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 =42;
end
% There are a total of 10 entries in each of the rate and state variable arrays.
% There are a total of 47 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 (millisecond)');
LEGEND_STATES(:,1) = strpad('Gi in component Gi (millimolar)');
LEGEND_ALGEBRAIC(:,5) = strpad('Jglut in component Jglut (millimolar_per_millisecond)');
LEGEND_ALGEBRAIC(:,7) = strpad('Jgk in component Jgk (millimolar_per_millisecond)');
LEGEND_STATES(:,2) = strpad('Ge in component Ge (millimolar)');
LEGEND_ALGEBRAIC(:,2) = strpad('G_infinity in component Ge (millimolar)');
LEGEND_CONSTANTS(:,1) = strpad('tau_G in component Ge (millisecond)');
LEGEND_CONSTANTS(:,2) = strpad('Gmax in component Ge (millimolar)');
LEGEND_CONSTANTS(:,3) = strpad('Gmin in component Ge (millimolar)');
LEGEND_CONSTANTS(:,4) = strpad('SG in component Ge (dimensionless)');
LEGEND_CONSTANTS(:,5) = strpad('I_ in component Ge (dimensionless)');
LEGEND_STATES(:,3) = strpad('I in component I (dimensionless)');
LEGEND_STATES(:,4) = strpad('G6P in component G6P (millimolar)');
LEGEND_CONSTANTS(:,6) = strpad('kappa in component model_parameters (dimensionless)');
LEGEND_ALGEBRAIC(:,42) = strpad('JPFK in component JPFK (micromolar_per_millisecond)');
LEGEND_STATES(:,5) = strpad('FBP in component FBP (micromolar)');
LEGEND_ALGEBRAIC(:,8) = strpad('JGPDH in component JGPDH (micromolar_per_millisecond)');
LEGEND_ALGEBRAIC(:,1) = strpad('F6P in component F6P (millimolar)');
LEGEND_CONSTANTS(:,7) = strpad('Kglut in component Jglut (millimolar)');
LEGEND_CONSTANTS(:,8) = strpad('Vglut in component Jglut (millimolar_per_millisecond)');
LEGEND_CONSTANTS(:,9) = strpad('Kgk in component Jgk (millimolar)');
LEGEND_CONSTANTS(:,10) = strpad('Vgk in component Jgk (millimolar_per_millisecond)');
LEGEND_CONSTANTS(:,11) = strpad('ngk in component Jgk (dimensionless)');
LEGEND_CONSTANTS(:,12) = strpad('lambda in component JPFK (dimensionless)');
LEGEND_CONSTANTS(:,13) = strpad('Vmax in component JPFK (micromolar_per_millisecond)');
LEGEND_CONSTANTS(:,47) = strpad('w0000 in component w (dimensionless)');
LEGEND_ALGEBRAIC(:,26) = strpad('w1000 in component w (dimensionless)');
LEGEND_ALGEBRAIC(:,9) = strpad('w0100 in component w (dimensionless)');
LEGEND_ALGEBRAIC(:,10) = strpad('w0010 in component w (dimensionless)');
LEGEND_ALGEBRAIC(:,28) = strpad('w0001 in component w (dimensionless)');
LEGEND_ALGEBRAIC(:,30) = strpad('w1100 in component w (dimensionless)');
LEGEND_ALGEBRAIC(:,32) = strpad('w1010 in component w (dimensionless)');
LEGEND_ALGEBRAIC(:,34) = strpad('w1001 in component w (dimensionless)');
LEGEND_ALGEBRAIC(:,35) = strpad('w0101 in component w (dimensionless)');
LEGEND_ALGEBRAIC(:,36) = strpad('w0011 in component w (dimensionless)');
LEGEND_ALGEBRAIC(:,11) = strpad('w0110 in component w (dimensionless)');
LEGEND_ALGEBRAIC(:,37) = strpad('w1110 in component w (dimensionless)');
LEGEND_ALGEBRAIC(:,38) = strpad('w0111 in component w (dimensionless)');
LEGEND_ALGEBRAIC(:,39) = strpad('w1011 in component w (dimensionless)');
LEGEND_ALGEBRAIC(:,40) = strpad('w1101 in component w (dimensionless)');
LEGEND_ALGEBRAIC(:,41) = strpad('w1111 in component w (dimensionless)');
LEGEND_CONSTANTS(:,14) = strpad('f13 in component w (dimensionless)');
LEGEND_CONSTANTS(:,15) = strpad('f23 in component w (dimensionless)');
LEGEND_CONSTANTS(:,16) = strpad('f41 in component w (dimensionless)');
LEGEND_CONSTANTS(:,17) = strpad('f42 in component w (dimensionless)');
LEGEND_CONSTANTS(:,18) = strpad('f43 in component w (dimensionless)');
LEGEND_CONSTANTS(:,19) = strpad('K1 in component w (micromolar)');
LEGEND_CONSTANTS(:,20) = strpad('K2 in component w (micromolar)');
LEGEND_CONSTANTS(:,21) = strpad('K3 in component w (micromolar)');
LEGEND_CONSTANTS(:,22) = strpad('K4 in component w (micromolar)');
LEGEND_ALGEBRAIC(:,24) = strpad('AMP in component AMP (micromolar)');
LEGEND_ALGEBRAIC(:,25) = strpad('ATP in component ATP (micromolar)');
LEGEND_CONSTANTS(:,23) = strpad('Atot in component ATP (micromolar)');
LEGEND_STATES(:,6) = strpad('ADP in component ADP (micromolar)');
LEGEND_CONSTANTS(:,24) = strpad('tau_a in component ADP (millisecond)');
LEGEND_CONSTANTS(:,25) = strpad('r in component ADP (dimensionless)');
LEGEND_CONSTANTS(:,26) = strpad('r1 in component ADP (micromolar)');
LEGEND_ALGEBRAIC(:,12) = strpad('gamma in component gamma (dimensionless)');
LEGEND_STATES(:,7) = strpad('Ca in component Ca (micromolar)');
LEGEND_CONSTANTS(:,27) = strpad('v_gamma in component gamma (dimensionless)');
LEGEND_CONSTANTS(:,28) = strpad('k_gamma in component gamma (micromolar_per_millisecond)');
LEGEND_STATES(:,8) = strpad('v in component membrane (millivolt)');
LEGEND_CONSTANTS(:,29) = strpad('cm in component membrane (femtofarad)');
LEGEND_ALGEBRAIC(:,15) = strpad('I_Ca in component I_Ca (picoampere)');
LEGEND_ALGEBRAIC(:,13) = strpad('I_K in component I_K (picoampere)');
LEGEND_ALGEBRAIC(:,18) = strpad('I_K_Ca in component I_K_Ca (picoampere)');
LEGEND_ALGEBRAIC(:,33) = strpad('I_K_ATP in component I_K_ATP (picoampere)');
LEGEND_CONSTANTS(:,30) = strpad('gK_ in component I_K (picosiemens)');
LEGEND_CONSTANTS(:,31) = strpad('vK in component model_parameters (millivolt)');
LEGEND_STATES(:,9) = strpad('n in component n (dimensionless)');
LEGEND_ALGEBRAIC(:,6) = strpad('n_infinity in component n (dimensionless)');
LEGEND_ALGEBRAIC(:,3) = strpad('tau_n in component n (millisecond)');
LEGEND_CONSTANTS(:,32) = strpad('gCa_ in component I_Ca (picosiemens)');
LEGEND_CONSTANTS(:,33) = strpad('vCa in component model_parameters (millivolt)');
LEGEND_ALGEBRAIC(:,14) = strpad('m_infinity in component m (dimensionless)');
LEGEND_CONSTANTS(:,34) = strpad('gkCa_ in component I_K_Ca (picosiemens)');
LEGEND_ALGEBRAIC(:,16) = strpad('gkCa in component I_K_Ca (picosiemens)');
LEGEND_CONSTANTS(:,35) = strpad('KD in component I_K_Ca (micromolar)');
LEGEND_CONSTANTS(:,36) = strpad('gkATP_ in component I_K_ATP (picosiemens)');
LEGEND_ALGEBRAIC(:,31) = strpad('gkATP in component I_K_ATP (picosiemens)');
LEGEND_ALGEBRAIC(:,29) = strpad('o_infinity in component I_K_ATP (dimensionless)');
LEGEND_ALGEBRAIC(:,20) = strpad('MgADP in component I_K_ATP (micromolar)');
LEGEND_ALGEBRAIC(:,22) = strpad('ADP3_ in component I_K_ATP (micromolar)');
LEGEND_ALGEBRAIC(:,27) = strpad('ATP4_ in component I_K_ATP (micromolar)');
LEGEND_CONSTANTS(:,37) = strpad('fcyt in component Ca (dimensionless)');
LEGEND_ALGEBRAIC(:,17) = strpad('Jmem in component Jmem (micromolar_per_millisecond)');
LEGEND_ALGEBRAIC(:,23) = strpad('Jer in component Jer (micromolar_per_millisecond)');
LEGEND_STATES(:,10) = strpad('Caer in component Caer (micromolar)');
LEGEND_CONSTANTS(:,38) = strpad('fer in component Caer (dimensionless)');
LEGEND_CONSTANTS(:,39) = strpad('Vcyt_Ver in component Caer (dimensionless)');
LEGEND_CONSTANTS(:,40) = strpad('kPMCA in component Jmem (first_order_rate_constant)');
LEGEND_CONSTANTS(:,41) = strpad('alpha in component Jmem (micromolar_per_millisecond)');
LEGEND_ALGEBRAIC(:,21) = strpad('Jleak in component Jleak (micromolar_per_millisecond)');
LEGEND_ALGEBRAIC(:,19) = strpad('JSERCA in component JSERCA (micromolar_per_millisecond)');
LEGEND_CONSTANTS(:,42) = strpad('kSERCA in component JSERCA (first_order_rate_constant)');
LEGEND_CONSTANTS(:,43) = strpad('pleak in component Jleak (first_order_rate_constant)');
LEGEND_ALGEBRAIC(:,4) = strpad('I_infinity in component I (dimensionless)');
LEGEND_CONSTANTS(:,44) = strpad('tau_I in component I (millisecond)');
LEGEND_CONSTANTS(:,45) = strpad('I_slope in component I (per_micromolar)');
LEGEND_CONSTANTS(:,46) = strpad('Canull in component I (micromolar)');
LEGEND_RATES(:,1) = strpad('d/dt Gi in component Gi (millimolar)');
LEGEND_RATES(:,2) = strpad('d/dt Ge in component Ge (millimolar)');
LEGEND_RATES(:,4) = strpad('d/dt G6P in component G6P (millimolar)');
LEGEND_RATES(:,5) = strpad('d/dt FBP in component FBP (micromolar)');
LEGEND_RATES(:,6) = strpad('d/dt ADP in component ADP (micromolar)');
LEGEND_RATES(:,8) = strpad('d/dt v in component membrane (millivolt)');
LEGEND_RATES(:,9) = strpad('d/dt n in component n (dimensionless)');
LEGEND_RATES(:,7) = strpad('d/dt Ca in component Ca (micromolar)');
LEGEND_RATES(:,10) = strpad('d/dt Caer in component Caer (micromolar)');
LEGEND_RATES(:,3) = strpad('d/dt I in component I (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;
STATES(:,2) = 7;
CONSTANTS(:,1) = 450000;
CONSTANTS(:,2) = 15;
CONSTANTS(:,3) = 1;
CONSTANTS(:,4) = 1;
CONSTANTS(:,5) = 5;
STATES(:,3) = 0;
STATES(:,4) = 200;
CONSTANTS(:,6) = 0.005;
STATES(:,5) = 40;
CONSTANTS(:,7) = 7;
CONSTANTS(:,8) = 8;
CONSTANTS(:,9) = 7;
CONSTANTS(:,10) = 0.8;
CONSTANTS(:,11) = 4;
CONSTANTS(:,12) = 0.06;
CONSTANTS(:,13) = 2;
CONSTANTS(:,14) = 0.02;
CONSTANTS(:,15) = 0.2;
CONSTANTS(:,16) = 20;
CONSTANTS(:,17) = 20;
CONSTANTS(:,18) = 20;
CONSTANTS(:,19) = 30;
CONSTANTS(:,20) = 1;
CONSTANTS(:,21) = 50000;
CONSTANTS(:,22) = 1000;
CONSTANTS(:,23) = 3000;
STATES(:,6) = 780;
CONSTANTS(:,24) = 300000;
CONSTANTS(:,25) = 0.5;
CONSTANTS(:,26) = 0.35;
STATES(:,7) = 0.1;
CONSTANTS(:,27) = 2.2;
CONSTANTS(:,28) = 0.1;
STATES(:,8) = -60;
CONSTANTS(:,29) = 5300;
CONSTANTS(:,30) = 2700;
CONSTANTS(:,31) = -75;
STATES(:,9) = 0;
CONSTANTS(:,32) = 1000;
CONSTANTS(:,33) = 25;
CONSTANTS(:,34) = 400;
CONSTANTS(:,35) = 0.5;
CONSTANTS(:,36) = 40000;
CONSTANTS(:,37) = 0.01;
STATES(:,10) = 185;
CONSTANTS(:,38) = 0.01;
CONSTANTS(:,39) = 31;
CONSTANTS(:,40) = 0.18;
CONSTANTS(:,41) = 4.5e-6;
CONSTANTS(:,42) = 0.4;
CONSTANTS(:,43) = 0.0002;
CONSTANTS(:,44) = 10000;
CONSTANTS(:,45) = 210;
CONSTANTS(:,46) = 0.055;
CONSTANTS(:,47) = 1.00000;
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(:,2) = CONSTANTS(:,3)+(CONSTANTS(:,2) - CONSTANTS(:,3))./(1.00000+exp((STATES(:,3) - CONSTANTS(:,5))./CONSTANTS(:,4)));
RATES(:,2) = (ALGEBRAIC(:,2) - STATES(:,2))./CONSTANTS(:,1);
ALGEBRAIC(:,4) = piecewise({STATES(:,7)>=CONSTANTS(:,46), CONSTANTS(:,45).*(STATES(:,7) - CONSTANTS(:,46)) , STATES(:,7)<CONSTANTS(:,46), 0.00000 }, NaN);
RATES(:,3) = (ALGEBRAIC(:,4) - STATES(:,3))./CONSTANTS(:,44);
ALGEBRAIC(:,6) = 1.00000./(1.00000+exp( - (STATES(:,8)+16.0000)./5.60000));
ALGEBRAIC(:,3) = 1.00000./( 0.0350000.*cosh((STATES(:,8)+16.0000)./22.4000));
RATES(:,9) = (ALGEBRAIC(:,6) - STATES(:,9))./ALGEBRAIC(:,3);
ALGEBRAIC(:,5) = ( CONSTANTS(:,8).*(STATES(:,2) - STATES(:,1)).*CONSTANTS(:,7))./( (CONSTANTS(:,7)+STATES(:,2)).*(CONSTANTS(:,7)+STATES(:,1)));
ALGEBRAIC(:,7) = ( CONSTANTS(:,10).*power(STATES(:,1), CONSTANTS(:,11)))./(power(CONSTANTS(:,9), CONSTANTS(:,11))+power(STATES(:,1), CONSTANTS(:,11)));
RATES(:,1) = ALGEBRAIC(:,5) - ALGEBRAIC(:,7);
ALGEBRAIC(:,14) = 1.00000./(1.00000+exp( - (STATES(:,8)+20.0000)./12.0000));
ALGEBRAIC(:,15) = CONSTANTS(:,32).*ALGEBRAIC(:,14).*(STATES(:,8) - CONSTANTS(:,33));
ALGEBRAIC(:,17) = - ( CONSTANTS(:,41).*ALGEBRAIC(:,15)+ CONSTANTS(:,40).*STATES(:,7));
ALGEBRAIC(:,21) = CONSTANTS(:,43).*(STATES(:,10) - STATES(:,7));
ALGEBRAIC(:,19) = CONSTANTS(:,42).*STATES(:,7);
ALGEBRAIC(:,23) = ALGEBRAIC(:,21) - ALGEBRAIC(:,19);
RATES(:,7) = CONSTANTS(:,37).*(ALGEBRAIC(:,17)+ALGEBRAIC(:,23));
RATES(:,10) = - CONSTANTS(:,38).*CONSTANTS(:,39).*ALGEBRAIC(:,23);
[CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS, STATES, ALGEBRAIC);
ALGEBRAIC(:,8) = 0.200000.*power((STATES(:,5)./1.00000), 1.0 ./ 2);
ALGEBRAIC(:,12) = ( CONSTANTS(:,27).*ALGEBRAIC(:,8))./(CONSTANTS(:,28)+ALGEBRAIC(:,8));
RATES(:,6) = (1.00000./CONSTANTS(:,24)).*(ALGEBRAIC(:,25) - STATES(:,6).*exp( (CONSTANTS(:,25)+ALGEBRAIC(:,12)).*(1.00000 - STATES(:,7)./CONSTANTS(:,26))));
ALGEBRAIC(:,13) = CONSTANTS(:,30).*STATES(:,9).*(STATES(:,8) - CONSTANTS(:,31));
ALGEBRAIC(:,16) = ( CONSTANTS(:,34).*power(STATES(:,7), 2.00000))./(power(CONSTANTS(:,35), 2.00000)+power(STATES(:,7), 2.00000));
ALGEBRAIC(:,18) = ALGEBRAIC(:,16).*(STATES(:,8) - CONSTANTS(:,31));
ALGEBRAIC(:,20) = 0.165000.*STATES(:,6);
ALGEBRAIC(:,22) = 0.135000.*STATES(:,6);
ALGEBRAIC(:,27) = 0.00500000.*ALGEBRAIC(:,25);
ALGEBRAIC(:,29) = ( 0.0800000.*(1.00000+( 2.00000.*ALGEBRAIC(:,20))./17.0000)+ 0.890000.*power(ALGEBRAIC(:,20)./17.0000, 2.00000))./( power(1.00000+ALGEBRAIC(:,20)./17.0000, 2.00000).*(1.00000+ALGEBRAIC(:,22)./26.0000+ALGEBRAIC(:,27)./1.00000));
ALGEBRAIC(:,31) = CONSTANTS(:,36).*ALGEBRAIC(:,29);
ALGEBRAIC(:,33) = ALGEBRAIC(:,31).*(STATES(:,8) - CONSTANTS(:,31));
RATES(:,8) = - (ALGEBRAIC(:,13)+ALGEBRAIC(:,15)+ALGEBRAIC(:,18)+ALGEBRAIC(:,33))./CONSTANTS(:,29);
ALGEBRAIC(:,26) = power(ALGEBRAIC(:,24)./CONSTANTS(:,19), 1.00000);
ALGEBRAIC(:,9) = power(STATES(:,5)./CONSTANTS(:,20), 1.00000);
ALGEBRAIC(:,1) = 0.300000.*STATES(:,4);
ALGEBRAIC(:,10) = power(power(ALGEBRAIC(:,1), 2.00000)./CONSTANTS(:,21), 1.00000);
ALGEBRAIC(:,28) = power(power(ALGEBRAIC(:,25), 2.00000)./CONSTANTS(:,22), 1.00000);
ALGEBRAIC(:,30) = power(ALGEBRAIC(:,24)./CONSTANTS(:,19), 1.00000).*power(STATES(:,5)./CONSTANTS(:,20), 1.00000);
ALGEBRAIC(:,32) = (1.00000./power(CONSTANTS(:,14), 1.00000.*1.00000)).*power(ALGEBRAIC(:,24)./CONSTANTS(:,19), 1.00000).*power(power(ALGEBRAIC(:,1), 2.00000)./CONSTANTS(:,21), 1.00000);
ALGEBRAIC(:,34) = (1.00000./power(CONSTANTS(:,16), 1.00000.*1.00000)).*power(ALGEBRAIC(:,24)./CONSTANTS(:,19), 1.00000).*power(power(ALGEBRAIC(:,25), 2.00000)./CONSTANTS(:,22), 1.00000);
ALGEBRAIC(:,35) = (1.00000./power(CONSTANTS(:,17), 1.00000.*1.00000)).*power(STATES(:,5)./CONSTANTS(:,20), 1.00000).*power(power(ALGEBRAIC(:,25), 2.00000)./CONSTANTS(:,22), 1.00000);
ALGEBRAIC(:,36) = (1.00000./power(CONSTANTS(:,18), 1.00000.*1.00000)).*power(power(ALGEBRAIC(:,1), 2.00000)./CONSTANTS(:,21), 1.00000).*power(power(ALGEBRAIC(:,25), 2.00000)./CONSTANTS(:,22), 1.00000);
ALGEBRAIC(:,11) = (1.00000./power(CONSTANTS(:,15), 1.00000.*1.00000)).*power(STATES(:,5)./CONSTANTS(:,20), 1.00000).*power(power(ALGEBRAIC(:,1), 2.00000)./CONSTANTS(:,21), 1.00000);
ALGEBRAIC(:,37) = (1.00000./( power(CONSTANTS(:,14), 1.00000.*1.00000).*power(CONSTANTS(:,15), 1.00000.*1.00000))).*power(ALGEBRAIC(:,24)./CONSTANTS(:,19), 1.00000).*power(STATES(:,5)./CONSTANTS(:,20), 1.00000).*power(power(ALGEBRAIC(:,1), 2.00000)./CONSTANTS(:,21), 1.00000);
ALGEBRAIC(:,38) = (1.00000./( power(CONSTANTS(:,15), 1.00000.*1.00000).*power(CONSTANTS(:,17), 1.00000.*1.00000).*power(CONSTANTS(:,18), 1.00000.*1.00000))).*power(STATES(:,5)./CONSTANTS(:,20), 1.00000).*power(power(ALGEBRAIC(:,1), 2.00000)./CONSTANTS(:,21), 1.00000).*power(power(ALGEBRAIC(:,25), 2.00000)./CONSTANTS(:,22), 1.00000);
ALGEBRAIC(:,39) = (1.00000./( power(CONSTANTS(:,14), 1.00000.*1.00000).*power(CONSTANTS(:,16), 1.00000.*1.00000).*power(CONSTANTS(:,18), 1.00000.*1.00000))).*power(ALGEBRAIC(:,24)./CONSTANTS(:,19), 1.00000).*power(power(ALGEBRAIC(:,1), 2.00000)./CONSTANTS(:,21), 1.00000).*power(power(ALGEBRAIC(:,25), 2.00000)./CONSTANTS(:,22), 1.00000);
ALGEBRAIC(:,40) = (1.00000./( power(CONSTANTS(:,16), 1.00000.*1.00000).*power(CONSTANTS(:,17), 1.00000.*1.00000))).*power(ALGEBRAIC(:,24)./CONSTANTS(:,19), 1.00000).*power(STATES(:,5)./CONSTANTS(:,20), 1.00000).*power(power(ALGEBRAIC(:,25), 2.00000)./CONSTANTS(:,22), 1.00000);
ALGEBRAIC(:,41) = (1.00000./( power(CONSTANTS(:,14), 1.00000.*1.00000).*power(CONSTANTS(:,15), 1.00000.*1.00000).*power(CONSTANTS(:,16), 1.00000.*1.00000).*power(CONSTANTS(:,17), 1.00000.*1.00000).*power(CONSTANTS(:,18), 1.00000.*1.00000))).*power(ALGEBRAIC(:,24)./CONSTANTS(:,19), 1.00000).*power(STATES(:,5)./CONSTANTS(:,20), 1.00000).*power(power(ALGEBRAIC(:,1), 2.00000)./CONSTANTS(:,21), 1.00000).*power(power(ALGEBRAIC(:,25), 2.00000)./CONSTANTS(:,22), 1.00000);
ALGEBRAIC(:,42) = ( CONSTANTS(:,13).*( (1.00000 - CONSTANTS(:,12)).*ALGEBRAIC(:,37)+ CONSTANTS(:,12).*(ALGEBRAIC(:,10)+ALGEBRAIC(:,32)+ALGEBRAIC(:,36)+ALGEBRAIC(:,37)+ALGEBRAIC(:,38)+ALGEBRAIC(:,39)+ALGEBRAIC(:,11)+ALGEBRAIC(:,41))))./(CONSTANTS(:,47)+ALGEBRAIC(:,26)+ALGEBRAIC(:,9)+ALGEBRAIC(:,10)+ALGEBRAIC(:,28)+ALGEBRAIC(:,30)+ALGEBRAIC(:,32)+ALGEBRAIC(:,34)+ALGEBRAIC(:,35)+ALGEBRAIC(:,36)+ALGEBRAIC(:,11)+ALGEBRAIC(:,37)+ALGEBRAIC(:,38)+ALGEBRAIC(:,39)+ALGEBRAIC(:,40)+ALGEBRAIC(:,41));
RATES(:,4) = CONSTANTS(:,6).*(ALGEBRAIC(:,7) - ALGEBRAIC(:,42));
RATES(:,5) = CONSTANTS(:,6).*(ALGEBRAIC(:,42) - 0.500000.*ALGEBRAIC(:,8));
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(:,2) = CONSTANTS(:,3)+(CONSTANTS(:,2) - CONSTANTS(:,3))./(1.00000+exp((STATES(:,3) - CONSTANTS(:,5))./CONSTANTS(:,4)));
ALGEBRAIC(:,4) = piecewise({STATES(:,7)>=CONSTANTS(:,46), CONSTANTS(:,45).*(STATES(:,7) - CONSTANTS(:,46)) , STATES(:,7)<CONSTANTS(:,46), 0.00000 }, NaN);
ALGEBRAIC(:,6) = 1.00000./(1.00000+exp( - (STATES(:,8)+16.0000)./5.60000));
ALGEBRAIC(:,3) = 1.00000./( 0.0350000.*cosh((STATES(:,8)+16.0000)./22.4000));
ALGEBRAIC(:,5) = ( CONSTANTS(:,8).*(STATES(:,2) - STATES(:,1)).*CONSTANTS(:,7))./( (CONSTANTS(:,7)+STATES(:,2)).*(CONSTANTS(:,7)+STATES(:,1)));
ALGEBRAIC(:,7) = ( CONSTANTS(:,10).*power(STATES(:,1), CONSTANTS(:,11)))./(power(CONSTANTS(:,9), CONSTANTS(:,11))+power(STATES(:,1), CONSTANTS(:,11)));
ALGEBRAIC(:,14) = 1.00000./(1.00000+exp( - (STATES(:,8)+20.0000)./12.0000));
ALGEBRAIC(:,15) = CONSTANTS(:,32).*ALGEBRAIC(:,14).*(STATES(:,8) - CONSTANTS(:,33));
ALGEBRAIC(:,17) = - ( CONSTANTS(:,41).*ALGEBRAIC(:,15)+ CONSTANTS(:,40).*STATES(:,7));
ALGEBRAIC(:,21) = CONSTANTS(:,43).*(STATES(:,10) - STATES(:,7));
ALGEBRAIC(:,19) = CONSTANTS(:,42).*STATES(:,7);
ALGEBRAIC(:,23) = ALGEBRAIC(:,21) - ALGEBRAIC(:,19);
ALGEBRAIC(:,8) = 0.200000.*power((STATES(:,5)./1.00000), 1.0 ./ 2);
ALGEBRAIC(:,12) = ( CONSTANTS(:,27).*ALGEBRAIC(:,8))./(CONSTANTS(:,28)+ALGEBRAIC(:,8));
ALGEBRAIC(:,13) = CONSTANTS(:,30).*STATES(:,9).*(STATES(:,8) - CONSTANTS(:,31));
ALGEBRAIC(:,16) = ( CONSTANTS(:,34).*power(STATES(:,7), 2.00000))./(power(CONSTANTS(:,35), 2.00000)+power(STATES(:,7), 2.00000));
ALGEBRAIC(:,18) = ALGEBRAIC(:,16).*(STATES(:,8) - CONSTANTS(:,31));
ALGEBRAIC(:,20) = 0.165000.*STATES(:,6);
ALGEBRAIC(:,22) = 0.135000.*STATES(:,6);
ALGEBRAIC(:,27) = 0.00500000.*ALGEBRAIC(:,25);
ALGEBRAIC(:,29) = ( 0.0800000.*(1.00000+( 2.00000.*ALGEBRAIC(:,20))./17.0000)+ 0.890000.*power(ALGEBRAIC(:,20)./17.0000, 2.00000))./( power(1.00000+ALGEBRAIC(:,20)./17.0000, 2.00000).*(1.00000+ALGEBRAIC(:,22)./26.0000+ALGEBRAIC(:,27)./1.00000));
ALGEBRAIC(:,31) = CONSTANTS(:,36).*ALGEBRAIC(:,29);
ALGEBRAIC(:,33) = ALGEBRAIC(:,31).*(STATES(:,8) - CONSTANTS(:,31));
ALGEBRAIC(:,26) = power(ALGEBRAIC(:,24)./CONSTANTS(:,19), 1.00000);
ALGEBRAIC(:,9) = power(STATES(:,5)./CONSTANTS(:,20), 1.00000);
ALGEBRAIC(:,1) = 0.300000.*STATES(:,4);
ALGEBRAIC(:,10) = power(power(ALGEBRAIC(:,1), 2.00000)./CONSTANTS(:,21), 1.00000);
ALGEBRAIC(:,28) = power(power(ALGEBRAIC(:,25), 2.00000)./CONSTANTS(:,22), 1.00000);
ALGEBRAIC(:,30) = power(ALGEBRAIC(:,24)./CONSTANTS(:,19), 1.00000).*power(STATES(:,5)./CONSTANTS(:,20), 1.00000);
ALGEBRAIC(:,32) = (1.00000./power(CONSTANTS(:,14), 1.00000.*1.00000)).*power(ALGEBRAIC(:,24)./CONSTANTS(:,19), 1.00000).*power(power(ALGEBRAIC(:,1), 2.00000)./CONSTANTS(:,21), 1.00000);
ALGEBRAIC(:,34) = (1.00000./power(CONSTANTS(:,16), 1.00000.*1.00000)).*power(ALGEBRAIC(:,24)./CONSTANTS(:,19), 1.00000).*power(power(ALGEBRAIC(:,25), 2.00000)./CONSTANTS(:,22), 1.00000);
ALGEBRAIC(:,35) = (1.00000./power(CONSTANTS(:,17), 1.00000.*1.00000)).*power(STATES(:,5)./CONSTANTS(:,20), 1.00000).*power(power(ALGEBRAIC(:,25), 2.00000)./CONSTANTS(:,22), 1.00000);
ALGEBRAIC(:,36) = (1.00000./power(CONSTANTS(:,18), 1.00000.*1.00000)).*power(power(ALGEBRAIC(:,1), 2.00000)./CONSTANTS(:,21), 1.00000).*power(power(ALGEBRAIC(:,25), 2.00000)./CONSTANTS(:,22), 1.00000);
ALGEBRAIC(:,11) = (1.00000./power(CONSTANTS(:,15), 1.00000.*1.00000)).*power(STATES(:,5)./CONSTANTS(:,20), 1.00000).*power(power(ALGEBRAIC(:,1), 2.00000)./CONSTANTS(:,21), 1.00000);
ALGEBRAIC(:,37) = (1.00000./( power(CONSTANTS(:,14), 1.00000.*1.00000).*power(CONSTANTS(:,15), 1.00000.*1.00000))).*power(ALGEBRAIC(:,24)./CONSTANTS(:,19), 1.00000).*power(STATES(:,5)./CONSTANTS(:,20), 1.00000).*power(power(ALGEBRAIC(:,1), 2.00000)./CONSTANTS(:,21), 1.00000);
ALGEBRAIC(:,38) = (1.00000./( power(CONSTANTS(:,15), 1.00000.*1.00000).*power(CONSTANTS(:,17), 1.00000.*1.00000).*power(CONSTANTS(:,18), 1.00000.*1.00000))).*power(STATES(:,5)./CONSTANTS(:,20), 1.00000).*power(power(ALGEBRAIC(:,1), 2.00000)./CONSTANTS(:,21), 1.00000).*power(power(ALGEBRAIC(:,25), 2.00000)./CONSTANTS(:,22), 1.00000);
ALGEBRAIC(:,39) = (1.00000./( power(CONSTANTS(:,14), 1.00000.*1.00000).*power(CONSTANTS(:,16), 1.00000.*1.00000).*power(CONSTANTS(:,18), 1.00000.*1.00000))).*power(ALGEBRAIC(:,24)./CONSTANTS(:,19), 1.00000).*power(power(ALGEBRAIC(:,1), 2.00000)./CONSTANTS(:,21), 1.00000).*power(power(ALGEBRAIC(:,25), 2.00000)./CONSTANTS(:,22), 1.00000);
ALGEBRAIC(:,40) = (1.00000./( power(CONSTANTS(:,16), 1.00000.*1.00000).*power(CONSTANTS(:,17), 1.00000.*1.00000))).*power(ALGEBRAIC(:,24)./CONSTANTS(:,19), 1.00000).*power(STATES(:,5)./CONSTANTS(:,20), 1.00000).*power(power(ALGEBRAIC(:,25), 2.00000)./CONSTANTS(:,22), 1.00000);
ALGEBRAIC(:,41) = (1.00000./( power(CONSTANTS(:,14), 1.00000.*1.00000).*power(CONSTANTS(:,15), 1.00000.*1.00000).*power(CONSTANTS(:,16), 1.00000.*1.00000).*power(CONSTANTS(:,17), 1.00000.*1.00000).*power(CONSTANTS(:,18), 1.00000.*1.00000))).*power(ALGEBRAIC(:,24)./CONSTANTS(:,19), 1.00000).*power(STATES(:,5)./CONSTANTS(:,20), 1.00000).*power(power(ALGEBRAIC(:,1), 2.00000)./CONSTANTS(:,21), 1.00000).*power(power(ALGEBRAIC(:,25), 2.00000)./CONSTANTS(:,22), 1.00000);
ALGEBRAIC(:,42) = ( CONSTANTS(:,13).*( (1.00000 - CONSTANTS(:,12)).*ALGEBRAIC(:,37)+ CONSTANTS(:,12).*(ALGEBRAIC(:,10)+ALGEBRAIC(:,32)+ALGEBRAIC(:,36)+ALGEBRAIC(:,37)+ALGEBRAIC(:,38)+ALGEBRAIC(:,39)+ALGEBRAIC(:,11)+ALGEBRAIC(:,41))))./(CONSTANTS(:,47)+ALGEBRAIC(:,26)+ALGEBRAIC(:,9)+ALGEBRAIC(:,10)+ALGEBRAIC(:,28)+ALGEBRAIC(:,30)+ALGEBRAIC(:,32)+ALGEBRAIC(:,34)+ALGEBRAIC(:,35)+ALGEBRAIC(:,36)+ALGEBRAIC(:,11)+ALGEBRAIC(:,37)+ALGEBRAIC(:,38)+ALGEBRAIC(:,39)+ALGEBRAIC(:,40)+ALGEBRAIC(:,41));
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(:,24) = soln(1);
ALGEBRAIC(:,25) = soln(2);
else
SET_ALGEBRAIC(:,24) = logical(1);
SET_ALGEBRAIC(:,25) = 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(:,24) = soln(1);
TEMP_ALGEBRAIC(:,25) = soln(2);
ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
end
end
end
function resid = residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
ALGEBRAIC(:,24) = algebraicCandidate(1);
ALGEBRAIC(:,25) = algebraicCandidate(2);
resid(1) = ALGEBRAIC(:,25) - (CONSTANTS(:,23) - (STATES(:,6)+ALGEBRAIC(:,24)));
resid(2) = ALGEBRAIC(:,24) - power(STATES(:,6), 2.00000)./ALGEBRAIC(:,25);
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