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 =7;
end
% There are a total of 20 entries in each of the rate and state variable arrays.
% There are a total of 33 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_ALGEBRAIC(:,1) = strpad('x1 in component x1 (molar)');
    LEGEND_STATES(:,1) = strpad('x2 in component x2 (molar)');
    LEGEND_CONSTANTS(:,1) = strpad('k1 in component reaction_constants (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,2) = strpad('k_minus1 in component reaction_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,21) = strpad('k4 in component reaction_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,3) = strpad('k_minus4 in component reaction_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,22) = strpad('k_minus3 in component reaction_constants (second_order_rate_constant)');
    LEGEND_STATES(:,2) = strpad('x3 in component x3 (molar)');
    LEGEND_STATES(:,3) = strpad('x5 in component x5 (molar)');
    LEGEND_STATES(:,4) = strpad('x6 in component x6 (molar)');
    LEGEND_CONSTANTS(:,4) = strpad('PTP in component reaction_constants (molar)');
    LEGEND_CONSTANTS(:,5) = strpad('k3 in component reaction_constants (first_order_rate_constant)');
    LEGEND_STATES(:,5) = strpad('x4 in component x4 (molar)');
    LEGEND_CONSTANTS(:,23) = strpad('k2 in component reaction_constants (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,24) = strpad('k_minus2 in component reaction_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,6) = strpad('k4b in component reaction_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,7) = strpad('k_minus4b in component reaction_constants (first_order_rate_constant)');
    LEGEND_STATES(:,6) = strpad('x7 in component x7 (molar)');
    LEGEND_STATES(:,7) = strpad('x8 in component x8 (molar)');
    LEGEND_ALGEBRAIC(:,2) = strpad('k5 in component reaction_constants (rate)');
    LEGEND_CONSTANTS(:,8) = strpad('k_minus5 in component reaction_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,9) = strpad('k6 in component reaction_constants (second_order_rate_constant)');
    LEGEND_STATES(:,8) = strpad('x9 in component x9 (molar)');
    LEGEND_CONSTANTS(:,10) = strpad('k7 in component reaction_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,25) = strpad('k_minus7 in component reaction_constants (second_order_rate_constant)');
    LEGEND_STATES(:,9) = strpad('x10 in component x10 (molar)');
    LEGEND_CONSTANTS(:,11) = strpad('IRp in component reaction_constants (molar)');
    LEGEND_CONSTANTS(:,26) = strpad('k8 in component reaction_constants (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,12) = strpad('k_minus8 in component reaction_constants (first_order_rate_constant)');
    LEGEND_STATES(:,10) = strpad('x11 in component x11 (molar)');
    LEGEND_STATES(:,11) = strpad('x12 in component x12 (molar)');
    LEGEND_STATES(:,12) = strpad('x13 in component x13 (percentage)');
    LEGEND_ALGEBRAIC(:,3) = strpad('k9 in component reaction_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,27) = strpad('k_minus9 in component reaction_constants (second_order_rate_constant)');
    LEGEND_CONSTANTS(:,28) = strpad('k10 in component reaction_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,13) = strpad('k_minus10 in component reaction_constants (second_order_rate_constant)');
    LEGEND_STATES(:,13) = strpad('x14 in component x14 (percentage)');
    LEGEND_STATES(:,14) = strpad('x15 in component x15 (percentage)');
    LEGEND_CONSTANTS(:,14) = strpad('PTEN in component reaction_constants (molar)');
    LEGEND_CONSTANTS(:,15) = strpad('SHIP in component reaction_constants (molar)');
    LEGEND_STATES(:,15) = strpad('x16 in component x16 (percentage)');
    LEGEND_ALGEBRAIC(:,4) = strpad('k11 in component reaction_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,29) = strpad('k_minus11 in component reaction_constants (first_order_rate_constant)');
    LEGEND_STATES(:,16) = strpad('x17 in component x17 (percentage)');
    LEGEND_STATES(:,17) = strpad('x18 in component x18 (percentage)');
    LEGEND_ALGEBRAIC(:,5) = strpad('k12 in component reaction_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,30) = strpad('k_minus12 in component reaction_constants (first_order_rate_constant)');
    LEGEND_STATES(:,18) = strpad('x19 in component x19 (percentage)');
    LEGEND_STATES(:,19) = strpad('x20 in component x20 (percentage)');
    LEGEND_CONSTANTS(:,31) = strpad('k13 in component reaction_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,16) = strpad('k_minus13 in component reaction_constants (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,7) = strpad('k13b in component reaction_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,32) = strpad('k14 in component reaction_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,17) = strpad('k_minus14 in component reaction_constants (first_order_rate_constant)');
    LEGEND_STATES(:,20) = strpad('x21 in component x21 (percentage)');
    LEGEND_CONSTANTS(:,33) = strpad('k9_basal in component reaction_constants (first_order_rate_constant)');
    LEGEND_CONSTANTS(:,18) = strpad('k9_stimulated in component reaction_constants (first_order_rate_constant)');
    LEGEND_ALGEBRAIC(:,6) = strpad('effect in component reaction_constants (dimensionless)');
    LEGEND_CONSTANTS(:,19) = strpad('APequil in component reaction_constants (dimensionless)');
    LEGEND_CONSTANTS(:,20) = strpad('PI3K in component reaction_constants (molar)');
    LEGEND_RATES(:,1) = strpad('d/dt x2 in component x2 (molar)');
    LEGEND_RATES(:,2) = strpad('d/dt x3 in component x3 (molar)');
    LEGEND_RATES(:,5) = strpad('d/dt x4 in component x4 (molar)');
    LEGEND_RATES(:,3) = strpad('d/dt x5 in component x5 (molar)');
    LEGEND_RATES(:,4) = strpad('d/dt x6 in component x6 (molar)');
    LEGEND_RATES(:,6) = strpad('d/dt x7 in component x7 (molar)');
    LEGEND_RATES(:,7) = strpad('d/dt x8 in component x8 (molar)');
    LEGEND_RATES(:,8) = strpad('d/dt x9 in component x9 (molar)');
    LEGEND_RATES(:,9) = strpad('d/dt x10 in component x10 (molar)');
    LEGEND_RATES(:,10) = strpad('d/dt x11 in component x11 (molar)');
    LEGEND_RATES(:,11) = strpad('d/dt x12 in component x12 (molar)');
    LEGEND_RATES(:,12) = strpad('d/dt x13 in component x13 (percentage)');
    LEGEND_RATES(:,13) = strpad('d/dt x14 in component x14 (percentage)');
    LEGEND_RATES(:,14) = strpad('d/dt x15 in component x15 (percentage)');
    LEGEND_RATES(:,15) = strpad('d/dt x16 in component x16 (percentage)');
    LEGEND_RATES(:,16) = strpad('d/dt x17 in component x17 (percentage)');
    LEGEND_RATES(:,17) = strpad('d/dt x18 in component x18 (percentage)');
    LEGEND_RATES(:,18) = strpad('d/dt x19 in component x19 (percentage)');
    LEGEND_RATES(:,19) = strpad('d/dt x20 in component x20 (percentage)');
    LEGEND_RATES(:,20) = strpad('d/dt x21 in component x21 (percentage)');
    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) = 9e-13;
    CONSTANTS(:,1) = 6e7;
    CONSTANTS(:,2) = 0.2;
    CONSTANTS(:,3) = 0.003;
    STATES(:,2) = 0;
    STATES(:,3) = 0;
    STATES(:,4) = 1e-13;
    CONSTANTS(:,4) = 1;
    CONSTANTS(:,5) = 2500;
    STATES(:,5) = 0;
    CONSTANTS(:,6) = 2.1e-3;
    CONSTANTS(:,7) = 2.1e-4;
    STATES(:,6) = 0;
    STATES(:,7) = 0;
    CONSTANTS(:,8) = 1.67e-18;
    CONSTANTS(:,9) = 0.461;
    STATES(:,8) = 1e-13;
    CONSTANTS(:,10) = 4.16;
    STATES(:,9) = 1e-13;
    CONSTANTS(:,11) = 8.97e-13;
    CONSTANTS(:,12) = 10;
    STATES(:,10) = 1e-13;
    STATES(:,11) = 0;
    STATES(:,12) = 0.31;
    CONSTANTS(:,13) = 2.77;
    STATES(:,13) = 99.4;
    STATES(:,14) = 0.29;
    CONSTANTS(:,14) = 1;
    CONSTANTS(:,15) = 1;
    STATES(:,15) = 100;
    STATES(:,16) = 0;
    STATES(:,17) = 100;
    STATES(:,18) = 0;
    STATES(:,19) = 96;
    CONSTANTS(:,16) = 0.167;
    CONSTANTS(:,17) = 0.001155;
    STATES(:,20) = 4;
    CONSTANTS(:,18) = 1.39;
    CONSTANTS(:,19) = 9.09;
    CONSTANTS(:,20) = 5e-15;
    CONSTANTS(:,21) = CONSTANTS(:,3)./9.00000;
    CONSTANTS(:,22) = CONSTANTS(:,2)./1.00000;
    CONSTANTS(:,23) = CONSTANTS(:,1);
    CONSTANTS(:,24) =  100.000.*CONSTANTS(:,2);
    CONSTANTS(:,25) =  (2.50000./7.45000).*CONSTANTS(:,10);
    CONSTANTS(:,26) =  (( CONSTANTS(:,12).*5.00000)./70.7750).*1.00000e+12;
    CONSTANTS(:,27) =  (94.0000./3.10000).*CONSTANTS(:,18);
    CONSTANTS(:,28) =  (3.10000./2.90000).*CONSTANTS(:,13);
    CONSTANTS(:,29) =  10.0000.*log(2.00000).*1.00000;
    CONSTANTS(:,30) =  10.0000.*log(2.00000).*1.00000;
    CONSTANTS(:,31) =  (4.00000./96.0000).*CONSTANTS(:,16);
    CONSTANTS(:,32) = CONSTANTS(:,17)./96.0000;
    CONSTANTS(:,33) =  (0.310000./99.4000).*CONSTANTS(:,27);
    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(:,6) =  CONSTANTS(:,6).*STATES(:,5) - ( CONSTANTS(:,7).*STATES(:,6)+ CONSTANTS(:,9).*CONSTANTS(:,4).*STATES(:,6));
    RATES(:,7) =  CONSTANTS(:,6).*STATES(:,3) - ( CONSTANTS(:,7).*STATES(:,7)+ CONSTANTS(:,9).*CONSTANTS(:,4).*STATES(:,7));
    RATES(:,8) =  CONSTANTS(:,25).*CONSTANTS(:,4).*STATES(:,9) - ( CONSTANTS(:,10).*STATES(:,8).*(STATES(:,5)+STATES(:,3)))./CONSTANTS(:,11);
    RATES(:,9) = (( CONSTANTS(:,10).*STATES(:,8).*(STATES(:,5)+STATES(:,3)))./CONSTANTS(:,11)+ CONSTANTS(:,12).*STATES(:,11)) -  ( CONSTANTS(:,25).*CONSTANTS(:,4)+ CONSTANTS(:,26).*STATES(:,10)).*STATES(:,9);
    RATES(:,10) =  CONSTANTS(:,12).*STATES(:,11) -  CONSTANTS(:,26).*STATES(:,9).*STATES(:,10);
    RATES(:,11) =  CONSTANTS(:,26).*STATES(:,9).*STATES(:,10) -  CONSTANTS(:,12).*STATES(:,11);
    RATES(:,14) =  CONSTANTS(:,13).*CONSTANTS(:,15).*STATES(:,12) -  CONSTANTS(:,28).*STATES(:,14);
    ALGEBRAIC(:,1) = piecewise({VOI<15.0000, 1.00000e-07 }, 0.00000);
    RATES(:,1) = ( CONSTANTS(:,2).*STATES(:,2)+ CONSTANTS(:,22).*CONSTANTS(:,4).*STATES(:,3)+ CONSTANTS(:,3).*STATES(:,4)) - ( CONSTANTS(:,1).*ALGEBRAIC(:,1).*STATES(:,1)+ CONSTANTS(:,21).*STATES(:,1));
    RATES(:,2) =  CONSTANTS(:,1).*ALGEBRAIC(:,1).*STATES(:,1) - ( CONSTANTS(:,2).*STATES(:,2)+ CONSTANTS(:,5).*STATES(:,2));
    RATES(:,5) = ( CONSTANTS(:,23).*ALGEBRAIC(:,1).*STATES(:,3)+ CONSTANTS(:,7).*STATES(:,6)) - ( CONSTANTS(:,24).*STATES(:,5)+ CONSTANTS(:,6).*STATES(:,5));
    RATES(:,3) = ( CONSTANTS(:,5).*STATES(:,2)+ CONSTANTS(:,24).*STATES(:,5)+ CONSTANTS(:,7).*STATES(:,7)) - ( CONSTANTS(:,23).*ALGEBRAIC(:,1).*STATES(:,3)+ CONSTANTS(:,22).*CONSTANTS(:,4).*STATES(:,3)+ CONSTANTS(:,6).*STATES(:,3));
    ALGEBRAIC(:,2) = piecewise({STATES(:,4)+STATES(:,6)+STATES(:,7)>1.00000e-13,  10.0000.*CONSTANTS(:,8) },  60.0000.*CONSTANTS(:,8));
    RATES(:,4) = (ALGEBRAIC(:,2)+ CONSTANTS(:,9).*CONSTANTS(:,4).*(STATES(:,6)+STATES(:,7))+ CONSTANTS(:,21).*STATES(:,1)) - ( CONSTANTS(:,8).*STATES(:,4)+ CONSTANTS(:,3).*STATES(:,4));
    ALGEBRAIC(:,3) = ( (CONSTANTS(:,18) - CONSTANTS(:,33)).*STATES(:,11))./CONSTANTS(:,20)+CONSTANTS(:,33);
    RATES(:,12) = ( ALGEBRAIC(:,3).*STATES(:,13)+ CONSTANTS(:,28).*STATES(:,14)) -  ( CONSTANTS(:,27).*CONSTANTS(:,14)+ CONSTANTS(:,13).*CONSTANTS(:,15)).*STATES(:,12);
    RATES(:,13) =  CONSTANTS(:,27).*CONSTANTS(:,14).*STATES(:,12) -  ALGEBRAIC(:,3).*STATES(:,13);
    ALGEBRAIC(:,4) = ( 0.100000.*CONSTANTS(:,29).*(STATES(:,12) - 0.310000))./(3.10000 - 0.310000);
    RATES(:,15) =  CONSTANTS(:,29).*STATES(:,16) -  ALGEBRAIC(:,4).*STATES(:,15);
    RATES(:,16) =  ALGEBRAIC(:,4).*STATES(:,15) -  CONSTANTS(:,29).*STATES(:,16);
    ALGEBRAIC(:,5) = ( 0.100000.*CONSTANTS(:,30).*(STATES(:,12) - 0.310000))./(3.10000 - 0.310000);
    RATES(:,17) =  CONSTANTS(:,30).*STATES(:,18) -  ALGEBRAIC(:,5).*STATES(:,17);
    RATES(:,18) =  ALGEBRAIC(:,5).*STATES(:,17) -  CONSTANTS(:,30).*STATES(:,18);
    ALGEBRAIC(:,6) = ( 0.200000.*STATES(:,16)+ 0.800000.*STATES(:,18))./CONSTANTS(:,19);
    ALGEBRAIC(:,7) =  (40.0000./60.0000 - 4.00000./96.0000).*CONSTANTS(:,16).*ALGEBRAIC(:,6);
    RATES(:,19) = ( CONSTANTS(:,16).*STATES(:,20)+CONSTANTS(:,32)) - ( (CONSTANTS(:,31)+ALGEBRAIC(:,7)).*STATES(:,19)+ CONSTANTS(:,17).*STATES(:,19));
    RATES(:,20) =   - CONSTANTS(:,16).*STATES(:,20)+ (CONSTANTS(:,31)+ALGEBRAIC(:,7)).*STATES(:,19);
   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) = piecewise({VOI<15.0000, 1.00000e-07 }, 0.00000);
    ALGEBRAIC(:,2) = piecewise({STATES(:,4)+STATES(:,6)+STATES(:,7)>1.00000e-13,  10.0000.*CONSTANTS(:,8) },  60.0000.*CONSTANTS(:,8));
    ALGEBRAIC(:,3) = ( (CONSTANTS(:,18) - CONSTANTS(:,33)).*STATES(:,11))./CONSTANTS(:,20)+CONSTANTS(:,33);
    ALGEBRAIC(:,4) = ( 0.100000.*CONSTANTS(:,29).*(STATES(:,12) - 0.310000))./(3.10000 - 0.310000);
    ALGEBRAIC(:,5) = ( 0.100000.*CONSTANTS(:,30).*(STATES(:,12) - 0.310000))./(3.10000 - 0.310000);
    ALGEBRAIC(:,6) = ( 0.200000.*STATES(:,16)+ 0.800000.*STATES(:,18))./CONSTANTS(:,19);
    ALGEBRAIC(:,7) =  (40.0000./60.0000 - 4.00000./96.0000).*CONSTANTS(:,16).*ALGEBRAIC(:,6);
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