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 =34;
end
% There are a total of 15 entries in each of the rate and state variable arrays.
% There are a total of 59 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_ALGEBRAIC(:,1) = strpad('L_iso in component beta_1_adrenergic_parameters (uM)');
LEGEND_CONSTANTS(:,1) = strpad('K_H in component beta_1_adrenergic_parameters (uM)');
LEGEND_CONSTANTS(:,2) = strpad('K_L in component beta_1_adrenergic_parameters (uM)');
LEGEND_CONSTANTS(:,3) = strpad('K_C in component beta_1_adrenergic_parameters (uM)');
LEGEND_ALGEBRAIC(:,2) = strpad('L_ach in component muscarinic_parameters (uM)');
LEGEND_CONSTANTS(:,4) = strpad('K_H in component muscarinic_parameters (uM)');
LEGEND_CONSTANTS(:,5) = strpad('K_L in component muscarinic_parameters (uM)');
LEGEND_CONSTANTS(:,6) = strpad('K_C in component muscarinic_parameters (uM)');
LEGEND_CONSTANTS(:,7) = strpad('k_PDE2 in component PDE_parameters (per_sec)');
LEGEND_CONSTANTS(:,8) = strpad('Km_PDE2 in component PDE_parameters (uM)');
LEGEND_CONSTANTS(:,9) = strpad('k_PDE3 in component PDE_parameters (per_sec)');
LEGEND_CONSTANTS(:,10) = strpad('Km_PDE3 in component PDE_parameters (uM)');
LEGEND_CONSTANTS(:,11) = strpad('k_PDE4 in component PDE_parameters (per_sec)');
LEGEND_CONSTANTS(:,12) = strpad('Km_PDE4 in component PDE_parameters (uM)');
LEGEND_CONSTANTS(:,13) = strpad('k_act1 in component G_s_parameters (per_sec)');
LEGEND_CONSTANTS(:,14) = strpad('k_act2 in component G_s_parameters (per_sec)');
LEGEND_CONSTANTS(:,15) = strpad('k_hydr in component G_s_parameters (per_sec)');
LEGEND_CONSTANTS(:,16) = strpad('k_reas in component G_s_parameters (per_uM_per_sec)');
LEGEND_CONSTANTS(:,17) = strpad('k_act1 in component G_i_parameters (per_sec)');
LEGEND_CONSTANTS(:,18) = strpad('k_act2 in component G_i_parameters (per_sec)');
LEGEND_CONSTANTS(:,19) = strpad('k_hydr in component G_i_parameters (per_sec)');
LEGEND_CONSTANTS(:,20) = strpad('k_reas in component G_i_parameters (per_uM_per_sec)');
LEGEND_ALGEBRAIC(:,13) = strpad('R in component caveolar_beta_1_adrenergic_receptor_module (uM)');
LEGEND_ALGEBRAIC(:,14) = strpad('LR in component caveolar_beta_1_adrenergic_receptor_module (uM)');
LEGEND_ALGEBRAIC(:,15) = strpad('LRG in component caveolar_beta_1_adrenergic_receptor_module (uM)');
LEGEND_ALGEBRAIC(:,16) = strpad('RG in component caveolar_beta_1_adrenergic_receptor_module (uM)');
LEGEND_CONSTANTS(:,21) = strpad('R_Total in component caveolar_beta_1_adrenergic_receptor_module (uM)');
LEGEND_ALGEBRAIC(:,6) = strpad('Gs_alpha_beta_gamma in component caveolar_G_s_protein_activation_module (uM)');
LEGEND_ALGEBRAIC(:,17) = strpad('R in component caveolar_muscarinic_receptor_module (uM)');
LEGEND_ALGEBRAIC(:,18) = strpad('LR in component caveolar_muscarinic_receptor_module (uM)');
LEGEND_ALGEBRAIC(:,19) = strpad('LRG in component caveolar_muscarinic_receptor_module (uM)');
LEGEND_ALGEBRAIC(:,20) = strpad('RG in component caveolar_muscarinic_receptor_module (uM)');
LEGEND_CONSTANTS(:,22) = strpad('R_Total in component caveolar_muscarinic_receptor_module (uM)');
LEGEND_ALGEBRAIC(:,7) = strpad('Gi_alpha_beta_gamma in component caveolar_G_i_protein_activation_module (uM)');
LEGEND_STATES(:,1) = strpad('Gs_alpha_GTP in component caveolar_G_s_protein_activation_module (uM)');
LEGEND_STATES(:,2) = strpad('Gs_beta_gamma in component caveolar_G_s_protein_activation_module (uM)');
LEGEND_STATES(:,3) = strpad('Gs_alpha_GDP in component caveolar_G_s_protein_activation_module (uM)');
LEGEND_CONSTANTS(:,23) = strpad('Gs_Total in component caveolar_G_s_protein_activation_module (uM)');
LEGEND_STATES(:,4) = strpad('Gi_alpha_GTP in component caveolar_G_i_protein_activation_module (uM)');
LEGEND_STATES(:,5) = strpad('Gi_beta_gamma in component caveolar_G_i_protein_activation_module (uM)');
LEGEND_STATES(:,6) = strpad('Gi_alpha_GDP in component caveolar_G_i_protein_activation_module (uM)');
LEGEND_CONSTANTS(:,24) = strpad('Gi_Total in component caveolar_G_i_protein_activation_module (uM)');
LEGEND_ALGEBRAIC(:,21) = strpad('R in component extracaveolar_beta_1_adrenergic_receptor_module (uM)');
LEGEND_ALGEBRAIC(:,22) = strpad('LR in component extracaveolar_beta_1_adrenergic_receptor_module (uM)');
LEGEND_ALGEBRAIC(:,23) = strpad('LRG in component extracaveolar_beta_1_adrenergic_receptor_module (uM)');
LEGEND_ALGEBRAIC(:,24) = strpad('RG in component extracaveolar_beta_1_adrenergic_receptor_module (uM)');
LEGEND_CONSTANTS(:,25) = strpad('R_Total in component extracaveolar_beta_1_adrenergic_receptor_module (uM)');
LEGEND_ALGEBRAIC(:,8) = strpad('Gs_alpha_beta_gamma in component extracaveolar_G_s_protein_activation_module (uM)');
LEGEND_ALGEBRAIC(:,25) = strpad('R in component extracaveolar_muscarinic_receptor_module (uM)');
LEGEND_ALGEBRAIC(:,26) = strpad('LR in component extracaveolar_muscarinic_receptor_module (uM)');
LEGEND_ALGEBRAIC(:,27) = strpad('LRG in component extracaveolar_muscarinic_receptor_module (uM)');
LEGEND_ALGEBRAIC(:,28) = strpad('RG in component extracaveolar_muscarinic_receptor_module (uM)');
LEGEND_CONSTANTS(:,26) = strpad('R_Total in component extracaveolar_muscarinic_receptor_module (uM)');
LEGEND_ALGEBRAIC(:,9) = strpad('Gi_alpha_beta_gamma in component extracaveolar_G_i_protein_activation_module (uM)');
LEGEND_STATES(:,7) = strpad('Gs_alpha_GTP in component extracaveolar_G_s_protein_activation_module (uM)');
LEGEND_STATES(:,8) = strpad('Gs_beta_gamma in component extracaveolar_G_s_protein_activation_module (uM)');
LEGEND_STATES(:,9) = strpad('Gs_alpha_GDP in component extracaveolar_G_s_protein_activation_module (uM)');
LEGEND_CONSTANTS(:,27) = strpad('Gs_Total in component extracaveolar_G_s_protein_activation_module (uM)');
LEGEND_STATES(:,10) = strpad('Gi_alpha_GTP in component extracaveolar_G_i_protein_activation_module (uM)');
LEGEND_STATES(:,11) = strpad('Gi_beta_gamma in component extracaveolar_G_i_protein_activation_module (uM)');
LEGEND_STATES(:,12) = strpad('Gi_alpha_GDP in component extracaveolar_G_i_protein_activation_module (uM)');
LEGEND_CONSTANTS(:,28) = strpad('Gi_Total in component extracaveolar_G_i_protein_activation_module (uM)');
LEGEND_ALGEBRAIC(:,10) = strpad('dcAMP_AC_56_dt in component AC56_module (uM_per_sec)');
LEGEND_ALGEBRAIC(:,3) = strpad('k_AC56 in component AC56_module (per_sec)');
LEGEND_CONSTANTS(:,29) = strpad('AC_56 in component AC56_module (uM)');
LEGEND_CONSTANTS(:,30) = strpad('AF56 in component AC56_module (dimensionless)');
LEGEND_CONSTANTS(:,31) = strpad('MW_AC56 in component AC56_module (kDa)');
LEGEND_CONSTANTS(:,32) = strpad('ATP in component AC56_module (uM)');
LEGEND_CONSTANTS(:,33) = strpad('Km_ATP in component AC56_module (uM)');
LEGEND_ALGEBRAIC(:,11) = strpad('dcAMP_AC_47_ecav_dt in component AC47_ecav_module (uM_per_sec)');
LEGEND_ALGEBRAIC(:,4) = strpad('k_AC47_ecav in component AC47_ecav_module (per_sec)');
LEGEND_CONSTANTS(:,34) = strpad('AC_47_ecav in component AC47_ecav_module (uM)');
LEGEND_CONSTANTS(:,35) = strpad('AF47 in component AC47_ecav_module (dimensionless)');
LEGEND_CONSTANTS(:,36) = strpad('MW_AC47 in component AC47_ecav_module (kDa)');
LEGEND_CONSTANTS(:,37) = strpad('ATP in component AC47_ecav_module (uM)');
LEGEND_CONSTANTS(:,38) = strpad('Km_ATP in component AC47_ecav_module (uM)');
LEGEND_CONSTANTS(:,56) = strpad('dcAMP_AC_47_cyt_dt in component AC47_cyt_module (uM_per_sec)');
LEGEND_CONSTANTS(:,39) = strpad('k_AC47_cyt in component AC47_cyt_module (per_sec)');
LEGEND_CONSTANTS(:,40) = strpad('AC_47_cyt in component AC47_cyt_module (uM)');
LEGEND_CONSTANTS(:,41) = strpad('AF47 in component AC47_cyt_module (dimensionless)');
LEGEND_CONSTANTS(:,42) = strpad('ATP in component AC47_cyt_module (uM)');
LEGEND_CONSTANTS(:,43) = strpad('Km_ATP in component AC47_cyt_module (uM)');
LEGEND_ALGEBRAIC(:,29) = strpad('dcAMP_cav_PDE2_dt in component caveolar_PDE_module (uM_per_sec)');
LEGEND_ALGEBRAIC(:,32) = strpad('dcAMP_cav_PDE3_dt in component caveolar_PDE_module (uM_per_sec)');
LEGEND_ALGEBRAIC(:,34) = strpad('dcAMP_cav_PDE4_dt in component caveolar_PDE_module (uM_per_sec)');
LEGEND_STATES(:,13) = strpad('cAMP_cav in component cAMP_flux_module (uM)');
LEGEND_CONSTANTS(:,44) = strpad('PDE2 in component caveolar_PDE_module (uM)');
LEGEND_CONSTANTS(:,45) = strpad('PDE3 in component caveolar_PDE_module (uM)');
LEGEND_CONSTANTS(:,46) = strpad('PDE4 in component caveolar_PDE_module (uM)');
LEGEND_ALGEBRAIC(:,30) = strpad('dcAMP_ecav_PDE2_dt in component extracaveolar_PDE_module (uM_per_sec)');
LEGEND_ALGEBRAIC(:,33) = strpad('dcAMP_ecav_PDE4_dt in component extracaveolar_PDE_module (uM_per_sec)');
LEGEND_STATES(:,14) = strpad('cAMP_ecav in component cAMP_flux_module (uM)');
LEGEND_CONSTANTS(:,47) = strpad('PDE2 in component extracaveolar_PDE_module (uM)');
LEGEND_CONSTANTS(:,48) = strpad('PDE4 in component extracaveolar_PDE_module (uM)');
LEGEND_ALGEBRAIC(:,5) = strpad('dcAMP_cyt_PDE2_dt in component bulk_cytoplasmic_PDE_module (uM_per_sec)');
LEGEND_ALGEBRAIC(:,12) = strpad('dcAMP_cyt_PDE3_dt in component bulk_cytoplasmic_PDE_module (uM_per_sec)');
LEGEND_ALGEBRAIC(:,31) = strpad('dcAMP_cyt_PDE4_dt in component bulk_cytoplasmic_PDE_module (uM_per_sec)');
LEGEND_STATES(:,15) = strpad('cAMP_cyt in component cAMP_flux_module (uM)');
LEGEND_CONSTANTS(:,49) = strpad('PDE2 in component bulk_cytoplasmic_PDE_module (uM)');
LEGEND_CONSTANTS(:,50) = strpad('PDE3 in component bulk_cytoplasmic_PDE_module (uM)');
LEGEND_CONSTANTS(:,51) = strpad('PDE4 in component bulk_cytoplasmic_PDE_module (uM)');
LEGEND_CONSTANTS(:,57) = strpad('V_cav in component cAMP_flux_module (liter)');
LEGEND_CONSTANTS(:,58) = strpad('V_ecav in component cAMP_flux_module (liter)');
LEGEND_CONSTANTS(:,59) = strpad('V_cyt in component cAMP_flux_module (liter)');
LEGEND_CONSTANTS(:,52) = strpad('V_cell in component cAMP_flux_module (liter)');
LEGEND_CONSTANTS(:,53) = strpad('J_cav_ecav in component cAMP_flux_module (liters_per_second)');
LEGEND_CONSTANTS(:,54) = strpad('J_cav_cyt in component cAMP_flux_module (liters_per_second)');
LEGEND_CONSTANTS(:,55) = strpad('J_ecav_cyt in component cAMP_flux_module (liters_per_second)');
LEGEND_RATES(:,1) = strpad('d/dt Gs_alpha_GTP in component caveolar_G_s_protein_activation_module (uM)');
LEGEND_RATES(:,2) = strpad('d/dt Gs_beta_gamma in component caveolar_G_s_protein_activation_module (uM)');
LEGEND_RATES(:,3) = strpad('d/dt Gs_alpha_GDP in component caveolar_G_s_protein_activation_module (uM)');
LEGEND_RATES(:,4) = strpad('d/dt Gi_alpha_GTP in component caveolar_G_i_protein_activation_module (uM)');
LEGEND_RATES(:,5) = strpad('d/dt Gi_beta_gamma in component caveolar_G_i_protein_activation_module (uM)');
LEGEND_RATES(:,6) = strpad('d/dt Gi_alpha_GDP in component caveolar_G_i_protein_activation_module (uM)');
LEGEND_RATES(:,7) = strpad('d/dt Gs_alpha_GTP in component extracaveolar_G_s_protein_activation_module (uM)');
LEGEND_RATES(:,8) = strpad('d/dt Gs_beta_gamma in component extracaveolar_G_s_protein_activation_module (uM)');
LEGEND_RATES(:,9) = strpad('d/dt Gs_alpha_GDP in component extracaveolar_G_s_protein_activation_module (uM)');
LEGEND_RATES(:,10) = strpad('d/dt Gi_alpha_GTP in component extracaveolar_G_i_protein_activation_module (uM)');
LEGEND_RATES(:,11) = strpad('d/dt Gi_beta_gamma in component extracaveolar_G_i_protein_activation_module (uM)');
LEGEND_RATES(:,12) = strpad('d/dt Gi_alpha_GDP in component extracaveolar_G_i_protein_activation_module (uM)');
LEGEND_RATES(:,13) = strpad('d/dt cAMP_cav in component cAMP_flux_module (uM)');
LEGEND_RATES(:,14) = strpad('d/dt cAMP_ecav in component cAMP_flux_module (uM)');
LEGEND_RATES(:,15) = strpad('d/dt cAMP_cyt in component cAMP_flux_module (uM)');
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 = [];
CONSTANTS(:,1) = 0.035;
CONSTANTS(:,2) = 0.386;
CONSTANTS(:,3) = 8.809;
CONSTANTS(:,4) = 0.16;
CONSTANTS(:,5) = 11;
CONSTANTS(:,6) = 30;
CONSTANTS(:,7) = 20;
CONSTANTS(:,8) = 50;
CONSTANTS(:,9) = 1.25;
CONSTANTS(:,10) = 0.08;
CONSTANTS(:,11) = 2.5;
CONSTANTS(:,12) = 2.2;
CONSTANTS(:,13) = 5;
CONSTANTS(:,14) = 0.1;
CONSTANTS(:,15) = 0.8;
CONSTANTS(:,16) = 1.21e3;
CONSTANTS(:,17) = 2.5;
CONSTANTS(:,18) = 0.05;
CONSTANTS(:,19) = 0.8;
CONSTANTS(:,20) = 1.21e3;
CONSTANTS(:,21) = 0.633;
CONSTANTS(:,22) = 0.633;
STATES(:,1) = 0.041983438;
STATES(:,2) = 0.042634499;
STATES(:,3) = 0.000651061;
CONSTANTS(:,23) = 10;
STATES(:,4) = 0.012644961;
STATES(:,5) = 0.013274751;
STATES(:,6) = 0.00062979;
CONSTANTS(:,24) = 20;
CONSTANTS(:,25) = 0.633;
CONSTANTS(:,26) = 0.633;
STATES(:,7) = 0.083866891;
STATES(:,8) = 0.084522918;
STATES(:,9) = 0.000656025;
CONSTANTS(:,27) = 10;
STATES(:,10) = 0.001018705;
STATES(:,11) = 0.001475253;
STATES(:,12) = 0.000456548;
CONSTANTS(:,28) = 1;
CONSTANTS(:,29) = 3.379;
CONSTANTS(:,30) = 500;
CONSTANTS(:,31) = 130;
CONSTANTS(:,32) = 5000;
CONSTANTS(:,33) = 315;
CONSTANTS(:,34) = 0.2;
CONSTANTS(:,35) = 130;
CONSTANTS(:,36) = 130;
CONSTANTS(:,37) = 5000;
CONSTANTS(:,38) = 315;
CONSTANTS(:,39) = 1.08e-3;
CONSTANTS(:,40) = 0.136;
CONSTANTS(:,41) = 130;
CONSTANTS(:,42) = 5000;
CONSTANTS(:,43) = 315;
STATES(:,13) = 0.11750433;
CONSTANTS(:,44) = 4.5;
CONSTANTS(:,45) = 5.6;
CONSTANTS(:,46) = 2;
STATES(:,14) = 1.092200547;
CONSTANTS(:,47) = 0.02;
CONSTANTS(:,48) = 0.16;
STATES(:,15) = 0.992583576;
CONSTANTS(:,49) = 5e-3;
CONSTANTS(:,50) = 7.5e-3;
CONSTANTS(:,51) = 5e-3;
CONSTANTS(:,52) = 38e-12;
CONSTANTS(:,53) = 7.5e-15;
CONSTANTS(:,54) = 7.5e-14;
CONSTANTS(:,55) = 1.5e-17;
CONSTANTS(:,56) = ( CONSTANTS(:,39).*CONSTANTS(:,40).*CONSTANTS(:,41).*CONSTANTS(:,42))./(CONSTANTS(:,43)+CONSTANTS(:,42));
CONSTANTS(:,57) = 0.0100000.*CONSTANTS(:,52);
CONSTANTS(:,58) = 0.0200000.*CONSTANTS(:,52);
CONSTANTS(:,59) = 0.500000.*CONSTANTS(:,52);
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(:,3) = STATES(:,1).*CONSTANTS(:,15) - STATES(:,3).*STATES(:,2).*CONSTANTS(:,16);
RATES(:,6) = STATES(:,4).*CONSTANTS(:,19) - STATES(:,6).*STATES(:,5).*CONSTANTS(:,20);
RATES(:,9) = STATES(:,7).*CONSTANTS(:,15) - STATES(:,9).*STATES(:,8).*CONSTANTS(:,16);
RATES(:,12) = STATES(:,10).*CONSTANTS(:,19) - STATES(:,12).*STATES(:,11).*CONSTANTS(:,20);
ALGEBRAIC(:,1) = piecewise({VOI>120.000&VOI<=720.000, 1.00000 }, 1.00000);
ALGEBRAIC(:,6) = (CONSTANTS(:,23) - STATES(:,1)) - STATES(:,3);
[CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS, STATES, ALGEBRAIC);
RATES(:,1) = ( ALGEBRAIC(:,16).*CONSTANTS(:,14)+ ALGEBRAIC(:,15).*CONSTANTS(:,13)) - STATES(:,1).*CONSTANTS(:,15);
RATES(:,2) = ( ALGEBRAIC(:,16).*CONSTANTS(:,14)+ ALGEBRAIC(:,15).*CONSTANTS(:,13)) - STATES(:,3).*STATES(:,2).*CONSTANTS(:,16);
ALGEBRAIC(:,2) = piecewise({VOI>240.000&VOI<=540.000, 0.00000 }, 0.00000);
ALGEBRAIC(:,7) = (CONSTANTS(:,24) - STATES(:,4)) - STATES(:,6);
[CONSTANTS, STATES, ALGEBRAIC] = rootfind_1(VOI, CONSTANTS, STATES, ALGEBRAIC);
RATES(:,4) = ( ALGEBRAIC(:,20).*CONSTANTS(:,18)+ ALGEBRAIC(:,19).*CONSTANTS(:,17)) - STATES(:,4).*CONSTANTS(:,19);
RATES(:,5) = ( ALGEBRAIC(:,20).*CONSTANTS(:,18)+ ALGEBRAIC(:,19).*CONSTANTS(:,17)) - STATES(:,6).*STATES(:,5).*CONSTANTS(:,20);
ALGEBRAIC(:,8) = (CONSTANTS(:,27) - STATES(:,7)) - STATES(:,9);
[CONSTANTS, STATES, ALGEBRAIC] = rootfind_2(VOI, CONSTANTS, STATES, ALGEBRAIC);
RATES(:,7) = ( ALGEBRAIC(:,24).*CONSTANTS(:,14)+ ALGEBRAIC(:,23).*CONSTANTS(:,13)) - STATES(:,7).*CONSTANTS(:,15);
RATES(:,8) = ( ALGEBRAIC(:,24).*CONSTANTS(:,14)+ ALGEBRAIC(:,23).*CONSTANTS(:,13)) - STATES(:,9).*STATES(:,8).*CONSTANTS(:,16);
ALGEBRAIC(:,9) = (CONSTANTS(:,28) - STATES(:,10)) - STATES(:,12);
[CONSTANTS, STATES, ALGEBRAIC] = rootfind_3(VOI, CONSTANTS, STATES, ALGEBRAIC);
RATES(:,10) = ( ALGEBRAIC(:,28).*CONSTANTS(:,18)+ ALGEBRAIC(:,27).*CONSTANTS(:,17)) - STATES(:,10).*CONSTANTS(:,19);
RATES(:,11) = ( ALGEBRAIC(:,28).*CONSTANTS(:,18)+ ALGEBRAIC(:,27).*CONSTANTS(:,17)) - STATES(:,12).*STATES(:,11).*CONSTANTS(:,20);
ALGEBRAIC(:,5) = ( CONSTANTS(:,7).*CONSTANTS(:,49).*STATES(:,15))./(CONSTANTS(:,8)+STATES(:,15));
ALGEBRAIC(:,12) = ( CONSTANTS(:,9).*CONSTANTS(:,50).*STATES(:,15))./(CONSTANTS(:,10)+STATES(:,15));
ALGEBRAIC(:,31) = ( CONSTANTS(:,11).*CONSTANTS(:,51).*STATES(:,15))./(CONSTANTS(:,12)+STATES(:,15));
RATES(:,15) = (CONSTANTS(:,56) - (ALGEBRAIC(:,5)+ALGEBRAIC(:,12)+ALGEBRAIC(:,31)))+( CONSTANTS(:,54).*(STATES(:,13) - STATES(:,15)))./CONSTANTS(:,59)+( CONSTANTS(:,55).*(STATES(:,14) - STATES(:,15)))./CONSTANTS(:,59);
ALGEBRAIC(:,4) = (( (0.0630000+( 2.01000.*power( STATES(:,7).*1000.00, 1.00430))./(31.5440+power( STATES(:,7).*1000.00, 1.00430))).*(1.00000+( (1.00000./3.01000).*49.1000.*power( STATES(:,11).*1000.00, 0.892100))./(25.4400+power( STATES(:,11).*1000.00, 0.892100))).*CONSTANTS(:,36))./60.0000).*0.00100000;
ALGEBRAIC(:,11) = ( ALGEBRAIC(:,4).*CONSTANTS(:,34).*CONSTANTS(:,35).*CONSTANTS(:,37))./(CONSTANTS(:,38)+CONSTANTS(:,37));
ALGEBRAIC(:,30) = ( CONSTANTS(:,7).*CONSTANTS(:,47).*STATES(:,14))./(CONSTANTS(:,8)+STATES(:,14));
ALGEBRAIC(:,33) = ( CONSTANTS(:,11).*CONSTANTS(:,48).*STATES(:,14))./(CONSTANTS(:,12)+STATES(:,14));
RATES(:,14) = ((ALGEBRAIC(:,11) - (ALGEBRAIC(:,30)+ALGEBRAIC(:,33)))+( CONSTANTS(:,53).*(STATES(:,13) - STATES(:,14)))./CONSTANTS(:,58)) - ( CONSTANTS(:,55).*(STATES(:,14) - STATES(:,15)))./CONSTANTS(:,58);
ALGEBRAIC(:,3) = (( (0.700000+( 3.82340.*power(STATES(:,1)./1.00000, 0.978700))./(0.198600+power(STATES(:,1)./1.00000, 0.978700))).*(1.00000+( (1.00000./1.44320).* - 1.00610.*power(STATES(:,4)./1.00000, 0.835600))./(0.191800+power(STATES(:,4)./1.00000, 0.835600))).*CONSTANTS(:,31))./60.0000).*0.00100000;
ALGEBRAIC(:,10) = ( ALGEBRAIC(:,3).*CONSTANTS(:,29).*CONSTANTS(:,30).*CONSTANTS(:,32))./(CONSTANTS(:,33)+CONSTANTS(:,32));
ALGEBRAIC(:,29) = ( CONSTANTS(:,7).*CONSTANTS(:,44).*STATES(:,13))./(CONSTANTS(:,8)+STATES(:,13));
ALGEBRAIC(:,32) = ( CONSTANTS(:,9).*CONSTANTS(:,45).*STATES(:,13))./(CONSTANTS(:,10)+STATES(:,13));
ALGEBRAIC(:,34) = ( CONSTANTS(:,11).*CONSTANTS(:,46).*STATES(:,13))./(CONSTANTS(:,12)+STATES(:,13));
RATES(:,13) = ((ALGEBRAIC(:,10) - (ALGEBRAIC(:,29)+ALGEBRAIC(:,32)+ALGEBRAIC(:,34))) - ( CONSTANTS(:,53).*(STATES(:,13) - STATES(:,14)))./CONSTANTS(:,57)) - ( CONSTANTS(:,54).*(STATES(:,13) - STATES(:,15)))./CONSTANTS(:,57);
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>120.000&VOI<=720.000, 1.00000 }, 1.00000);
ALGEBRAIC(:,6) = (CONSTANTS(:,23) - STATES(:,1)) - STATES(:,3);
ALGEBRAIC(:,2) = piecewise({VOI>240.000&VOI<=540.000, 0.00000 }, 0.00000);
ALGEBRAIC(:,7) = (CONSTANTS(:,24) - STATES(:,4)) - STATES(:,6);
ALGEBRAIC(:,8) = (CONSTANTS(:,27) - STATES(:,7)) - STATES(:,9);
ALGEBRAIC(:,9) = (CONSTANTS(:,28) - STATES(:,10)) - STATES(:,12);
ALGEBRAIC(:,5) = ( CONSTANTS(:,7).*CONSTANTS(:,49).*STATES(:,15))./(CONSTANTS(:,8)+STATES(:,15));
ALGEBRAIC(:,12) = ( CONSTANTS(:,9).*CONSTANTS(:,50).*STATES(:,15))./(CONSTANTS(:,10)+STATES(:,15));
ALGEBRAIC(:,31) = ( CONSTANTS(:,11).*CONSTANTS(:,51).*STATES(:,15))./(CONSTANTS(:,12)+STATES(:,15));
ALGEBRAIC(:,4) = (( (0.0630000+( 2.01000.*power( STATES(:,7).*1000.00, 1.00430))./(31.5440+power( STATES(:,7).*1000.00, 1.00430))).*(1.00000+( (1.00000./3.01000).*49.1000.*power( STATES(:,11).*1000.00, 0.892100))./(25.4400+power( STATES(:,11).*1000.00, 0.892100))).*CONSTANTS(:,36))./60.0000).*0.00100000;
ALGEBRAIC(:,11) = ( ALGEBRAIC(:,4).*CONSTANTS(:,34).*CONSTANTS(:,35).*CONSTANTS(:,37))./(CONSTANTS(:,38)+CONSTANTS(:,37));
ALGEBRAIC(:,30) = ( CONSTANTS(:,7).*CONSTANTS(:,47).*STATES(:,14))./(CONSTANTS(:,8)+STATES(:,14));
ALGEBRAIC(:,33) = ( CONSTANTS(:,11).*CONSTANTS(:,48).*STATES(:,14))./(CONSTANTS(:,12)+STATES(:,14));
ALGEBRAIC(:,3) = (( (0.700000+( 3.82340.*power(STATES(:,1)./1.00000, 0.978700))./(0.198600+power(STATES(:,1)./1.00000, 0.978700))).*(1.00000+( (1.00000./1.44320).* - 1.00610.*power(STATES(:,4)./1.00000, 0.835600))./(0.191800+power(STATES(:,4)./1.00000, 0.835600))).*CONSTANTS(:,31))./60.0000).*0.00100000;
ALGEBRAIC(:,10) = ( ALGEBRAIC(:,3).*CONSTANTS(:,29).*CONSTANTS(:,30).*CONSTANTS(:,32))./(CONSTANTS(:,33)+CONSTANTS(:,32));
ALGEBRAIC(:,29) = ( CONSTANTS(:,7).*CONSTANTS(:,44).*STATES(:,13))./(CONSTANTS(:,8)+STATES(:,13));
ALGEBRAIC(:,32) = ( CONSTANTS(:,9).*CONSTANTS(:,45).*STATES(:,13))./(CONSTANTS(:,10)+STATES(:,13));
ALGEBRAIC(:,34) = ( CONSTANTS(:,11).*CONSTANTS(:,46).*STATES(:,13))./(CONSTANTS(:,12)+STATES(:,13));
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) ~= 4), initialGuess_0 = [0.1,0.1,0.1,0.1];, 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);
ALGEBRAIC(:,15) = soln(3);
ALGEBRAIC(:,16) = soln(4);
else
SET_ALGEBRAIC(:,13) = logical(1);
SET_ALGEBRAIC(:,14) = logical(1);
SET_ALGEBRAIC(:,15) = logical(1);
SET_ALGEBRAIC(:,16) = 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);
TEMP_ALGEBRAIC(:,15) = soln(3);
TEMP_ALGEBRAIC(:,16) = soln(4);
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);
ALGEBRAIC(:,15) = algebraicCandidate(3);
ALGEBRAIC(:,16) = algebraicCandidate(4);
resid(1) = ALGEBRAIC(:,13) - (((CONSTANTS(:,21) - ALGEBRAIC(:,14)) - ALGEBRAIC(:,15)) - ALGEBRAIC(:,16));
resid(2) = ALGEBRAIC(:,14) - ( ALGEBRAIC(:,1).*ALGEBRAIC(:,13))./CONSTANTS(:,2);
resid(3) = ALGEBRAIC(:,15) - ( ALGEBRAIC(:,1).*ALGEBRAIC(:,13).*ALGEBRAIC(:,6))./( CONSTANTS(:,1).*CONSTANTS(:,3));
resid(4) = ALGEBRAIC(:,16) - ( ALGEBRAIC(:,13).*ALGEBRAIC(:,6))./CONSTANTS(:,3);
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) ~= 4), initialGuess_1 = [0.1,0.1,0.1,0.1];, 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(:,17) = soln(1);
ALGEBRAIC(:,18) = soln(2);
ALGEBRAIC(:,19) = soln(3);
ALGEBRAIC(:,20) = soln(4);
else
SET_ALGEBRAIC(:,17) = logical(1);
SET_ALGEBRAIC(:,18) = logical(1);
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(:,17) = soln(1);
TEMP_ALGEBRAIC(:,18) = soln(2);
TEMP_ALGEBRAIC(:,19) = soln(3);
TEMP_ALGEBRAIC(:,20) = soln(4);
ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
end
end
end
function resid = residualSN_1(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
ALGEBRAIC(:,17) = algebraicCandidate(1);
ALGEBRAIC(:,18) = algebraicCandidate(2);
ALGEBRAIC(:,19) = algebraicCandidate(3);
ALGEBRAIC(:,20) = algebraicCandidate(4);
resid(1) = ALGEBRAIC(:,17) - (((CONSTANTS(:,22) - ALGEBRAIC(:,18)) - ALGEBRAIC(:,19)) - ALGEBRAIC(:,20));
resid(2) = ALGEBRAIC(:,18) - ( ALGEBRAIC(:,2).*ALGEBRAIC(:,17))./CONSTANTS(:,5);
resid(3) = ALGEBRAIC(:,19) - ( ALGEBRAIC(:,2).*ALGEBRAIC(:,17).*ALGEBRAIC(:,7))./( CONSTANTS(:,4).*CONSTANTS(:,6));
resid(4) = ALGEBRAIC(:,20) - ( ALGEBRAIC(:,17).*ALGEBRAIC(:,7))./CONSTANTS(:,6);
end
% Functions required for solving differential algebraic equation
function [CONSTANTS, STATES, ALGEBRAIC] = rootfind_2(VOI, CONSTANTS_IN, STATES_IN, ALGEBRAIC_IN)
ALGEBRAIC = ALGEBRAIC_IN;
CONSTANTS = CONSTANTS_IN;
STATES = STATES_IN;
global initialGuess_2;
if (length(initialGuess_2) ~= 4), initialGuess_2 = [0.1,0.1,0.1,0.1];, end
options = optimset('Display', 'off', 'TolX', 1E-6);
if length(VOI) == 1
residualfn = @(algebraicCandidate)residualSN_2(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES);
soln = fsolve(residualfn, initialGuess_2, options);
initialGuess_2 = soln;
ALGEBRAIC(:,21) = soln(1);
ALGEBRAIC(:,22) = soln(2);
ALGEBRAIC(:,23) = soln(3);
ALGEBRAIC(:,24) = soln(4);
else
SET_ALGEBRAIC(:,21) = logical(1);
SET_ALGEBRAIC(:,22) = logical(1);
SET_ALGEBRAIC(:,23) = logical(1);
SET_ALGEBRAIC(:,24) = logical(1);
for i=1:length(VOI)
residualfn = @(algebraicCandidate)residualSN_2(algebraicCandidate, ALGEBRAIC(i,:), VOI(i), CONSTANTS, STATES(i,:));
soln = fsolve(residualfn, initialGuess_2, options);
initialGuess_2 = soln;
TEMP_ALGEBRAIC(:,21) = soln(1);
TEMP_ALGEBRAIC(:,22) = soln(2);
TEMP_ALGEBRAIC(:,23) = soln(3);
TEMP_ALGEBRAIC(:,24) = soln(4);
ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
end
end
end
function resid = residualSN_2(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
ALGEBRAIC(:,21) = algebraicCandidate(1);
ALGEBRAIC(:,22) = algebraicCandidate(2);
ALGEBRAIC(:,23) = algebraicCandidate(3);
ALGEBRAIC(:,24) = algebraicCandidate(4);
resid(1) = ALGEBRAIC(:,21) - (((CONSTANTS(:,25) - ALGEBRAIC(:,22)) - ALGEBRAIC(:,23)) - ALGEBRAIC(:,24));
resid(2) = ALGEBRAIC(:,22) - ( ALGEBRAIC(:,1).*ALGEBRAIC(:,21))./CONSTANTS(:,2);
resid(3) = ALGEBRAIC(:,23) - ( ALGEBRAIC(:,1).*ALGEBRAIC(:,21).*ALGEBRAIC(:,8))./( CONSTANTS(:,1).*CONSTANTS(:,3));
resid(4) = ALGEBRAIC(:,24) - ( ALGEBRAIC(:,21).*ALGEBRAIC(:,8))./CONSTANTS(:,3);
end
% Functions required for solving differential algebraic equation
function [CONSTANTS, STATES, ALGEBRAIC] = rootfind_3(VOI, CONSTANTS_IN, STATES_IN, ALGEBRAIC_IN)
ALGEBRAIC = ALGEBRAIC_IN;
CONSTANTS = CONSTANTS_IN;
STATES = STATES_IN;
global initialGuess_3;
if (length(initialGuess_3) ~= 4), initialGuess_3 = [0.1,0.1,0.1,0.1];, end
options = optimset('Display', 'off', 'TolX', 1E-6);
if length(VOI) == 1
residualfn = @(algebraicCandidate)residualSN_3(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES);
soln = fsolve(residualfn, initialGuess_3, options);
initialGuess_3 = soln;
ALGEBRAIC(:,25) = soln(1);
ALGEBRAIC(:,26) = soln(2);
ALGEBRAIC(:,27) = soln(3);
ALGEBRAIC(:,28) = soln(4);
else
SET_ALGEBRAIC(:,25) = logical(1);
SET_ALGEBRAIC(:,26) = logical(1);
SET_ALGEBRAIC(:,27) = logical(1);
SET_ALGEBRAIC(:,28) = logical(1);
for i=1:length(VOI)
residualfn = @(algebraicCandidate)residualSN_3(algebraicCandidate, ALGEBRAIC(i,:), VOI(i), CONSTANTS, STATES(i,:));
soln = fsolve(residualfn, initialGuess_3, options);
initialGuess_3 = soln;
TEMP_ALGEBRAIC(:,25) = soln(1);
TEMP_ALGEBRAIC(:,26) = soln(2);
TEMP_ALGEBRAIC(:,27) = soln(3);
TEMP_ALGEBRAIC(:,28) = soln(4);
ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
end
end
end
function resid = residualSN_3(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
ALGEBRAIC(:,25) = algebraicCandidate(1);
ALGEBRAIC(:,26) = algebraicCandidate(2);
ALGEBRAIC(:,27) = algebraicCandidate(3);
ALGEBRAIC(:,28) = algebraicCandidate(4);
resid(1) = ALGEBRAIC(:,25) - (((CONSTANTS(:,26) - ALGEBRAIC(:,26)) - ALGEBRAIC(:,27)) - ALGEBRAIC(:,28));
resid(2) = ALGEBRAIC(:,26) - ( ALGEBRAIC(:,2).*ALGEBRAIC(:,25))./CONSTANTS(:,5);
resid(3) = ALGEBRAIC(:,27) - ( ALGEBRAIC(:,2).*ALGEBRAIC(:,25).*ALGEBRAIC(:,9))./( CONSTANTS(:,4).*CONSTANTS(:,6));
resid(4) = ALGEBRAIC(:,28) - ( ALGEBRAIC(:,25).*ALGEBRAIC(:,9))./CONSTANTS(:,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