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 =5;
end
% There are a total of 13 entries in each of the rate and state variable arrays.
% There are a total of 45 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 (minute)');
    LEGEND_STATES(:,1) = strpad('r in component r (dimensionless)');
    LEGEND_ALGEBRAIC(:,1) = strpad('c1 in component c1 (dimensionless)');
    LEGEND_STATES(:,2) = strpad('c2 in component c2 (dimensionless)');
    LEGEND_CONSTANTS(:,1) = strpad('L in component model_parameters (nanomolar)');
    LEGEND_CONSTANTS(:,2) = strpad('kt in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,3) = strpad('kxR0 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,4) = strpad('k_minusx in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,5) = strpad('KDL in component model_parameters (nanomolar)');
    LEGEND_CONSTANTS(:,6) = strpad('ke in component model_parameters (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,2) = strpad('e_PI3K in component e_PI3K (dimensionless)');
    LEGEND_CONSTANTS(:,7) = strpad('kappa_PI3K in component e_PI3K (dimensionless)');
    LEGEND_CONSTANTS(:,8) = strpad('alpha_PI3K in component e_PI3K (dimensionless)');
    LEGEND_STATES(:,3) = strpad('m_3PI in component m_3PI (dimensionless)');
    LEGEND_CONSTANTS(:,9) = strpad('k_3PI in component m_3PI (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,3) = strpad('e_GEF in component e_GEF (dimensionless)');
    LEGEND_CONSTANTS(:,10) = strpad('K_GR in component e_GEF (dimensionless)');
    LEGEND_CONSTANTS(:,11) = strpad('K_GP in component e_GEF (dimensionless)');
    LEGEND_STATES(:,4) = strpad('f_GEF in component f_GEF (dimensionless)');
    LEGEND_STATES(:,5) = strpad('m_Ras in component m_Ras (dimensionless)');
    LEGEND_CONSTANTS(:,12) = strpad('k_Ras in component m_Ras (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,13) = strpad('gamma in component m_Ras (dimensionless)');
    LEGEND_STATES(:,6) = strpad('x1 in component x1 (dimensionless)');
    LEGEND_CONSTANTS(:,14) = strpad('kd_x1 in component x1 (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,15) = strpad('KM_x11 in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,16) = strpad('KM_x12 in component model_parameters (dimensionless)');
    LEGEND_STATES(:,7) = strpad('y in component y (dimensionless)');
    LEGEND_ALGEBRAIC(:,4) = strpad('yp in component yp (dimensionless)');
    LEGEND_STATES(:,8) = strpad('x2 in component x2 (dimensionless)');
    LEGEND_CONSTANTS(:,17) = strpad('kd_x2 in component x2 (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,18) = strpad('K_x2 in component x2 (dimensionless)');
    LEGEND_CONSTANTS(:,19) = strpad('KM_x21 in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,20) = strpad('KM_x22 in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,21) = strpad('Vmax_yph1_KM_yph1 in component y (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,22) = strpad('KM_yph1 in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,23) = strpad('KM_yph2 in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,24) = strpad('Vmax_x11_KM_x11 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,25) = strpad('Vmax_x21_KM_x21 in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,9) = strpad('ypp in component ypp (dimensionless)');
    LEGEND_CONSTANTS(:,26) = strpad('Vmax_yph2_KM_yph2 in component ypp (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,27) = strpad('KM_y1 in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,28) = strpad('KM_y2 in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,29) = strpad('Vmax_x12_KM_x12 in component model_parameters (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,30) = strpad('Vmax_x22_KM_x22 in component model_parameters (first_order_rate_constant)');
    LEGEND_STATES(:,10) = strpad('z in component z (dimensionless)');
    LEGEND_ALGEBRAIC(:,5) = strpad('zp in component zp (dimensionless)');
    LEGEND_CONSTANTS(:,31) = strpad('Vmax_zph1_KM_zph1 in component z (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,32) = strpad('Vmax_y1_KM_y1 in component z (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,33) = strpad('KM_zph1 in component model_parameters (dimensionless)');
    LEGEND_CONSTANTS(:,34) = strpad('KM_zph2 in component model_parameters (dimensionless)');
    LEGEND_STATES(:,11) = strpad('zpp in component zpp (dimensionless)');
    LEGEND_STATES(:,12) = strpad('e_ph in component e_ph (dimensionless)');
    LEGEND_CONSTANTS(:,35) = strpad('Vmax_zph2_KM_zph2 in component zpp (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,36) = strpad('Vmax_y2_KM_y2 in component zpp (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,37) = strpad('n in component f_GEF (dimensionless)');
    LEGEND_CONSTANTS(:,38) = strpad('Kf in component f_GEF (dimensionless)');
    LEGEND_CONSTANTS(:,39) = strpad('Zf in component f_GEF (dimensionless)');
    LEGEND_CONSTANTS(:,40) = strpad('k_FB_f in component f_GEF (first_order_rate_constant)');
    LEGEND_STATES(:,13) = strpad('w in component w (dimensionless)');
    LEGEND_CONSTANTS(:,41) = strpad('kd_w in component w (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,42) = strpad('k_FB_ph in component e_ph (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,43) = strpad('p in component e_ph (dimensionless)');
    LEGEND_CONSTANTS(:,44) = strpad('Wph in component e_ph (dimensionless)');
    LEGEND_CONSTANTS(:,45) = strpad('Kph in component e_ph (dimensionless)');
    LEGEND_RATES(:,1) = strpad('d/dt r in component r (dimensionless)');
    LEGEND_RATES(:,2) = strpad('d/dt c2 in component c2 (dimensionless)');
    LEGEND_RATES(:,3) = strpad('d/dt m_3PI in component m_3PI (dimensionless)');
    LEGEND_RATES(:,5) = strpad('d/dt m_Ras in component m_Ras (dimensionless)');
    LEGEND_RATES(:,6) = strpad('d/dt x1 in component x1 (dimensionless)');
    LEGEND_RATES(:,8) = strpad('d/dt x2 in component x2 (dimensionless)');
    LEGEND_RATES(:,7) = strpad('d/dt y in component y (dimensionless)');
    LEGEND_RATES(:,9) = strpad('d/dt ypp in component ypp (dimensionless)');
    LEGEND_RATES(:,10) = strpad('d/dt z in component z (dimensionless)');
    LEGEND_RATES(:,11) = strpad('d/dt zpp in component zpp (dimensionless)');
    LEGEND_RATES(:,4) = strpad('d/dt f_GEF in component f_GEF (dimensionless)');
    LEGEND_RATES(:,13) = strpad('d/dt w in component w (dimensionless)');
    LEGEND_RATES(:,12) = strpad('d/dt e_ph in component e_ph (dimensionless)');
    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) = 0.5;
    STATES(:,2) = 0.0;
    CONSTANTS(:,1) = 1.0;
    CONSTANTS(:,2) = 0.005;
    CONSTANTS(:,3) = 0.3;
    CONSTANTS(:,4) = 0.07;
    CONSTANTS(:,5) = 1.5;
    CONSTANTS(:,6) = 0.2;
    CONSTANTS(:,7) = 0.3;
    CONSTANTS(:,8) = 80.0;
    STATES(:,3) = 0.0;
    CONSTANTS(:,9) = 1.0;
    CONSTANTS(:,10) = 495.0;
    CONSTANTS(:,11) = 5.09;
    STATES(:,4) = 1.0;
    STATES(:,5) = 0.0;
    CONSTANTS(:,12) = 1.0;
    CONSTANTS(:,13) = 0.1;
    STATES(:,6) = 0.0;
    CONSTANTS(:,14) = 0.745;
    CONSTANTS(:,15) = 30.3;
    CONSTANTS(:,16) = 45.5;
    STATES(:,7) = 1.0;
    STATES(:,8) = 0.0;
    CONSTANTS(:,17) = 2.85;
    CONSTANTS(:,18) = 6.77;
    CONSTANTS(:,19) = 21.6;
    CONSTANTS(:,20) = 15.7;
    CONSTANTS(:,21) = 4.40;
    CONSTANTS(:,22) = 44.0;
    CONSTANTS(:,23) = 12.7;
    CONSTANTS(:,24) = 1.18;
    CONSTANTS(:,25) = 0.405;
    STATES(:,9) = 0.0;
    CONSTANTS(:,26) = 6.77;
    CONSTANTS(:,27) = 31.9;
    CONSTANTS(:,28) = 8.81;
    CONSTANTS(:,29) = 4.71;
    CONSTANTS(:,30) = 2.41;
    STATES(:,10) = 1.0;
    CONSTANTS(:,31) = 0.451;
    CONSTANTS(:,32) = 11.8;
    CONSTANTS(:,33) = 14.0;
    CONSTANTS(:,34) = 31.5;
    STATES(:,11) = 0.0;
    STATES(:,12) = 1.0;
    CONSTANTS(:,35) = 0.228;
    CONSTANTS(:,36) = 31.9;
    CONSTANTS(:,37) = 1.03;
    CONSTANTS(:,38) = 3.76;
    CONSTANTS(:,39) = 0.272;
    CONSTANTS(:,40) = 0.976;
    STATES(:,13) = 0.0;
    CONSTANTS(:,41) = 0.0333;
    CONSTANTS(:,42) = 2.34;
    CONSTANTS(:,43) = 1.98;
    CONSTANTS(:,44) = 0.385;
    CONSTANTS(:,45) = 4.64;
    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(:,4) =   - CONSTANTS(:,40).*( (power(STATES(:,11), CONSTANTS(:,37))./(power(CONSTANTS(:,39), CONSTANTS(:,37))+power(STATES(:,11), CONSTANTS(:,37)))).*STATES(:,4) -  (1.00000./CONSTANTS(:,38)).*(1.00000 - STATES(:,4)));
    RATES(:,13) =  CONSTANTS(:,41).*(STATES(:,11) - STATES(:,13));
    RATES(:,12) =  CONSTANTS(:,42).*(power(STATES(:,13), CONSTANTS(:,43))./(power(CONSTANTS(:,44), CONSTANTS(:,43))+power(STATES(:,13), CONSTANTS(:,43))) -  (1.00000./CONSTANTS(:,45)).*(STATES(:,12) - 1.00000));
    ALGEBRAIC(:,1) = ( CONSTANTS(:,1).*STATES(:,1))./CONSTANTS(:,5);
    RATES(:,1) =  power(1.00000+CONSTANTS(:,1)./CONSTANTS(:,5), -1.00000).*( CONSTANTS(:,2).*(1.00000 - (STATES(:,1)+ALGEBRAIC(:,1)))+ 2.00000.*( CONSTANTS(:,4).*STATES(:,2) -  CONSTANTS(:,3).*power(ALGEBRAIC(:,1), 2.00000)));
    RATES(:,2) =  CONSTANTS(:,3).*power(ALGEBRAIC(:,1), 2.00000) -  (CONSTANTS(:,4)+CONSTANTS(:,6)).*STATES(:,2);
    ALGEBRAIC(:,2) = ((1.00000+CONSTANTS(:,7)+ 2.00000.*CONSTANTS(:,8).*STATES(:,2)) - power(power(1.00000+CONSTANTS(:,7)+ 2.00000.*CONSTANTS(:,8).*STATES(:,2), 2.00000), 1.0 ./ 2))./2.00000;
    RATES(:,3) =  CONSTANTS(:,9).*(ALGEBRAIC(:,2) - STATES(:,3));
    ALGEBRAIC(:,3) =  (( CONSTANTS(:,10).*STATES(:,2)+ CONSTANTS(:,11).*STATES(:,3))./(1.00000+ CONSTANTS(:,10).*STATES(:,2)+ CONSTANTS(:,11).*STATES(:,3))).*STATES(:,4);
    RATES(:,5) =  CONSTANTS(:,12).*( (1.00000+CONSTANTS(:,13)).*ALGEBRAIC(:,3) -  (1.00000+ CONSTANTS(:,13).*ALGEBRAIC(:,3)).*STATES(:,5));
    ALGEBRAIC(:,4) = 1.00000 - (STATES(:,7)+STATES(:,9));
    RATES(:,6) =  CONSTANTS(:,14).*(STATES(:,5) - STATES(:,6)./(1.00000+STATES(:,7)./CONSTANTS(:,15)+ALGEBRAIC(:,4)./CONSTANTS(:,16)));
    RATES(:,8) =  CONSTANTS(:,17).*(( (1.00000+CONSTANTS(:,18)).*STATES(:,3))./(1.00000+ CONSTANTS(:,18).*STATES(:,3)) - STATES(:,8)./(1.00000+STATES(:,7)./CONSTANTS(:,19)+ALGEBRAIC(:,4)./CONSTANTS(:,20)));
    RATES(:,7) = ( CONSTANTS(:,21).*ALGEBRAIC(:,4))./(1.00000+ALGEBRAIC(:,4)./CONSTANTS(:,22)+STATES(:,9)./CONSTANTS(:,23)) - (( CONSTANTS(:,24).*STATES(:,6).*STATES(:,7))./(1.00000+STATES(:,7)./CONSTANTS(:,15)+ALGEBRAIC(:,4)./CONSTANTS(:,16))+( CONSTANTS(:,25).*STATES(:,8).*STATES(:,7))./(1.00000+STATES(:,7)./CONSTANTS(:,19)+ALGEBRAIC(:,4)./CONSTANTS(:,20)));
    ALGEBRAIC(:,5) = 1.00000 - (STATES(:,10)+STATES(:,11));
    RATES(:,9) = (( CONSTANTS(:,29).*STATES(:,6).*ALGEBRAIC(:,4))./(1.00000+STATES(:,7)./CONSTANTS(:,15)+ALGEBRAIC(:,4)./CONSTANTS(:,16))+( CONSTANTS(:,30).*STATES(:,8).*ALGEBRAIC(:,4))./(1.00000+STATES(:,7)./CONSTANTS(:,19)+ALGEBRAIC(:,4)./CONSTANTS(:,20))) - (( CONSTANTS(:,26).*STATES(:,9))./( (1.00000+STATES(:,10)./CONSTANTS(:,27)+ALGEBRAIC(:,5)./CONSTANTS(:,16)).*(1.00000+ALGEBRAIC(:,4)./CONSTANTS(:,22))+STATES(:,9)./CONSTANTS(:,23)));
    RATES(:,10) = ( CONSTANTS(:,31).*STATES(:,12).*ALGEBRAIC(:,5))./(1.00000+ALGEBRAIC(:,5)./CONSTANTS(:,33)+STATES(:,11)./CONSTANTS(:,34)) - ( CONSTANTS(:,32).*STATES(:,9))./(1.00000+STATES(:,10)./CONSTANTS(:,27)+ALGEBRAIC(:,5)./CONSTANTS(:,28));
    RATES(:,11) = ( CONSTANTS(:,36).*ALGEBRAIC(:,5))./(1.00000+STATES(:,10)./CONSTANTS(:,27)+ALGEBRAIC(:,5)./CONSTANTS(:,28)) - ( CONSTANTS(:,35).*STATES(:,12).*STATES(:,11))./(1.00000+ALGEBRAIC(:,5)./CONSTANTS(:,33)+STATES(:,11)./CONSTANTS(:,34));
   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(:,1).*STATES(:,1))./CONSTANTS(:,5);
    ALGEBRAIC(:,2) = ((1.00000+CONSTANTS(:,7)+ 2.00000.*CONSTANTS(:,8).*STATES(:,2)) - power(power(1.00000+CONSTANTS(:,7)+ 2.00000.*CONSTANTS(:,8).*STATES(:,2), 2.00000), 1.0 ./ 2))./2.00000;
    ALGEBRAIC(:,3) =  (( CONSTANTS(:,10).*STATES(:,2)+ CONSTANTS(:,11).*STATES(:,3))./(1.00000+ CONSTANTS(:,10).*STATES(:,2)+ CONSTANTS(:,11).*STATES(:,3))).*STATES(:,4);
    ALGEBRAIC(:,4) = 1.00000 - (STATES(:,7)+STATES(:,9));
    ALGEBRAIC(:,5) = 1.00000 - (STATES(:,10)+STATES(:,11));
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