0;
    CONSTANTS(:,5) = 1.0e-3;
    CONSTANTS(:,6) = 10.0e-3;
    STATES(:,2) = 9.127e-4;
    STATES(:,3) = 7.282e-4;
    STATES(:,4) = 7.300e-3;
    CONSTANTS(:,7) = 7.282e-4;
    CONSTANTS(:,8) = 7.300e-3;
    CONSTANTS(:,9) = 1.00e-1;
    CONSTANTS(:,10) = 1.00e0;
    CONSTANTS(:,11) = 1.00e0;
    CONSTANTS(:,12) = 1.00e0;
    STATES(:,5) = 0.02;
    CONSTANTS(:,13) = 0e0;
    CONSTANTS(:,14) = 2e4;
    CONSTANTS(:,15) = 1e3;
    STATES(:,6) = 0.01;
    CONSTANTS(:,16) = 0e0;
    CONSTANTS(:,17) = 1e2;
    CONSTANTS(:,18) = 1e0;
    CONSTANTS(:,19) = 1e2;
    STATES(:,7) = 0.01;
    CONSTANTS(:,20) = 3.5e-1;
    CONSTANTS(:,21) = 1e1;
    CONSTANTS(:,22) = 0.0;
    CONSTANTS(:,23) = 2e5;
    STATES(:,8) = 7.734e-4;
    STATES(:,9) = 0.01;
    CONSTANTS(:,24) = 3e6;
    CONSTANTS(:,25) = 10;
    CONSTANTS(:,26) = 1e2;
    CONSTANTS(:,27) = 0;
    CONSTANTS(:,28) = 1e3;
    CONSTANTS(:,29) = 1e-2;
    CONSTANTS(:,30) = 10;
    CONSTANTS(:,31) = 5.8e-4;
    CONSTANTS(:,32) = 1.7e-2;
    CONSTANTS(:,33) = 0.35;
    CONSTANTS(:,34) = 7e-4;
    CONSTANTS(:,35) = 1e-4;
    CONSTANTS(:,36) = 0.189;
    CONSTANTS(:,37) = 0.189;
    CONSTANTS(:,38) = 0.7;
    CONSTANTS(:,39) = 0.05;
    CONSTANTS(:,40) = 0.7;
    CONSTANTS(:,41) = 5e-3;
    CONSTANTS(:,42) = 250;
    CONSTANTS(:,43) = 0.02;
    CONSTANTS(:,44) = 3;
    CONSTANTS(:,45) = 0;
    CONSTANTS(:,46) = 86;
    CONSTANTS(:,47) =  CONSTANTS(:,39).*CONSTANTS(:,40);
    CONSTANTS(:,48) = CONSTANTS(:,45)./CONSTANTS(:,46);
    CONSTANTS(:,49) = CONSTANTS(:,42)./CONSTANTS(:,46);
    CONSTANTS(:,50) = CONSTANTS(:,44)./CONSTANTS(:,43);
    CONSTANTS(:,51) = (CONSTANTS(:,48)+CONSTANTS(:,49))./(CONSTANTS(:,48)+CONSTANTS(:,50));
    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(:,5)./CONSTANTS(:,2)).*STATES(:,3)+ (1.00000./CONSTANTS(:,3)).*STATES(:,4)) - ( (CONSTANTS(:,6)./CONSTANTS(:,1)).*STATES(:,2)+ CONSTANTS(:,4).*STATES(:,1));
    RATES(:,4) =  CONSTANTS(:,9).*(STATES(:,3) - CONSTANTS(:,7)) -  CONSTANTS(:,10).*(STATES(:,4) - CONSTANTS(:,8));
    RATES(:,9) = (CONSTANTS(:,28)+CONSTANTS(:,27)) - ( CONSTANTS(:,26).*STATES(:,5)+ CONSTANTS(:,28).*((1.00000+ (CONSTANTS(:,29)./CONSTANTS(:,30)).*STATES(:,7)+ (CONSTANTS(:,31)./CONSTANTS(:,32)).*CONSTANTS(:,25))./( CONSTANTS(:,24).*CONSTANTS(:,51).*STATES(:,3))).*STATES(:,9));
    ALGEBRAIC(:,4) = (STATES(:,2)+ CONSTANTS(:,39).*CONSTANTS(:,41))./(STATES(:,2)+CONSTANTS(:,41));
    RATES(:,7) = ( (CONSTANTS(:,23)./1.00000).*ALGEBRAIC(:,4).*STATES(:,8)+CONSTANTS(:,22)+ CONSTANTS(:,21).*STATES(:,5)) -  CONSTANTS(:,20).*STATES(:,7);
    RATES(:,8) = ( CONSTANTS(:,34).*ALGEBRAIC(:,4)+ CONSTANTS(:,35).*STATES(:,6)) -  (CONSTANTS(:,47)./ALGEBRAIC(:,4)).*STATES(:,8);
    RATES(:,3) =  (CONSTANTS(:,47)./ALGEBRAIC(:,4)).*STATES(:,8) -  CONSTANTS(:,36).*STATES(:,3);
    ALGEBRAIC(:,2) =  (( ( (CONSTANTS(:,31)./CONSTANTS(:,32)).*CONSTANTS(:,24)).*CONSTANTS(:,51).*STATES(:,3))./(1.00000+( CONSTANTS(:,31).*CONSTANTS(:,25))./CONSTANTS(:,32)+ (CONSTANTS(:,29)./( CONSTANTS(:,30).*CONSTANTS(:,33))).*( ((CONSTANTS(:,23)./1.00000)./CONSTANTS(:,51)).*STATES(:,8)+CONSTANTS(:,22)))).*(1.00000+CONSTANTS(:,27)./CONSTANTS(:,28));
    RATES(:,2) =  CONSTANTS(:,37).*ALGEBRAIC(:,2) -  CONSTANTS(:,38).*ALGEBRAIC(:,4).*STATES(:,2);
    ALGEBRAIC(:,1) =  power(STATES(:,1), 2.00000).* pi;
    ALGEBRAIC(:,3) = piecewise({VOI>=100.000&VOI<130.000, 10000.0 }, 100.000);
    ALGEBRAIC(:,5) = ALGEBRAIC(:,3)./ALGEBRAIC(:,1);
    ALGEBRAIC(:,6) = ( ALGEBRAIC(:,5).*STATES(:,4))./(1.00000+exp( - ( CONSTANTS(:,11).*ALGEBRAIC(:,5)+ CONSTANTS(:,12).*STATES(:,4))));
    RATES(:,5) = ( CONSTANTS(:,14).*ALGEBRAIC(:,6)+CONSTANTS(:,13)) -  CONSTANTS(:,15).*STATES(:,5);
    RATES(:,6) = ( CONSTANTS(:,19).*ALGEBRAIC(:,6)+ CONSTANTS(:,18).*STATES(:,5)+CONSTANTS(:,16)) -  CONSTANTS(:,17).*STATES(:,6);
   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(:,4) = (STATES(:,2)+ CONSTANTS(:,39).*CONSTANTS(:,41))./(STATES(:,2)+CONSTANTS(:,41));
    ALGEBRAIC(:,2) =  (( ( (CONSTANTS(:,31)./CONSTANTS(:,32)).*CONSTANTS(:,24)).*CONSTANTS(:,51).*STATES(:,3))./(1.00000+( CONSTANTS(:,31).*CONSTANTS(:,25))./CONSTANTS(:,32)+ (CONSTANTS(:,29)./( CONSTANTS(:,30).*CONSTANTS(:,33))).*( ((CONSTANTS(:,23)./1.00000)./CONSTANTS(:,51)).*STATES(:,8)+CONSTANTS(:,22)))).*(1.00000+CONSTANTS(:,27)./CONSTANTS(:,28));
    ALGEBRAIC(:,1) =  power(STATES(:,1), 2.00000).* pi;
    ALGEBRAIC(:,3) = piecewise({VOI>=100.000&VOI<130.000, 10000.0 }, 100.000);
    ALGEBRAIC(:,5) = ALGEBRAIC(:,3)./ALGEBRAIC(:,1);
    ALGEBRAIC(:,6) = ( ALGEBRAIC(:,5).*STATES(:,4))./(1.00000+exp( - ( CONSTANTS(:,11).*ALGEBRAIC(:,5)+ CONSTANTS(:,12).*STATES(:,4))));
end

% Compute result of a piecewise function
function x = piecewise(cases, default)
    set = [0];
    for i = 1:2:length(cases)
        if (length(cases{i+1}) == 1)
            x(cases{i} & ~set,:) = cases{i+1};
        else
            x(cases{i} & ~set,:) = cases{i+1}(cases{i} & ~set);
        end
        set = set | cases{i};
        if(set), break, end
    end
    if (length(default) == 1)
        x(~set,:) = default;
    else
        x(~set,:) = default(~set);
    end
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