Generated Code
The following is matlab code generated by the CellML API from this CellML file. (Back to language selection)
The raw code is available.
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 =22;
end
% There are a total of 13 entries in each of the rate and state variable arrays.
% There are a total of 67 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_STATES(:,1) = strpad('GlcI in component GlcI (millimolar)');
LEGEND_ALGEBRAIC(:,6) = strpad('vHK in component vHK (flux)');
LEGEND_ALGEBRAIC(:,5) = strpad('vGlcTr in component vGlcTr (flux)');
LEGEND_STATES(:,2) = strpad('hexose_P in component hexose_P (millimolar)');
LEGEND_ALGEBRAIC(:,7) = strpad('vPFK in component vPFK (flux)');
LEGEND_STATES(:,3) = strpad('Fru16BP in component Fru16BP (millimolar)');
LEGEND_ALGEBRAIC(:,15) = strpad('vALD in component vALD (flux)');
LEGEND_STATES(:,4) = strpad('triose_P in component triose_P (millimolar)');
LEGEND_ALGEBRAIC(:,17) = strpad('vGAPDH in component vGAPDH (flux)');
LEGEND_ALGEBRAIC(:,18) = strpad('vGDH in component vGDH (flux)');
LEGEND_ALGEBRAIC(:,9) = strpad('vGPO in component vGPO (flux)');
LEGEND_STATES(:,5) = strpad('BPGA13 in component BPGA13 (millimolar)');
LEGEND_ALGEBRAIC(:,21) = strpad('vPGK in component vPGK (flux)');
LEGEND_STATES(:,6) = strpad('N in component N (millimolar)');
LEGEND_ALGEBRAIC(:,22) = strpad('vPK in component vPK (flux)');
LEGEND_STATES(:,7) = strpad('Pyr in component Pyr (millimolar)');
LEGEND_ALGEBRAIC(:,10) = strpad('vPyrTr in component vPyrTr (flux)');
LEGEND_STATES(:,8) = strpad('NADH in component NADH (millimolar)');
LEGEND_STATES(:,9) = strpad('NAD in component NAD (millimolar)');
LEGEND_STATES(:,10) = strpad('Gly3P in component Gly3P (millimolar)');
LEGEND_ALGEBRAIC(:,12) = strpad('vGlyK in component vGlyK (flux)');
LEGEND_STATES(:,11) = strpad('Gly in component Gly (millimolar)');
LEGEND_STATES(:,12) = strpad('P in component P (millimolar)');
LEGEND_ALGEBRAIC(:,11) = strpad('vATPase in component vATPase (flux)');
LEGEND_ALGEBRAIC(:,1) = strpad('ATP in component ATP (millimolar)');
LEGEND_CONSTANTS(:,1) = strpad('sumA in component ATP (millimolar)');
LEGEND_CONSTANTS(:,2) = strpad('Keq_AK in component ATP (dimensionless)');
LEGEND_ALGEBRAIC(:,2) = strpad('ADP in component ADP (millimolar)');
LEGEND_ALGEBRAIC(:,13) = strpad('DHAP in component DHAP (millimolar)');
LEGEND_ALGEBRAIC(:,4) = strpad('Fru6P in component Fru6P (millimolar)');
LEGEND_ALGEBRAIC(:,14) = strpad('GAP in component GAP (millimolar)');
LEGEND_STATES(:,13) = strpad('Glc6P in component Glc6P (millimolar)');
LEGEND_CONSTANTS(:,3) = strpad('sumc4 in component DHAP (millimolar)');
LEGEND_CONSTANTS(:,4) = strpad('sumc5 in component DHAP (millimolar)');
LEGEND_ALGEBRAIC(:,3) = strpad('GlcE in component GlcE (millimolar)');
LEGEND_ALGEBRAIC(:,8) = strpad('vPGI in component vPGI (flux)');
LEGEND_ALGEBRAIC(:,19) = strpad('PGA3 in component PGA3 (millimolar)');
LEGEND_ALGEBRAIC(:,20) = strpad('PEP in component PEP (millimolar)');
LEGEND_CONSTANTS(:,5) = strpad('Keq_ENO in component PEP (dimensionless)');
LEGEND_CONSTANTS(:,6) = strpad('Keq_PGM in component PEP (dimensionless)');
LEGEND_CONSTANTS(:,7) = strpad('K_Glc in component vGlcTr (millimolar)');
LEGEND_CONSTANTS(:,8) = strpad('alpha in component vGlcTr (dimensionless)');
LEGEND_CONSTANTS(:,9) = strpad('vGlcTr_max in component vGlcTr (flux)');
LEGEND_CONSTANTS(:,10) = strpad('K_GlcI in component vHK (millimolar)');
LEGEND_CONSTANTS(:,11) = strpad('K_Glc6P in component vHK (millimolar)');
LEGEND_CONSTANTS(:,12) = strpad('K_ATP in component vHK (millimolar)');
LEGEND_CONSTANTS(:,13) = strpad('K_ADP in component vHK (millimolar)');
LEGEND_CONSTANTS(:,14) = strpad('vHK_max in component vHK (flux)');
LEGEND_CONSTANTS(:,15) = strpad('K_Glc6P in component vPGI (millimolar)');
LEGEND_CONSTANTS(:,16) = strpad('K_Fru6P in component vPGI (millimolar)');
LEGEND_CONSTANTS(:,17) = strpad('vPGI_max in component vPGI (flux)');
LEGEND_CONSTANTS(:,18) = strpad('Ki_1 in component vPFK (millimolar)');
LEGEND_CONSTANTS(:,19) = strpad('Ki_2 in component vPFK (millimolar)');
LEGEND_CONSTANTS(:,20) = strpad('KM_Fru6P in component vPFK (millimolar)');
LEGEND_CONSTANTS(:,21) = strpad('KM_ATP in component vPFK (millimolar)');
LEGEND_CONSTANTS(:,22) = strpad('vPFK_max in component vPFK (flux)');
LEGEND_CONSTANTS(:,23) = strpad('sumA in component vALD (millimolar)');
LEGEND_CONSTANTS(:,24) = strpad('KM_GAP in component vALD (millimolar)');
LEGEND_CONSTANTS(:,25) = strpad('Ki_GAP in component vALD (millimolar)');
LEGEND_CONSTANTS(:,26) = strpad('KM_DHAP in component vALD (millimolar)');
LEGEND_CONSTANTS(:,27) = strpad('vALD_max_forward in component vALD (flux)');
LEGEND_CONSTANTS(:,28) = strpad('vALD_max_reverse in component vALD (flux)');
LEGEND_ALGEBRAIC(:,16) = strpad('vTPI in component vTPI (flux)');
LEGEND_CONSTANTS(:,29) = strpad('K_DHAP in component vTPI (millimolar)');
LEGEND_CONSTANTS(:,30) = strpad('K_GAP in component vTPI (millimolar)');
LEGEND_CONSTANTS(:,31) = strpad('vTPI_max in component vTPI (flux)');
LEGEND_CONSTANTS(:,32) = strpad('K_NAD in component vGAPDH (millimolar)');
LEGEND_CONSTANTS(:,33) = strpad('K_GAP in component vGAPDH (millimolar)');
LEGEND_CONSTANTS(:,34) = strpad('K_BPGA13 in component vGAPDH (millimolar)');
LEGEND_CONSTANTS(:,35) = strpad('K_NADH in component vGAPDH (millimolar)');
LEGEND_CONSTANTS(:,36) = strpad('vGAPDH_max_forward in component vGAPDH (flux)');
LEGEND_CONSTANTS(:,37) = strpad('vGAPDH_max_reverse in component vGAPDH (flux)');
LEGEND_CONSTANTS(:,38) = strpad('vGAPDH_max in component vGAPDH (dimensionless)');
LEGEND_CONSTANTS(:,39) = strpad('K_NADH in component vGDH (millimolar)');
LEGEND_CONSTANTS(:,40) = strpad('K_Gly3P in component vGDH (millimolar)');
LEGEND_CONSTANTS(:,41) = strpad('K_DHAP in component vGDH (millimolar)');
LEGEND_CONSTANTS(:,42) = strpad('K_NAD in component vGDH (millimolar)');
LEGEND_CONSTANTS(:,43) = strpad('vGDH_max_forward in component vGDH (flux)');
LEGEND_CONSTANTS(:,44) = strpad('vGDH_max_reverse in component vGDH (flux)');
LEGEND_CONSTANTS(:,45) = strpad('vGDH_max in component vGDH (dimensionless)');
LEGEND_CONSTANTS(:,46) = strpad('K_Gly3P in component vGPO (millimolar)');
LEGEND_CONSTANTS(:,47) = strpad('vGPO_max in component vGPO (flux)');
LEGEND_CONSTANTS(:,48) = strpad('K_pyruvate in component vPyrTr (millimolar)');
LEGEND_CONSTANTS(:,49) = strpad('vPyrTr_max in component vPyrTr (flux)');
LEGEND_CONSTANTS(:,50) = strpad('K_ADP in component vPGK (millimolar)');
LEGEND_CONSTANTS(:,51) = strpad('K_BPGA13 in component vPGK (millimolar)');
LEGEND_CONSTANTS(:,52) = strpad('K_PGA3 in component vPGK (millimolar)');
LEGEND_CONSTANTS(:,53) = strpad('K_ATP in component vPGK (millimolar)');
LEGEND_CONSTANTS(:,54) = strpad('vPGK_max_forward in component vPGK (flux)');
LEGEND_CONSTANTS(:,55) = strpad('vPGK_max_reverse in component vPGK (flux)');
LEGEND_CONSTANTS(:,56) = strpad('vPGK_max in component vPGK (dimensionless)');
LEGEND_CONSTANTS(:,57) = strpad('KM_ADP in component vPK (millimolar)');
LEGEND_CONSTANTS(:,58) = strpad('n in component vPK (dimensionless)');
LEGEND_CONSTANTS(:,59) = strpad('vPK_max in component vPK (flux)');
LEGEND_CONSTANTS(:,60) = strpad('k in component vATPase (flux)');
LEGEND_CONSTANTS(:,61) = strpad('K_ADP in component vGlyK (millimolar)');
LEGEND_CONSTANTS(:,62) = strpad('K_Gly3P in component vGlyK (millimolar)');
LEGEND_CONSTANTS(:,63) = strpad('K_Gly in component vGlyK (millimolar)');
LEGEND_CONSTANTS(:,64) = strpad('K_ATP in component vGlyK (millimolar)');
LEGEND_CONSTANTS(:,65) = strpad('vGlyK_max_forward in component vGlyK (flux)');
LEGEND_CONSTANTS(:,66) = strpad('vGlyK_max_reverse in component vGlyK (flux)');
LEGEND_CONSTANTS(:,67) = strpad('vGlyK_max in component vGlyK (dimensionless)');
LEGEND_RATES(:,1) = strpad('d/dt GlcI in component GlcI (millimolar)');
LEGEND_RATES(:,2) = strpad('d/dt hexose_P in component hexose_P (millimolar)');
LEGEND_RATES(:,3) = strpad('d/dt Fru16BP in component Fru16BP (millimolar)');
LEGEND_RATES(:,4) = strpad('d/dt triose_P in component triose_P (millimolar)');
LEGEND_RATES(:,5) = strpad('d/dt BPGA13 in component BPGA13 (millimolar)');
LEGEND_RATES(:,6) = strpad('d/dt N in component N (millimolar)');
LEGEND_RATES(:,7) = strpad('d/dt Pyr in component Pyr (millimolar)');
LEGEND_RATES(:,8) = strpad('d/dt NADH in component NADH (millimolar)');
LEGEND_RATES(:,9) = strpad('d/dt NAD in component NAD (millimolar)');
LEGEND_RATES(:,10) = strpad('d/dt Gly3P in component Gly3P (millimolar)');
LEGEND_RATES(:,11) = strpad('d/dt Gly in component Gly (millimolar)');
LEGEND_RATES(:,12) = strpad('d/dt P in component P (millimolar)');
LEGEND_RATES(:,13) = strpad('d/dt Glc6P in component Glc6P (millimolar)');
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) = 0.0340009;
STATES(:,2) = 2.583763;
STATES(:,3) = 16.5371;
STATES(:,4) = 3.9391429;
STATES(:,5) = 0.0326745;
STATES(:,6) = 1.59603;
STATES(:,7) = 4.77413;
STATES(:,8) = 0.0448639;
STATES(:,9) = 0.0448639;
STATES(:,10) = 0.0;
STATES(:,11) = 0.0;
STATES(:,12) = 7.63936;
CONSTANTS(:,1) = 3.9;
CONSTANTS(:,2) = 0.442;
STATES(:,13) = 2.07199;
CONSTANTS(:,3) = 45.0;
CONSTANTS(:,4) = 5.0;
CONSTANTS(:,5) = 6.7;
CONSTANTS(:,6) = 0.187;
CONSTANTS(:,7) = 2.0;
CONSTANTS(:,8) = 0.75;
CONSTANTS(:,9) = 106.2;
CONSTANTS(:,10) = 0.1;
CONSTANTS(:,11) = 12.0;
CONSTANTS(:,12) = 0.116;
CONSTANTS(:,13) = 0.126;
CONSTANTS(:,14) = 625.0;
CONSTANTS(:,15) = 0.4;
CONSTANTS(:,16) = 0.12;
CONSTANTS(:,17) = 848.0;
CONSTANTS(:,18) = 15.8;
CONSTANTS(:,19) = 10.7;
CONSTANTS(:,20) = 0.82;
CONSTANTS(:,21) = 0.026;
CONSTANTS(:,22) = 780.0;
CONSTANTS(:,23) = 6.0;
CONSTANTS(:,24) = 0.067;
CONSTANTS(:,25) = 0.098;
CONSTANTS(:,26) = 0.015;
CONSTANTS(:,27) = 184.5;
CONSTANTS(:,28) = 219.555;
CONSTANTS(:,29) = 1.2;
CONSTANTS(:,30) = 0.25;
CONSTANTS(:,31) = 842.0;
CONSTANTS(:,32) = 0.45;
CONSTANTS(:,33) = 0.15;
CONSTANTS(:,34) = 0.1;
CONSTANTS(:,35) = 0.02;
CONSTANTS(:,36) = 1470.0;
CONSTANTS(:,37) = 984.9;
CONSTANTS(:,38) = 1.0;
CONSTANTS(:,39) = 0.01;
CONSTANTS(:,40) = 2.0;
CONSTANTS(:,41) = 0.1;
CONSTANTS(:,42) = 0.4;
CONSTANTS(:,43) = 533.0;
CONSTANTS(:,44) = 149.24;
CONSTANTS(:,45) = 1.0;
CONSTANTS(:,46) = 1.7;
CONSTANTS(:,47) = 368.0;
CONSTANTS(:,48) = 1.96;
CONSTANTS(:,49) = 200.0;
CONSTANTS(:,50) = 0.1;
CONSTANTS(:,51) = 0.05;
CONSTANTS(:,52) = 1.62;
CONSTANTS(:,53) = 0.29;
CONSTANTS(:,54) = 640.0;
CONSTANTS(:,55) = 18.56;
CONSTANTS(:,56) = 1.0;
CONSTANTS(:,57) = 0.114;
CONSTANTS(:,58) = 2.5;
CONSTANTS(:,59) = 2600;
CONSTANTS(:,60) = 50;
CONSTANTS(:,61) = 0.12;
CONSTANTS(:,62) = 5.1;
CONSTANTS(:,63) = 0.12;
CONSTANTS(:,64) = 0.19;
CONSTANTS(:,65) = 220.0;
CONSTANTS(:,66) = 334000.0;
CONSTANTS(:,67) = 1.0;
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(:,12).*(1.00000 - 4.00000.*CONSTANTS(:,2)) - CONSTANTS(:,1))+power(power(CONSTANTS(:,1) - (1.00000 - 4.00000.*CONSTANTS(:,2)).*STATES(:,12), 2.00000)+ 4.00000.*(1.00000 - 4.00000.*CONSTANTS(:,2)).*( - CONSTANTS(:,2).*power(STATES(:,12), 2.00000)), 0.500000))./( 2.00000.*(1.00000 - 4.00000.*CONSTANTS(:,2)));
ALGEBRAIC(:,2) = STATES(:,12) - 2.00000.*ALGEBRAIC(:,1);
ALGEBRAIC(:,6) = ( CONSTANTS(:,14).*STATES(:,1).*ALGEBRAIC(:,1))./( CONSTANTS(:,12).*CONSTANTS(:,10).*(1.00000+STATES(:,13)./CONSTANTS(:,11)+STATES(:,1)./CONSTANTS(:,10)).*(1.00000+ALGEBRAIC(:,1)./CONSTANTS(:,12)+ALGEBRAIC(:,2)./CONSTANTS(:,13)));
ALGEBRAIC(:,3) = piecewise({VOI>=60.0000&VOI<61.0000, 5.00000 }, 0.0500000);
ALGEBRAIC(:,5) = CONSTANTS(:,9).*((ALGEBRAIC(:,3) - STATES(:,1))./(CONSTANTS(:,7)+ALGEBRAIC(:,3)+STATES(:,1)+ CONSTANTS(:,8).*ALGEBRAIC(:,3).*(STATES(:,1)./CONSTANTS(:,7))));
RATES(:,1) = ALGEBRAIC(:,5) - ALGEBRAIC(:,6);
ALGEBRAIC(:,4) = STATES(:,2) - STATES(:,13);
ALGEBRAIC(:,7) = ( CONSTANTS(:,18).*CONSTANTS(:,22).*ALGEBRAIC(:,4).*ALGEBRAIC(:,1))./( CONSTANTS(:,21).*CONSTANTS(:,20).*(STATES(:,3)+CONSTANTS(:,18)).*(1.00000+STATES(:,3)./CONSTANTS(:,19)+ALGEBRAIC(:,4)./CONSTANTS(:,20)).*(1.00000+ALGEBRAIC(:,1)./CONSTANTS(:,21)));
RATES(:,2) = ALGEBRAIC(:,6) - ALGEBRAIC(:,7);
ALGEBRAIC(:,8) = ( CONSTANTS(:,17).*(STATES(:,13)./CONSTANTS(:,15) - ALGEBRAIC(:,4)./CONSTANTS(:,16)))./(1.00000+STATES(:,13)./CONSTANTS(:,15)+ALGEBRAIC(:,4)./CONSTANTS(:,16));
RATES(:,13) = ALGEBRAIC(:,6) - ALGEBRAIC(:,8);
ALGEBRAIC(:,12) = ( CONSTANTS(:,67).*(( CONSTANTS(:,65).*ALGEBRAIC(:,2).*STATES(:,10))./( CONSTANTS(:,61).*CONSTANTS(:,62)) - ( CONSTANTS(:,66).*ALGEBRAIC(:,1).*STATES(:,11))./( CONSTANTS(:,64).*CONSTANTS(:,63))))./( (1.00000+STATES(:,10)./CONSTANTS(:,62)+STATES(:,11)./CONSTANTS(:,63)).*(1.00000+ALGEBRAIC(:,2)./CONSTANTS(:,61)+ALGEBRAIC(:,1)./CONSTANTS(:,64)));
RATES(:,11) = ALGEBRAIC(:,12);
[CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS, STATES, ALGEBRAIC);
ALGEBRAIC(:,15) = (( CONSTANTS(:,27).*STATES(:,3))./( 0.00900000.*(1.00000+ALGEBRAIC(:,1)./0.680000+ALGEBRAIC(:,2)./1.51000+(CONSTANTS(:,23) - (ALGEBRAIC(:,1)+ALGEBRAIC(:,2)))./3.65000)) - ( CONSTANTS(:,28).*ALGEBRAIC(:,14).*ALGEBRAIC(:,13))./( CONSTANTS(:,26).*CONSTANTS(:,24)))./(1.00000+ALGEBRAIC(:,14)./CONSTANTS(:,24)+ALGEBRAIC(:,13)./CONSTANTS(:,26)+( ALGEBRAIC(:,14).*ALGEBRAIC(:,13))./( CONSTANTS(:,26).*CONSTANTS(:,24))+STATES(:,3)./( 0.00900000.*(1.00000+ALGEBRAIC(:,1)./0.680000+ALGEBRAIC(:,2)./1.51000+(CONSTANTS(:,23) - (ALGEBRAIC(:,1)+ALGEBRAIC(:,2)))./3.65000))+( STATES(:,3).*ALGEBRAIC(:,14))./( CONSTANTS(:,25).*0.00900000.*(1.00000+ALGEBRAIC(:,1)./0.680000+ALGEBRAIC(:,2)./1.51000+(CONSTANTS(:,23) - (ALGEBRAIC(:,1)+ALGEBRAIC(:,2)))./3.65000)));
RATES(:,3) = ALGEBRAIC(:,7) - ALGEBRAIC(:,15);
ALGEBRAIC(:,17) = CONSTANTS(:,38).*(( CONSTANTS(:,36).*( ALGEBRAIC(:,14).*((STATES(:,9)./CONSTANTS(:,33))./CONSTANTS(:,32)) - (CONSTANTS(:,37)./CONSTANTS(:,36)).*((( STATES(:,5).*STATES(:,8))./CONSTANTS(:,34))./CONSTANTS(:,35))))./( (1.00000+ALGEBRAIC(:,14)./CONSTANTS(:,33)+STATES(:,5)./CONSTANTS(:,34)).*(1.00000+STATES(:,9)./CONSTANTS(:,32)+STATES(:,8)./CONSTANTS(:,35))));
ALGEBRAIC(:,18) = ( CONSTANTS(:,45).*CONSTANTS(:,43).*(( STATES(:,8).*ALGEBRAIC(:,13))./( CONSTANTS(:,39).*CONSTANTS(:,41)) - ( CONSTANTS(:,44).*STATES(:,9).*STATES(:,10))./( CONSTANTS(:,40).*CONSTANTS(:,42).*CONSTANTS(:,43))))./( (1.00000+STATES(:,9)./CONSTANTS(:,42)+STATES(:,8)./CONSTANTS(:,39)).*(1.00000+ALGEBRAIC(:,13)./CONSTANTS(:,41)+STATES(:,10)./CONSTANTS(:,40)));
ALGEBRAIC(:,9) = ( CONSTANTS(:,47).*STATES(:,10))./(STATES(:,10)+CONSTANTS(:,46));
RATES(:,4) = ( 2.00000.*ALGEBRAIC(:,15)+ALGEBRAIC(:,9)) - (ALGEBRAIC(:,17)+ALGEBRAIC(:,18));
RATES(:,8) = ALGEBRAIC(:,17) - ALGEBRAIC(:,18);
RATES(:,9) = ALGEBRAIC(:,18) - ALGEBRAIC(:,17);
RATES(:,10) = ALGEBRAIC(:,18) - (ALGEBRAIC(:,12)+ALGEBRAIC(:,9));
[CONSTANTS, STATES, ALGEBRAIC] = rootfind_1(VOI, CONSTANTS, STATES, ALGEBRAIC);
ALGEBRAIC(:,21) = ( CONSTANTS(:,56).*CONSTANTS(:,54).*(( - CONSTANTS(:,55).*ALGEBRAIC(:,19).*ALGEBRAIC(:,1))./( CONSTANTS(:,53).*CONSTANTS(:,52).*CONSTANTS(:,54))+( STATES(:,5).*ALGEBRAIC(:,2))./( CONSTANTS(:,51).*CONSTANTS(:,50))))./( (1.00000+STATES(:,5)./CONSTANTS(:,51)+ALGEBRAIC(:,19)./CONSTANTS(:,52)).*(1.00000+ALGEBRAIC(:,2)./CONSTANTS(:,50)+ALGEBRAIC(:,1)./CONSTANTS(:,53)));
RATES(:,5) = ALGEBRAIC(:,17) - ALGEBRAIC(:,21);
ALGEBRAIC(:,22) = (( CONSTANTS(:,59).*power(ALGEBRAIC(:,20)./( 0.340000.*(1.00000+ALGEBRAIC(:,1)./0.570000+ALGEBRAIC(:,2)./0.640000)), CONSTANTS(:,58)).*ALGEBRAIC(:,2))./CONSTANTS(:,57))./( (1.00000+power(ALGEBRAIC(:,20)./( 0.340000.*(1.00000+ALGEBRAIC(:,1)./0.570000+ALGEBRAIC(:,2)./0.640000)), CONSTANTS(:,58))).*(1.00000+ALGEBRAIC(:,2)./CONSTANTS(:,57)));
RATES(:,6) = ALGEBRAIC(:,21) - ALGEBRAIC(:,22);
ALGEBRAIC(:,10) = (( CONSTANTS(:,49).*STATES(:,7))./CONSTANTS(:,48))./(1.00000+STATES(:,7)./CONSTANTS(:,48));
RATES(:,7) = ALGEBRAIC(:,22) - ALGEBRAIC(:,10);
ALGEBRAIC(:,11) = ( CONSTANTS(:,60).*ALGEBRAIC(:,1))./ALGEBRAIC(:,2);
RATES(:,12) = (ALGEBRAIC(:,21)+ALGEBRAIC(:,12)+ALGEBRAIC(:,22)) - (ALGEBRAIC(:,6)+ALGEBRAIC(:,7)+ALGEBRAIC(:,11));
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(:,12).*(1.00000 - 4.00000.*CONSTANTS(:,2)) - CONSTANTS(:,1))+power(power(CONSTANTS(:,1) - (1.00000 - 4.00000.*CONSTANTS(:,2)).*STATES(:,12), 2.00000)+ 4.00000.*(1.00000 - 4.00000.*CONSTANTS(:,2)).*( - CONSTANTS(:,2).*power(STATES(:,12), 2.00000)), 0.500000))./( 2.00000.*(1.00000 - 4.00000.*CONSTANTS(:,2)));
ALGEBRAIC(:,2) = STATES(:,12) - 2.00000.*ALGEBRAIC(:,1);
ALGEBRAIC(:,6) = ( CONSTANTS(:,14).*STATES(:,1).*ALGEBRAIC(:,1))./( CONSTANTS(:,12).*CONSTANTS(:,10).*(1.00000+STATES(:,13)./CONSTANTS(:,11)+STATES(:,1)./CONSTANTS(:,10)).*(1.00000+ALGEBRAIC(:,1)./CONSTANTS(:,12)+ALGEBRAIC(:,2)./CONSTANTS(:,13)));
ALGEBRAIC(:,3) = piecewise({VOI>=60.0000&VOI<61.0000, 5.00000 }, 0.0500000);
ALGEBRAIC(:,5) = CONSTANTS(:,9).*((ALGEBRAIC(:,3) - STATES(:,1))./(CONSTANTS(:,7)+ALGEBRAIC(:,3)+STATES(:,1)+ CONSTANTS(:,8).*ALGEBRAIC(:,3).*(STATES(:,1)./CONSTANTS(:,7))));
ALGEBRAIC(:,4) = STATES(:,2) - STATES(:,13);
ALGEBRAIC(:,7) = ( CONSTANTS(:,18).*CONSTANTS(:,22).*ALGEBRAIC(:,4).*ALGEBRAIC(:,1))./( CONSTANTS(:,21).*CONSTANTS(:,20).*(STATES(:,3)+CONSTANTS(:,18)).*(1.00000+STATES(:,3)./CONSTANTS(:,19)+ALGEBRAIC(:,4)./CONSTANTS(:,20)).*(1.00000+ALGEBRAIC(:,1)./CONSTANTS(:,21)));
ALGEBRAIC(:,8) = ( CONSTANTS(:,17).*(STATES(:,13)./CONSTANTS(:,15) - ALGEBRAIC(:,4)./CONSTANTS(:,16)))./(1.00000+STATES(:,13)./CONSTANTS(:,15)+ALGEBRAIC(:,4)./CONSTANTS(:,16));
ALGEBRAIC(:,12) = ( CONSTANTS(:,67).*(( CONSTANTS(:,65).*ALGEBRAIC(:,2).*STATES(:,10))./( CONSTANTS(:,61).*CONSTANTS(:,62)) - ( CONSTANTS(:,66).*ALGEBRAIC(:,1).*STATES(:,11))./( CONSTANTS(:,64).*CONSTANTS(:,63))))./( (1.00000+STATES(:,10)./CONSTANTS(:,62)+STATES(:,11)./CONSTANTS(:,63)).*(1.00000+ALGEBRAIC(:,2)./CONSTANTS(:,61)+ALGEBRAIC(:,1)./CONSTANTS(:,64)));
ALGEBRAIC(:,15) = (( CONSTANTS(:,27).*STATES(:,3))./( 0.00900000.*(1.00000+ALGEBRAIC(:,1)./0.680000+ALGEBRAIC(:,2)./1.51000+(CONSTANTS(:,23) - (ALGEBRAIC(:,1)+ALGEBRAIC(:,2)))./3.65000)) - ( CONSTANTS(:,28).*ALGEBRAIC(:,14).*ALGEBRAIC(:,13))./( CONSTANTS(:,26).*CONSTANTS(:,24)))./(1.00000+ALGEBRAIC(:,14)./CONSTANTS(:,24)+ALGEBRAIC(:,13)./CONSTANTS(:,26)+( ALGEBRAIC(:,14).*ALGEBRAIC(:,13))./( CONSTANTS(:,26).*CONSTANTS(:,24))+STATES(:,3)./( 0.00900000.*(1.00000+ALGEBRAIC(:,1)./0.680000+ALGEBRAIC(:,2)./1.51000+(CONSTANTS(:,23) - (ALGEBRAIC(:,1)+ALGEBRAIC(:,2)))./3.65000))+( STATES(:,3).*ALGEBRAIC(:,14))./( CONSTANTS(:,25).*0.00900000.*(1.00000+ALGEBRAIC(:,1)./0.680000+ALGEBRAIC(:,2)./1.51000+(CONSTANTS(:,23) - (ALGEBRAIC(:,1)+ALGEBRAIC(:,2)))./3.65000)));
ALGEBRAIC(:,17) = CONSTANTS(:,38).*(( CONSTANTS(:,36).*( ALGEBRAIC(:,14).*((STATES(:,9)./CONSTANTS(:,33))./CONSTANTS(:,32)) - (CONSTANTS(:,37)./CONSTANTS(:,36)).*((( STATES(:,5).*STATES(:,8))./CONSTANTS(:,34))./CONSTANTS(:,35))))./( (1.00000+ALGEBRAIC(:,14)./CONSTANTS(:,33)+STATES(:,5)./CONSTANTS(:,34)).*(1.00000+STATES(:,9)./CONSTANTS(:,32)+STATES(:,8)./CONSTANTS(:,35))));
ALGEBRAIC(:,18) = ( CONSTANTS(:,45).*CONSTANTS(:,43).*(( STATES(:,8).*ALGEBRAIC(:,13))./( CONSTANTS(:,39).*CONSTANTS(:,41)) - ( CONSTANTS(:,44).*STATES(:,9).*STATES(:,10))./( CONSTANTS(:,40).*CONSTANTS(:,42).*CONSTANTS(:,43))))./( (1.00000+STATES(:,9)./CONSTANTS(:,42)+STATES(:,8)./CONSTANTS(:,39)).*(1.00000+ALGEBRAIC(:,13)./CONSTANTS(:,41)+STATES(:,10)./CONSTANTS(:,40)));
ALGEBRAIC(:,9) = ( CONSTANTS(:,47).*STATES(:,10))./(STATES(:,10)+CONSTANTS(:,46));
ALGEBRAIC(:,21) = ( CONSTANTS(:,56).*CONSTANTS(:,54).*(( - CONSTANTS(:,55).*ALGEBRAIC(:,19).*ALGEBRAIC(:,1))./( CONSTANTS(:,53).*CONSTANTS(:,52).*CONSTANTS(:,54))+( STATES(:,5).*ALGEBRAIC(:,2))./( CONSTANTS(:,51).*CONSTANTS(:,50))))./( (1.00000+STATES(:,5)./CONSTANTS(:,51)+ALGEBRAIC(:,19)./CONSTANTS(:,52)).*(1.00000+ALGEBRAIC(:,2)./CONSTANTS(:,50)+ALGEBRAIC(:,1)./CONSTANTS(:,53)));
ALGEBRAIC(:,22) = (( CONSTANTS(:,59).*power(ALGEBRAIC(:,20)./( 0.340000.*(1.00000+ALGEBRAIC(:,1)./0.570000+ALGEBRAIC(:,2)./0.640000)), CONSTANTS(:,58)).*ALGEBRAIC(:,2))./CONSTANTS(:,57))./( (1.00000+power(ALGEBRAIC(:,20)./( 0.340000.*(1.00000+ALGEBRAIC(:,1)./0.570000+ALGEBRAIC(:,2)./0.640000)), CONSTANTS(:,58))).*(1.00000+ALGEBRAIC(:,2)./CONSTANTS(:,57)));
ALGEBRAIC(:,10) = (( CONSTANTS(:,49).*STATES(:,7))./CONSTANTS(:,48))./(1.00000+STATES(:,7)./CONSTANTS(:,48));
ALGEBRAIC(:,11) = ( CONSTANTS(:,60).*ALGEBRAIC(:,1))./ALGEBRAIC(:,2);
ALGEBRAIC(:,16) = ( CONSTANTS(:,31).*(ALGEBRAIC(:,13)./CONSTANTS(:,29) - ( 5.70000.*ALGEBRAIC(:,14))./CONSTANTS(:,30)))./(1.00000+ALGEBRAIC(:,14)./CONSTANTS(:,30)+ALGEBRAIC(:,13)./CONSTANTS(:,29));
end
% Functions required for solving differential algebraic equation
function [CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS_IN, STATES_IN, ALGEBRAIC_IN)
ALGEBRAIC = ALGEBRAIC_IN;
CONSTANTS = CONSTANTS_IN;
STATES = STATES_IN;
global initialGuess_0;
if (length(initialGuess_0) ~= 2), initialGuess_0 = [0.1,0.1];, end
options = optimset('Display', 'off', 'TolX', 1E-6);
if length(VOI) == 1
residualfn = @(algebraicCandidate)residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES);
soln = fsolve(residualfn, initialGuess_0, options);
initialGuess_0 = soln;
ALGEBRAIC(:,13) = soln(1);
ALGEBRAIC(:,14) = soln(2);
else
SET_ALGEBRAIC(:,13) = logical(1);
SET_ALGEBRAIC(:,14) = logical(1);
for i=1:length(VOI)
residualfn = @(algebraicCandidate)residualSN_0(algebraicCandidate, ALGEBRAIC(i,:), VOI(i), CONSTANTS, STATES(i,:));
soln = fsolve(residualfn, initialGuess_0, options);
initialGuess_0 = soln;
TEMP_ALGEBRAIC(:,13) = soln(1);
TEMP_ALGEBRAIC(:,14) = soln(2);
ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
end
end
end
function resid = residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
ALGEBRAIC(:,13) = algebraicCandidate(1);
ALGEBRAIC(:,14) = algebraicCandidate(2);
resid(1) = ALGEBRAIC(:,13) - ( CONSTANTS(:,4).*ALGEBRAIC(:,13))./((CONSTANTS(:,3)+CONSTANTS(:,4)) - (STATES(:,5)+ 2.00000.*STATES(:,3)+ALGEBRAIC(:,4)+ALGEBRAIC(:,14)+STATES(:,13)+STATES(:,12)));
resid(2) = ALGEBRAIC(:,14) - (STATES(:,4) - ALGEBRAIC(:,13));
end
% Functions required for solving differential algebraic equation
function [CONSTANTS, STATES, ALGEBRAIC] = rootfind_1(VOI, CONSTANTS_IN, STATES_IN, ALGEBRAIC_IN)
ALGEBRAIC = ALGEBRAIC_IN;
CONSTANTS = CONSTANTS_IN;
STATES = STATES_IN;
global initialGuess_1;
if (length(initialGuess_1) ~= 2), initialGuess_1 = [0.1,0.1];, end
options = optimset('Display', 'off', 'TolX', 1E-6);
if length(VOI) == 1
residualfn = @(algebraicCandidate)residualSN_1(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES);
soln = fsolve(residualfn, initialGuess_1, options);
initialGuess_1 = soln;
ALGEBRAIC(:,19) = soln(1);
ALGEBRAIC(:,20) = soln(2);
else
SET_ALGEBRAIC(:,19) = logical(1);
SET_ALGEBRAIC(:,20) = logical(1);
for i=1:length(VOI)
residualfn = @(algebraicCandidate)residualSN_1(algebraicCandidate, ALGEBRAIC(i,:), VOI(i), CONSTANTS, STATES(i,:));
soln = fsolve(residualfn, initialGuess_1, options);
initialGuess_1 = soln;
TEMP_ALGEBRAIC(:,19) = soln(1);
TEMP_ALGEBRAIC(:,20) = soln(2);
ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
end
end
end
function resid = residualSN_1(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
ALGEBRAIC(:,19) = algebraicCandidate(1);
ALGEBRAIC(:,20) = algebraicCandidate(2);
resid(1) = ALGEBRAIC(:,19) - (STATES(:,6) - ALGEBRAIC(:,20));
resid(2) = ALGEBRAIC(:,20) - CONSTANTS(:,5).*CONSTANTS(:,6).*ALGEBRAIC(:,19);
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