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 =29; end % There are a total of 9 entries in each of the rate and state variable arrays. % There are a total of 48 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_CONSTANTS(:,1) = strpad('isotonic_mode in component parameters (dimensionless)'); LEGEND_CONSTANTS(:,2) = strpad('alpha_1 in component parameters (per_um)'); LEGEND_CONSTANTS(:,3) = strpad('beta_1 in component parameters (mN)'); LEGEND_CONSTANTS(:,4) = strpad('alpha_2 in component parameters (per_um)'); LEGEND_CONSTANTS(:,5) = strpad('beta_2 in component parameters (mN)'); LEGEND_CONSTANTS(:,6) = strpad('alpha_3 in component parameters (per_um)'); LEGEND_CONSTANTS(:,7) = strpad('beta_3 in component parameters (mN)'); LEGEND_CONSTANTS(:,8) = strpad('lambda in component parameters (mN)'); LEGEND_CONSTANTS(:,9) = strpad('A_half in component parameters (dimensionless)'); LEGEND_CONSTANTS(:,10) = strpad('mu in component parameters (dimensionless)'); LEGEND_CONSTANTS(:,11) = strpad('chi in component parameters (dimensionless)'); LEGEND_CONSTANTS(:,12) = strpad('chi_0 in component parameters (dimensionless)'); LEGEND_CONSTANTS(:,13) = strpad('m_0 in component parameters (dimensionless)'); LEGEND_CONSTANTS(:,14) = strpad('v_max in component parameters (um_per_msec)'); LEGEND_CONSTANTS(:,15) = strpad('a in component parameters (dimensionless)'); LEGEND_CONSTANTS(:,16) = strpad('d_h in component parameters (dimensionless)'); LEGEND_CONSTANTS(:,17) = strpad('alpha_P in component parameters (dimensionless)'); LEGEND_CONSTANTS(:,18) = strpad('alpha_PG in component parameters (dimensionless)'); LEGEND_CONSTANTS(:,19) = strpad('S_0 in component parameters_izakov_et_al_1991 (um)'); LEGEND_ALGEBRAIC(:,4) = strpad('q_v in component parameters_izakov_et_al_1991 (per_millisecond)'); LEGEND_CONSTANTS(:,20) = strpad('q_1 in component parameters_izakov_et_al_1991 (per_millisecond)'); LEGEND_CONSTANTS(:,21) = strpad('q_2 in component parameters_izakov_et_al_1991 (per_millisecond)'); LEGEND_CONSTANTS(:,22) = strpad('q_3 in component parameters_izakov_et_al_1991 (per_millisecond)'); LEGEND_CONSTANTS(:,46) = strpad('v_1 in component parameters_izakov_et_al_1991 (um_per_msec)'); LEGEND_CONSTANTS(:,23) = strpad('alpha_P in component parameters_izakov_et_al_1991 (per_um)'); LEGEND_CONSTANTS(:,24) = strpad('alpha_S in component parameters_izakov_et_al_1991 (per_um)'); LEGEND_CONSTANTS(:,25) = strpad('alpha_G in component parameters_izakov_et_al_1991 (dimensionless)'); LEGEND_CONSTANTS(:,26) = strpad('a_on in component parameters_izakov_et_al_1991 (per_millisecond)'); LEGEND_CONSTANTS(:,27) = strpad('a_off in component parameters_izakov_et_al_1991 (per_millisecond)'); LEGEND_CONSTANTS(:,28) = strpad('k_A in component parameters_izakov_et_al_1991 (dimensionless)'); LEGEND_STATES(:,1) = strpad('v in component CE_velocity (um_per_msec)'); LEGEND_ALGEBRAIC(:,27) = strpad('F_CE in component force (mN)'); LEGEND_ALGEBRAIC(:,6) = strpad('F_muscle in component force (mN)'); LEGEND_ALGEBRAIC(:,1) = strpad('F_XSE in component force (mN)'); LEGEND_ALGEBRAIC(:,2) = strpad('F_SE in component force (mN)'); LEGEND_ALGEBRAIC(:,3) = strpad('F_PE in component force (mN)'); LEGEND_STATES(:,2) = strpad('N in component crossbridge_kinetics (dimensionless)'); LEGEND_ALGEBRAIC(:,14) = strpad('k_P_vis in component CE_velocity (mN)'); LEGEND_ALGEBRAIC(:,16) = strpad('k_S_vis in component PE_velocity (mN)'); LEGEND_STATES(:,3) = strpad('w in component PE_velocity (um_per_msec)'); LEGEND_STATES(:,4) = strpad('l_1 in component length (um)'); LEGEND_STATES(:,5) = strpad('l_2 in component length (um)'); LEGEND_STATES(:,6) = strpad('l_3 in component length (um)'); LEGEND_ALGEBRAIC(:,26) = strpad('p_v in component average_crossbridge_force (dimensionless)'); LEGEND_ALGEBRAIC(:,23) = strpad('K_chi in component crossbridge_kinetics (per_millisecond)'); LEGEND_ALGEBRAIC(:,7) = strpad('M_A in component crossbridge_kinetics (dimensionless)'); LEGEND_ALGEBRAIC(:,8) = strpad('n_1 in component crossbridge_kinetics (dimensionless)'); LEGEND_ALGEBRAIC(:,9) = strpad('L_oz in component crossbridge_kinetics (dimensionless)'); LEGEND_ALGEBRAIC(:,21) = strpad('k_p_v in component crossbridge_kinetics (per_millisecond)'); LEGEND_ALGEBRAIC(:,22) = strpad('k_m_v in component crossbridge_kinetics (per_millisecond)'); LEGEND_STATES(:,7) = strpad('A in component calcium_handling (dimensionless)'); LEGEND_ALGEBRAIC(:,20) = strpad('G_star in component average_crossbridge_force (dimensionless)'); LEGEND_ALGEBRAIC(:,10) = strpad('dl_1_dt in component length (um_per_msec)'); LEGEND_ALGEBRAIC(:,12) = strpad('dl_2_dt in component length (um_per_msec)'); LEGEND_ALGEBRAIC(:,5) = strpad('dl_3_dt in component length (um_per_msec)'); LEGEND_ALGEBRAIC(:,28) = strpad('phi_chi in component CE_velocity (um_per_msec2)'); LEGEND_ALGEBRAIC(:,29) = strpad('p_prime_v in component average_crossbridge_force (per_millisecond)'); LEGEND_CONSTANTS(:,29) = strpad('alpha_P_lengthening in component CE_velocity (per_um)'); LEGEND_CONSTANTS(:,30) = strpad('beta_P_lengthening in component CE_velocity (mN)'); LEGEND_CONSTANTS(:,31) = strpad('alpha_P_shortening in component CE_velocity (per_um)'); LEGEND_CONSTANTS(:,32) = strpad('beta_P_shortening in component CE_velocity (mN)'); LEGEND_CONSTANTS(:,33) = strpad('alpha_S_lengthening in component PE_velocity (per_um)'); LEGEND_CONSTANTS(:,34) = strpad('beta_S_lengthening in component PE_velocity (mN)'); LEGEND_CONSTANTS(:,35) = strpad('alpha_S_shortening in component PE_velocity (per_um)'); LEGEND_CONSTANTS(:,36) = strpad('beta_S_shortening in component PE_velocity (mN)'); LEGEND_ALGEBRAIC(:,19) = strpad('P_star in component average_crossbridge_force (dimensionless)'); LEGEND_ALGEBRAIC(:,18) = strpad('gamma in component average_crossbridge_force (dimensionless)'); LEGEND_CONSTANTS(:,47) = strpad('case_1 in component average_crossbridge_force (per_millisecond)'); LEGEND_ALGEBRAIC(:,24) = strpad('case_2 in component average_crossbridge_force (per_millisecond)'); LEGEND_CONSTANTS(:,48) = strpad('case_3 in component average_crossbridge_force (per_millisecond)'); LEGEND_ALGEBRAIC(:,25) = strpad('case_4 in component average_crossbridge_force (per_millisecond)'); LEGEND_ALGEBRAIC(:,15) = strpad('dA_dt in component calcium_handling (per_millisecond)'); LEGEND_ALGEBRAIC(:,11) = strpad('N_A in component calcium_handling (dimensionless)'); LEGEND_ALGEBRAIC(:,13) = strpad('pi_N_A in component calcium_handling (dimensionless)'); LEGEND_STATES(:,8) = strpad('B in component calcium_handling (dimensionless)'); LEGEND_ALGEBRAIC(:,17) = strpad('dB_dt in component calcium_handling (per_millisecond)'); LEGEND_STATES(:,9) = strpad('Ca_C in component calcium_handling (dimensionless)'); LEGEND_CONSTANTS(:,37) = strpad('A_tot in component calcium_handling (dimensionless)'); LEGEND_CONSTANTS(:,38) = strpad('B_tot in component calcium_handling (dimensionless)'); LEGEND_CONSTANTS(:,39) = strpad('b_on in component calcium_handling (per_millisecond)'); LEGEND_CONSTANTS(:,40) = strpad('b_off in component calcium_handling (per_millisecond)'); LEGEND_CONSTANTS(:,41) = strpad('a_c in component calcium_handling (per_millisecond2)'); LEGEND_CONSTANTS(:,42) = strpad('b_c in component calcium_handling (per_millisecond2)'); LEGEND_CONSTANTS(:,43) = strpad('r_Ca in component calcium_handling (per_millisecond)'); LEGEND_CONSTANTS(:,44) = strpad('q_Ca in component calcium_handling (dimensionless)'); LEGEND_CONSTANTS(:,45) = strpad('t_d in component calcium_handling (millisecond)'); LEGEND_RATES(:,2) = strpad('d/dt N in component crossbridge_kinetics (dimensionless)'); LEGEND_RATES(:,4) = strpad('d/dt l_1 in component length (um)'); LEGEND_RATES(:,5) = strpad('d/dt l_2 in component length (um)'); LEGEND_RATES(:,6) = strpad('d/dt l_3 in component length (um)'); LEGEND_RATES(:,1) = strpad('d/dt v in component CE_velocity (um_per_msec)'); LEGEND_RATES(:,3) = strpad('d/dt w in component PE_velocity (um_per_msec)'); LEGEND_RATES(:,7) = strpad('d/dt A in component calcium_handling (dimensionless)'); LEGEND_RATES(:,8) = strpad('d/dt B in component calcium_handling (dimensionless)'); LEGEND_RATES(:,9) = strpad('d/dt Ca_C in component calcium_handling (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 = []; CONSTANTS(:,1) = 1; CONSTANTS(:,2) = 19; CONSTANTS(:,3) = 2.9; CONSTANTS(:,4) = 14.6; CONSTANTS(:,5) = 0.01; CONSTANTS(:,6) = 48; CONSTANTS(:,7) = 0.1; CONSTANTS(:,8) = 960; CONSTANTS(:,9) = 0.6; CONSTANTS(:,10) = 3; CONSTANTS(:,11) = 0.705; CONSTANTS(:,12) = 3; CONSTANTS(:,13) = 0.9; CONSTANTS(:,14) = 0.0056; CONSTANTS(:,15) = 0.25; CONSTANTS(:,16) = 0.5; CONSTANTS(:,17) = 4; CONSTANTS(:,18) = 1; CONSTANTS(:,19) = 0.77; CONSTANTS(:,20) = 0.017; CONSTANTS(:,21) = 0.26; CONSTANTS(:,22) = 0.03; CONSTANTS(:,23) = 4; CONSTANTS(:,24) = 4; CONSTANTS(:,25) = 4; CONSTANTS(:,26) = 2.9e-2; CONSTANTS(:,27) = 0.2; CONSTANTS(:,28) = 2.8; STATES(:,1) = 0; STATES(:,2) = 1; STATES(:,3) = 0; STATES(:,4) = 1; STATES(:,5) = 1; STATES(:,6) = 1; STATES(:,7) = 0; CONSTANTS(:,29) = 16; CONSTANTS(:,30) = 15; CONSTANTS(:,31) = 16; CONSTANTS(:,32) = 15; CONSTANTS(:,33) = 39; CONSTANTS(:,34) = 80; CONSTANTS(:,35) = 46; CONSTANTS(:,36) = 60; STATES(:,8) = 0; STATES(:,9) = 0; CONSTANTS(:,37) = 1; CONSTANTS(:,38) = 0.4; CONSTANTS(:,39) = 2.6; CONSTANTS(:,40) = 0.182; CONSTANTS(:,41) = 0.005; CONSTANTS(:,42) = 0.03; CONSTANTS(:,43) = 0.65; CONSTANTS(:,44) = 50; CONSTANTS(:,45) = 33; CONSTANTS(:,46) = CONSTANTS(:,14)./10.0000; CONSTANTS(:,47) = ( CONSTANTS(:,15).*(0.400000+ 0.400000.*CONSTANTS(:,15)))./( CONSTANTS(:,14).*power( (CONSTANTS(:,15)+1.00000).*0.400000, 2.00000)); CONSTANTS(:,48) = ( 0.400000.*CONSTANTS(:,15)+1.00000)./( CONSTANTS(:,15).*CONSTANTS(:,14)); 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(:,5) = piecewise({CONSTANTS(:,1)==1.00000, 0.00000 }, - STATES(:,3)); RATES(:,6) = ALGEBRAIC(:,5); ALGEBRAIC(:,10) = STATES(:,1); RATES(:,4) = ALGEBRAIC(:,10); ALGEBRAIC(:,12) = STATES(:,3); RATES(:,5) = ALGEBRAIC(:,12); ALGEBRAIC(:,9) = (STATES(:,4)+CONSTANTS(:,19))./(0.460000+CONSTANTS(:,19)); ALGEBRAIC(:,11) = STATES(:,2)./( ALGEBRAIC(:,9).*STATES(:,7)); ALGEBRAIC(:,13) = piecewise({ALGEBRAIC(:,11)>=1.00000, 1.00000 }, power(0.0200000, ALGEBRAIC(:,11))); ALGEBRAIC(:,15) = CONSTANTS(:,26).*(CONSTANTS(:,37) - STATES(:,7)).*STATES(:,9) - CONSTANTS(:,27).*exp( - CONSTANTS(:,28).*STATES(:,7)).*ALGEBRAIC(:,13).*STATES(:,7); RATES(:,7) = ALGEBRAIC(:,15); ALGEBRAIC(:,17) = CONSTANTS(:,39).*(CONSTANTS(:,38) - STATES(:,8)).*STATES(:,9) - CONSTANTS(:,40).*STATES(:,8); RATES(:,8) = ALGEBRAIC(:,17); RATES(:,9) = piecewise({VOI<CONSTANTS(:,45), CONSTANTS(:,42).*VOI.*(1.00000 - exp( - CONSTANTS(:,41).*power(VOI, 2.00000))).*exp( - CONSTANTS(:,41).*power(VOI, 2.00000)) }, ( - ALGEBRAIC(:,15) - ALGEBRAIC(:,17)) - CONSTANTS(:,43).*exp( - CONSTANTS(:,44).*STATES(:,9)).*STATES(:,9)); ALGEBRAIC(:,7) = power(STATES(:,7), CONSTANTS(:,10))./(power(STATES(:,7), CONSTANTS(:,10))+power(CONSTANTS(:,9), CONSTANTS(:,10))); ALGEBRAIC(:,8) = 0.600000.*STATES(:,4)+0.500000; ALGEBRAIC(:,4) = piecewise({STATES(:,1)<=0.00000, CONSTANTS(:,20) - ( CONSTANTS(:,21).*STATES(:,1))./CONSTANTS(:,14) }, CONSTANTS(:,22)); ALGEBRAIC(:,18) = ( CONSTANTS(:,15).*CONSTANTS(:,16).*power(CONSTANTS(:,46)./CONSTANTS(:,14), 2.00000))./( 3.00000.*CONSTANTS(:,15).*CONSTANTS(:,16) - ( (CONSTANTS(:,15)+1.00000).*STATES(:,1))./CONSTANTS(:,14)); ALGEBRAIC(:,19) = piecewise({STATES(:,1)<=0.00000, ( CONSTANTS(:,15).*(1.00000+STATES(:,1)./CONSTANTS(:,14)))./(CONSTANTS(:,15) - STATES(:,1)./CONSTANTS(:,14)) }, (1.00000+CONSTANTS(:,16)) - ( power(CONSTANTS(:,16), 2.00000).*CONSTANTS(:,15))./( (( CONSTANTS(:,15).*CONSTANTS(:,16))./ALGEBRAIC(:,18)).*power(STATES(:,1)./CONSTANTS(:,14), 2.00000)+( (CONSTANTS(:,15)+1.00000).*STATES(:,1))./CONSTANTS(:,14)+ CONSTANTS(:,15).*CONSTANTS(:,16))); ALGEBRAIC(:,20) = piecewise({ - CONSTANTS(:,14)<=STATES(:,1)&STATES(:,1)<=0.00000, 1.00000+( 0.600000.*STATES(:,1))./CONSTANTS(:,14) , 0.00000<STATES(:,1)&STATES(:,1)<=CONSTANTS(:,46), ALGEBRAIC(:,19)./(( (( 0.400000.*CONSTANTS(:,15)+1.00000)./CONSTANTS(:,15)).*STATES(:,1))./CONSTANTS(:,14)+1.00000) }, ( ALGEBRAIC(:,19).*exp( - CONSTANTS(:,25).*power((STATES(:,1) - CONSTANTS(:,46))./CONSTANTS(:,14), CONSTANTS(:,18))))./(( (( 0.400000.*CONSTANTS(:,15)+1.00000)./CONSTANTS(:,15)).*STATES(:,1))./CONSTANTS(:,14)+1.00000)); ALGEBRAIC(:,21) = CONSTANTS(:,11).*CONSTANTS(:,12).*ALGEBRAIC(:,4).*CONSTANTS(:,13).*ALGEBRAIC(:,20); ALGEBRAIC(:,22) = CONSTANTS(:,12).*ALGEBRAIC(:,4).*(1.00000 - CONSTANTS(:,11).*CONSTANTS(:,13).*ALGEBRAIC(:,20)); ALGEBRAIC(:,23) = ALGEBRAIC(:,21).*ALGEBRAIC(:,7).*ALGEBRAIC(:,8).*ALGEBRAIC(:,9).*(1.00000 - STATES(:,2)) - ALGEBRAIC(:,22).*STATES(:,2); RATES(:,2) = ALGEBRAIC(:,23); ALGEBRAIC(:,14) = piecewise({ALGEBRAIC(:,10)<=0.00000, CONSTANTS(:,30).*exp( CONSTANTS(:,29).*STATES(:,4)) }, CONSTANTS(:,32).*exp( CONSTANTS(:,31).*STATES(:,4))); ALGEBRAIC(:,26) = ALGEBRAIC(:,19)./ALGEBRAIC(:,20); ALGEBRAIC(:,24) = ( CONSTANTS(:,15).*1.00000.*(1.00000+ 0.400000.*CONSTANTS(:,15)+( 1.20000.*STATES(:,1))./CONSTANTS(:,14)+ 0.600000.*power(STATES(:,1)./CONSTANTS(:,14), 2.00000)))./( CONSTANTS(:,14).*power( (CONSTANTS(:,15) - STATES(:,1)./CONSTANTS(:,14)).*(1.00000+( 0.600000.*STATES(:,1))./CONSTANTS(:,14)), 2.00000)); ALGEBRAIC(:,25) = (1.00000./CONSTANTS(:,14)).*exp( - CONSTANTS(:,25).*power(STATES(:,1)./CONSTANTS(:,14) - CONSTANTS(:,46)./CONSTANTS(:,14), CONSTANTS(:,18))).*(( 0.400000.*CONSTANTS(:,15)+1.00000)./CONSTANTS(:,15)+ CONSTANTS(:,25).*CONSTANTS(:,17).*(1.00000+( ( 0.400000.*CONSTANTS(:,15)+1.00000).*STATES(:,1))./( CONSTANTS(:,15).*CONSTANTS(:,14)))).*power(STATES(:,1)./CONSTANTS(:,14) - CONSTANTS(:,46)./CONSTANTS(:,14), CONSTANTS(:,18) - 1.00000); [CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS, STATES, ALGEBRAIC); RATES(:,1) = ALGEBRAIC(:,28); ALGEBRAIC(:,16) = piecewise({ALGEBRAIC(:,12)<=ALGEBRAIC(:,10), CONSTANTS(:,34).*exp( CONSTANTS(:,33).*(STATES(:,5) - STATES(:,4))) }, CONSTANTS(:,36).*exp( CONSTANTS(:,35).*(STATES(:,5) - STATES(:,4)))); RATES(:,3) = piecewise({CONSTANTS(:,1)==1.00000, (( ALGEBRAIC(:,16).*(ALGEBRAIC(:,28) - CONSTANTS(:,24).*power(STATES(:,3) - STATES(:,1), 2.00000)) - CONSTANTS(:,2).*CONSTANTS(:,3).*exp( CONSTANTS(:,2).*(STATES(:,5) - STATES(:,4))).*(STATES(:,3) - STATES(:,1)).*1.00000) - CONSTANTS(:,4).*CONSTANTS(:,5).*exp( CONSTANTS(:,4).*STATES(:,5)).*STATES(:,3).*1.00000)./ALGEBRAIC(:,16) }, (( ALGEBRAIC(:,16).*(ALGEBRAIC(:,28) - CONSTANTS(:,24).*power(STATES(:,3) - STATES(:,1), 2.00000)) - CONSTANTS(:,2).*CONSTANTS(:,3).*exp( CONSTANTS(:,2).*(STATES(:,5) - STATES(:,4))).*(STATES(:,3) - STATES(:,1)).*1.00000) - ( CONSTANTS(:,4).*CONSTANTS(:,5).*exp( CONSTANTS(:,4).*STATES(:,5))+ CONSTANTS(:,6).*CONSTANTS(:,7).*exp( CONSTANTS(:,6).*STATES(:,6))).*STATES(:,3).*1.00000)./ALGEBRAIC(:,16)); 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(:,5) = piecewise({CONSTANTS(:,1)==1.00000, 0.00000 }, - STATES(:,3)); ALGEBRAIC(:,10) = STATES(:,1); ALGEBRAIC(:,12) = STATES(:,3); ALGEBRAIC(:,9) = (STATES(:,4)+CONSTANTS(:,19))./(0.460000+CONSTANTS(:,19)); ALGEBRAIC(:,11) = STATES(:,2)./( ALGEBRAIC(:,9).*STATES(:,7)); ALGEBRAIC(:,13) = piecewise({ALGEBRAIC(:,11)>=1.00000, 1.00000 }, power(0.0200000, ALGEBRAIC(:,11))); ALGEBRAIC(:,15) = CONSTANTS(:,26).*(CONSTANTS(:,37) - STATES(:,7)).*STATES(:,9) - CONSTANTS(:,27).*exp( - CONSTANTS(:,28).*STATES(:,7)).*ALGEBRAIC(:,13).*STATES(:,7); ALGEBRAIC(:,17) = CONSTANTS(:,39).*(CONSTANTS(:,38) - STATES(:,8)).*STATES(:,9) - CONSTANTS(:,40).*STATES(:,8); ALGEBRAIC(:,7) = power(STATES(:,7), CONSTANTS(:,10))./(power(STATES(:,7), CONSTANTS(:,10))+power(CONSTANTS(:,9), CONSTANTS(:,10))); ALGEBRAIC(:,8) = 0.600000.*STATES(:,4)+0.500000; ALGEBRAIC(:,4) = piecewise({STATES(:,1)<=0.00000, CONSTANTS(:,20) - ( CONSTANTS(:,21).*STATES(:,1))./CONSTANTS(:,14) }, CONSTANTS(:,22)); ALGEBRAIC(:,18) = ( CONSTANTS(:,15).*CONSTANTS(:,16).*power(CONSTANTS(:,46)./CONSTANTS(:,14), 2.00000))./( 3.00000.*CONSTANTS(:,15).*CONSTANTS(:,16) - ( (CONSTANTS(:,15)+1.00000).*STATES(:,1))./CONSTANTS(:,14)); ALGEBRAIC(:,19) = piecewise({STATES(:,1)<=0.00000, ( CONSTANTS(:,15).*(1.00000+STATES(:,1)./CONSTANTS(:,14)))./(CONSTANTS(:,15) - STATES(:,1)./CONSTANTS(:,14)) }, (1.00000+CONSTANTS(:,16)) - ( power(CONSTANTS(:,16), 2.00000).*CONSTANTS(:,15))./( (( CONSTANTS(:,15).*CONSTANTS(:,16))./ALGEBRAIC(:,18)).*power(STATES(:,1)./CONSTANTS(:,14), 2.00000)+( (CONSTANTS(:,15)+1.00000).*STATES(:,1))./CONSTANTS(:,14)+ CONSTANTS(:,15).*CONSTANTS(:,16))); ALGEBRAIC(:,20) = piecewise({ - CONSTANTS(:,14)<=STATES(:,1)&STATES(:,1)<=0.00000, 1.00000+( 0.600000.*STATES(:,1))./CONSTANTS(:,14) , 0.00000<STATES(:,1)&STATES(:,1)<=CONSTANTS(:,46), ALGEBRAIC(:,19)./(( (( 0.400000.*CONSTANTS(:,15)+1.00000)./CONSTANTS(:,15)).*STATES(:,1))./CONSTANTS(:,14)+1.00000) }, ( ALGEBRAIC(:,19).*exp( - CONSTANTS(:,25).*power((STATES(:,1) - CONSTANTS(:,46))./CONSTANTS(:,14), CONSTANTS(:,18))))./(( (( 0.400000.*CONSTANTS(:,15)+1.00000)./CONSTANTS(:,15)).*STATES(:,1))./CONSTANTS(:,14)+1.00000)); ALGEBRAIC(:,21) = CONSTANTS(:,11).*CONSTANTS(:,12).*ALGEBRAIC(:,4).*CONSTANTS(:,13).*ALGEBRAIC(:,20); ALGEBRAIC(:,22) = CONSTANTS(:,12).*ALGEBRAIC(:,4).*(1.00000 - CONSTANTS(:,11).*CONSTANTS(:,13).*ALGEBRAIC(:,20)); ALGEBRAIC(:,23) = ALGEBRAIC(:,21).*ALGEBRAIC(:,7).*ALGEBRAIC(:,8).*ALGEBRAIC(:,9).*(1.00000 - STATES(:,2)) - ALGEBRAIC(:,22).*STATES(:,2); ALGEBRAIC(:,14) = piecewise({ALGEBRAIC(:,10)<=0.00000, CONSTANTS(:,30).*exp( CONSTANTS(:,29).*STATES(:,4)) }, CONSTANTS(:,32).*exp( CONSTANTS(:,31).*STATES(:,4))); ALGEBRAIC(:,26) = ALGEBRAIC(:,19)./ALGEBRAIC(:,20); ALGEBRAIC(:,24) = ( CONSTANTS(:,15).*1.00000.*(1.00000+ 0.400000.*CONSTANTS(:,15)+( 1.20000.*STATES(:,1))./CONSTANTS(:,14)+ 0.600000.*power(STATES(:,1)./CONSTANTS(:,14), 2.00000)))./( CONSTANTS(:,14).*power( (CONSTANTS(:,15) - STATES(:,1)./CONSTANTS(:,14)).*(1.00000+( 0.600000.*STATES(:,1))./CONSTANTS(:,14)), 2.00000)); ALGEBRAIC(:,25) = (1.00000./CONSTANTS(:,14)).*exp( - CONSTANTS(:,25).*power(STATES(:,1)./CONSTANTS(:,14) - CONSTANTS(:,46)./CONSTANTS(:,14), CONSTANTS(:,18))).*(( 0.400000.*CONSTANTS(:,15)+1.00000)./CONSTANTS(:,15)+ CONSTANTS(:,25).*CONSTANTS(:,17).*(1.00000+( ( 0.400000.*CONSTANTS(:,15)+1.00000).*STATES(:,1))./( CONSTANTS(:,15).*CONSTANTS(:,14)))).*power(STATES(:,1)./CONSTANTS(:,14) - CONSTANTS(:,46)./CONSTANTS(:,14), CONSTANTS(:,18) - 1.00000); ALGEBRAIC(:,16) = piecewise({ALGEBRAIC(:,12)<=ALGEBRAIC(:,10), CONSTANTS(:,34).*exp( CONSTANTS(:,33).*(STATES(:,5) - STATES(:,4))) }, CONSTANTS(:,36).*exp( CONSTANTS(:,35).*(STATES(:,5) - STATES(:,4)))); ALGEBRAIC(:,1) = CONSTANTS(:,7).*(exp( CONSTANTS(:,6).*STATES(:,6)) - 1.00000); ALGEBRAIC(:,2) = CONSTANTS(:,3).*(exp( CONSTANTS(:,2).*(STATES(:,5) - STATES(:,4))) - 1.00000); ALGEBRAIC(:,3) = CONSTANTS(:,5).*(exp( CONSTANTS(:,4).*STATES(:,5)) - 1.00000); ALGEBRAIC(:,6) = ALGEBRAIC(:,1); ALGEBRAIC(:,27) = CONSTANTS(:,8).*ALGEBRAIC(:,26).*STATES(:,2); 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(:,28) = soln(1); ALGEBRAIC(:,29) = soln(2); else SET_ALGEBRAIC(:,28) = logical(1); SET_ALGEBRAIC(:,29) = 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(:,28) = soln(1); TEMP_ALGEBRAIC(:,29) = soln(2); ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC); end end end function resid = residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES) ALGEBRAIC(:,28) = algebraicCandidate(1); ALGEBRAIC(:,29) = algebraicCandidate(2); resid(1) = ALGEBRAIC(:,28) - piecewise({CONSTANTS(:,1)==1.00000, ( CONSTANTS(:,8).*ALGEBRAIC(:,23).*ALGEBRAIC(:,26).*1.00000+ CONSTANTS(:,23).*ALGEBRAIC(:,14).*power(STATES(:,1), 2.00000)+ CONSTANTS(:,4).*CONSTANTS(:,5).*exp( CONSTANTS(:,4).*STATES(:,5)).*STATES(:,3).*1.00000)./( CONSTANTS(:,8).*STATES(:,2).*ALGEBRAIC(:,29).*1.00000+ALGEBRAIC(:,14)) }, ( CONSTANTS(:,8).*ALGEBRAIC(:,23).*ALGEBRAIC(:,26).*1.00000+ CONSTANTS(:,23).*ALGEBRAIC(:,14).*power(STATES(:,1), 2.00000)+ ( CONSTANTS(:,4).*CONSTANTS(:,5).*exp( CONSTANTS(:,4).*STATES(:,5))+ CONSTANTS(:,6).*CONSTANTS(:,7).*exp( CONSTANTS(:,6).*STATES(:,6))).*STATES(:,3).*1.00000)./( CONSTANTS(:,8).*STATES(:,2).*ALGEBRAIC(:,29).*1.00000+ALGEBRAIC(:,14))); resid(2) = ALGEBRAIC(:,29) - piecewise({STATES(:,1)<= - CONSTANTS(:,14), CONSTANTS(:,47).*ALGEBRAIC(:,28) , - CONSTANTS(:,14)<STATES(:,1)&STATES(:,1)<=0.00000, ALGEBRAIC(:,24).*ALGEBRAIC(:,28) , 0.00000<STATES(:,1)&STATES(:,1)<=CONSTANTS(:,46), CONSTANTS(:,48).*ALGEBRAIC(:,28) }, ALGEBRAIC(:,25).*ALGEBRAIC(:,28)); 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