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 =13;
end
% There are a total of 7 entries in each of the rate and state variable arrays.
% There are a total of 41 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(:,41) = strpad('F_SE in component F_SE (newton)');
LEGEND_CONSTANTS(:,1) = strpad('cT in component F_SE (dimensionless)');
LEGEND_CONSTANTS(:,2) = strpad('kT in component F_SE (dimensionless)');
LEGEND_CONSTANTS(:,3) = strpad('LT_r in component F_SE (dimensionless)');
LEGEND_CONSTANTS(:,4) = strpad('LT in component user_defined_constants (dimensionless)');
LEGEND_CONSTANTS(:,5) = strpad('F_max in component user_defined_constants (newton)');
LEGEND_ALGEBRAIC(:,2) = strpad('F_PE1 in component F_PE1 (dimensionless)');
LEGEND_CONSTANTS(:,6) = strpad('c1 in component F_PE1 (dimensionless)');
LEGEND_CONSTANTS(:,7) = strpad('k1 in component F_PE1 (dimensionless)');
LEGEND_CONSTANTS(:,8) = strpad('L_r1 in component F_PE1 (dimensionless)');
LEGEND_CONSTANTS(:,9) = strpad('eta in component F_PE1 (millisecond)');
LEGEND_STATES(:,1) = strpad('L in component L (dimensionless)');
LEGEND_CONSTANTS(:,10) = strpad('L_max in component user_defined_constants (dimensionless)');
LEGEND_STATES(:,2) = strpad('V in component V (first_order_rate_constant)');
LEGEND_ALGEBRAIC(:,5) = strpad('F_PE2 in component F_PE2 (dimensionless)');
LEGEND_CONSTANTS(:,11) = strpad('c2 in component F_PE2 (dimensionless)');
LEGEND_CONSTANTS(:,12) = strpad('k2 in component F_PE2 (dimensionless)');
LEGEND_CONSTANTS(:,13) = strpad('L_r2 in component F_PE2 (dimensionless)');
LEGEND_ALGEBRAIC(:,6) = strpad('FL in component FL (dimensionless)');
LEGEND_CONSTANTS(:,14) = strpad('beta in component FL (dimensionless)');
LEGEND_CONSTANTS(:,15) = strpad('omega in component FL (dimensionless)');
LEGEND_CONSTANTS(:,16) = strpad('rho in component FL (dimensionless)');
LEGEND_ALGEBRAIC(:,7) = strpad('FV in component FV (dimensionless)');
LEGEND_CONSTANTS(:,17) = strpad('av0 in component FV (dimensionless)');
LEGEND_CONSTANTS(:,18) = strpad('av1 in component FV (dimensionless)');
LEGEND_CONSTANTS(:,19) = strpad('av2 in component FV (dimensionless)');
LEGEND_CONSTANTS(:,20) = strpad('cv0 in component FV (dimensionless)');
LEGEND_CONSTANTS(:,21) = strpad('cv1 in component FV (dimensionless)');
LEGEND_CONSTANTS(:,22) = strpad('bv in component FV (first_order_rate_constant)');
LEGEND_CONSTANTS(:,23) = strpad('V_max in component FV (first_order_rate_constant)');
LEGEND_ALGEBRAIC(:,8) = strpad('Af in component Af (dimensionless)');
LEGEND_CONSTANTS(:,24) = strpad('af in component Af (dimensionless)');
LEGEND_CONSTANTS(:,25) = strpad('nf0 in component Af (dimensionless)');
LEGEND_CONSTANTS(:,26) = strpad('nf1 in component Af (dimensionless)');
LEGEND_CONSTANTS(:,27) = strpad('nf in component Af (dimensionless)');
LEGEND_STATES(:,3) = strpad('Y in component Y (dimensionless)');
LEGEND_STATES(:,4) = strpad('S in component S (dimensionless)');
LEGEND_STATES(:,5) = strpad('f_eff in component rise_and_fall_time (dimensionless)');
LEGEND_STATES(:,6) = strpad('L_eff in component L_eff (dimensionless)');
LEGEND_ALGEBRAIC(:,9) = strpad('F0 in component F0 (dimensionless)');
LEGEND_ALGEBRAIC(:,12) = strpad('F_CE in component F_CE (newton)');
LEGEND_ALGEBRAIC(:,13) = strpad('F_total in component F_total (newton)');
LEGEND_CONSTANTS(:,28) = strpad('T_L in component L_eff (millisecond)');
LEGEND_CONSTANTS(:,29) = strpad('T_s in component S (millisecond)');
LEGEND_CONSTANTS(:,30) = strpad('as1 in component S (dimensionless)');
LEGEND_CONSTANTS(:,31) = strpad('as2 in component S (dimensionless)');
LEGEND_ALGEBRAIC(:,1) = strpad('as_ in component S (dimensionless)');
LEGEND_CONSTANTS(:,32) = strpad('c_Y in component Y (dimensionless)');
LEGEND_CONSTANTS(:,33) = strpad('V_Y in component Y (first_order_rate_constant)');
LEGEND_CONSTANTS(:,34) = strpad('T_Y in component Y (millisecond)');
LEGEND_STATES(:,7) = strpad('f_int in component rise_and_fall_time (dimensionless)');
LEGEND_ALGEBRAIC(:,10) = strpad('df_eff_dt in component rise_and_fall_time (first_order_rate_constant)');
LEGEND_ALGEBRAIC(:,11) = strpad('T_f in component rise_and_fall_time (millisecond)');
LEGEND_CONSTANTS(:,35) = strpad('T_f1 in component rise_and_fall_time (millisecond)');
LEGEND_CONSTANTS(:,36) = strpad('T_f2 in component rise_and_fall_time (millisecond)');
LEGEND_CONSTANTS(:,37) = strpad('T_f3 in component rise_and_fall_time (millisecond)');
LEGEND_CONSTANTS(:,38) = strpad('T_f4 in component rise_and_fall_time (millisecond)');
LEGEND_CONSTANTS(:,39) = strpad('f_env in component user_defined_constants (dimensionless)');
LEGEND_CONSTANTS(:,40) = strpad('mass in component V (kilogram)');
LEGEND_ALGEBRAIC(:,3) = strpad('V0 in component V0 (first_order_rate_constant)');
LEGEND_ALGEBRAIC(:,4) = strpad('L0 in component L0 (dimensionless)');
LEGEND_RATES(:,6) = strpad('d/dt L_eff in component L_eff (dimensionless)');
LEGEND_RATES(:,4) = strpad('d/dt S in component S (dimensionless)');
LEGEND_RATES(:,3) = strpad('d/dt Y in component Y (dimensionless)');
LEGEND_RATES(:,7) = strpad('d/dt f_int in component rise_and_fall_time (dimensionless)');
LEGEND_RATES(:,5) = strpad('d/dt f_eff in component rise_and_fall_time (dimensionless)');
LEGEND_RATES(:,2) = strpad('d/dt V in component V (first_order_rate_constant)');
LEGEND_RATES(:,1) = strpad('d/dt L in component L (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) = 27.8;
CONSTANTS(:,2) = 0.0047;
CONSTANTS(:,3) = 0.964;
CONSTANTS(:,4) = 0.02;
CONSTANTS(:,5) = 23;
CONSTANTS(:,6) = 23;
CONSTANTS(:,7) = 0.046;
CONSTANTS(:,8) = 1.17;
CONSTANTS(:,9) = 0.001;
STATES(:,1) = 0.15;
CONSTANTS(:,10) = 0.13;
STATES(:,2) = 0.09314;
CONSTANTS(:,11) = 23;
CONSTANTS(:,12) = 0.046;
CONSTANTS(:,13) = 1.17;
CONSTANTS(:,14) = 1.55;
CONSTANTS(:,15) = 0.75;
CONSTANTS(:,16) = 2.12;
CONSTANTS(:,17) = -1.53;
CONSTANTS(:,18) = 0;
CONSTANTS(:,19) = 0;
CONSTANTS(:,20) = -5.7;
CONSTANTS(:,21) = 9.18;
CONSTANTS(:,22) = 0.69;
CONSTANTS(:,23) = -9.15;
CONSTANTS(:,24) = 0.56;
CONSTANTS(:,25) = 2.1;
CONSTANTS(:,26) = 3.3;
CONSTANTS(:,27) = 1;
STATES(:,3) = 1;
STATES(:,4) = 1;
STATES(:,5) = 0;
STATES(:,6) = 0.1497;
CONSTANTS(:,28) = 0.088;
CONSTANTS(:,29) = 43;
CONSTANTS(:,30) = 1.76;
CONSTANTS(:,31) = 0.96;
CONSTANTS(:,32) = 0.35;
CONSTANTS(:,33) = 0.1;
CONSTANTS(:,34) = 200;
STATES(:,7) = 0;
CONSTANTS(:,35) = 0.35;
CONSTANTS(:,36) = 0.1;
CONSTANTS(:,37) = 200;
CONSTANTS(:,38) = 200;
CONSTANTS(:,39) = 1;
CONSTANTS(:,40) = 0.005;
CONSTANTS(:,41) = CONSTANTS(:,1).*CONSTANTS(:,5).*CONSTANTS(:,2).*log(exp((CONSTANTS(:,4) - CONSTANTS(:,3))./CONSTANTS(:,2))+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
RATES(:,3) = (1.00000 - ( CONSTANTS(:,32).*(1.00000 - exp( - abs(STATES(:,2))./CONSTANTS(:,33)))+STATES(:,3)))./CONSTANTS(:,34);
RATES(:,1) = STATES(:,2);
ALGEBRAIC(:,1) = piecewise({STATES(:,5)<0.100000, CONSTANTS(:,30) }, CONSTANTS(:,31));
RATES(:,4) = (ALGEBRAIC(:,1) - STATES(:,4))./CONSTANTS(:,29);
ALGEBRAIC(:,8) = 1.00000 - exp( - power(( STATES(:,3).*STATES(:,4).*STATES(:,5))./( CONSTANTS(:,24).*CONSTANTS(:,27)), CONSTANTS(:,27)));
RATES(:,6) = power(STATES(:,1) - STATES(:,6), 3.00000)./( CONSTANTS(:,28).*(1.00000 - ALGEBRAIC(:,8)));
[CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS, STATES, ALGEBRAIC);
RATES(:,7) = (CONSTANTS(:,39) - STATES(:,7))./ALGEBRAIC(:,11);
RATES(:,5) = ALGEBRAIC(:,10);
ALGEBRAIC(:,2) = CONSTANTS(:,6).*CONSTANTS(:,7).*log(exp((STATES(:,1)./CONSTANTS(:,10) - CONSTANTS(:,8))./CONSTANTS(:,7))+1.00000)+ CONSTANTS(:,9).*STATES(:,2);
ALGEBRAIC(:,5) = CONSTANTS(:,11).*(exp( CONSTANTS(:,12).*(STATES(:,1) - CONSTANTS(:,13))) - 1.00000);
ALGEBRAIC(:,6) = exp( - power(abs((power(STATES(:,1), CONSTANTS(:,14)) - 1.00000)./CONSTANTS(:,15)), CONSTANTS(:,16)));
ALGEBRAIC(:,7) = piecewise({STATES(:,2)<=0.00000, (CONSTANTS(:,23) - STATES(:,2))./(CONSTANTS(:,23)+ (CONSTANTS(:,20)+ CONSTANTS(:,21).*STATES(:,1)).*STATES(:,2)) }, (CONSTANTS(:,22) - (CONSTANTS(:,17)+ CONSTANTS(:,18).*STATES(:,1)+ CONSTANTS(:,19).*power(STATES(:,1), 2.00000)).*STATES(:,2))./(CONSTANTS(:,22)+STATES(:,2)));
ALGEBRAIC(:,9) = ALGEBRAIC(:,8).*(ALGEBRAIC(:,6)+ALGEBRAIC(:,7)+ALGEBRAIC(:,5))+ALGEBRAIC(:,2);
ALGEBRAIC(:,12) = ALGEBRAIC(:,9).*CONSTANTS(:,5);
ALGEBRAIC(:,13) = CONSTANTS(:,41) - ALGEBRAIC(:,12);
RATES(:,2) = ALGEBRAIC(:,13)./( 1.00000.*CONSTANTS(:,40));
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({STATES(:,5)<0.100000, CONSTANTS(:,30) }, CONSTANTS(:,31));
ALGEBRAIC(:,8) = 1.00000 - exp( - power(( STATES(:,3).*STATES(:,4).*STATES(:,5))./( CONSTANTS(:,24).*CONSTANTS(:,27)), CONSTANTS(:,27)));
ALGEBRAIC(:,2) = CONSTANTS(:,6).*CONSTANTS(:,7).*log(exp((STATES(:,1)./CONSTANTS(:,10) - CONSTANTS(:,8))./CONSTANTS(:,7))+1.00000)+ CONSTANTS(:,9).*STATES(:,2);
ALGEBRAIC(:,5) = CONSTANTS(:,11).*(exp( CONSTANTS(:,12).*(STATES(:,1) - CONSTANTS(:,13))) - 1.00000);
ALGEBRAIC(:,6) = exp( - power(abs((power(STATES(:,1), CONSTANTS(:,14)) - 1.00000)./CONSTANTS(:,15)), CONSTANTS(:,16)));
ALGEBRAIC(:,7) = piecewise({STATES(:,2)<=0.00000, (CONSTANTS(:,23) - STATES(:,2))./(CONSTANTS(:,23)+ (CONSTANTS(:,20)+ CONSTANTS(:,21).*STATES(:,1)).*STATES(:,2)) }, (CONSTANTS(:,22) - (CONSTANTS(:,17)+ CONSTANTS(:,18).*STATES(:,1)+ CONSTANTS(:,19).*power(STATES(:,1), 2.00000)).*STATES(:,2))./(CONSTANTS(:,22)+STATES(:,2)));
ALGEBRAIC(:,9) = ALGEBRAIC(:,8).*(ALGEBRAIC(:,6)+ALGEBRAIC(:,7)+ALGEBRAIC(:,5))+ALGEBRAIC(:,2);
ALGEBRAIC(:,12) = ALGEBRAIC(:,9).*CONSTANTS(:,5);
ALGEBRAIC(:,13) = CONSTANTS(:,41) - ALGEBRAIC(:,12);
ALGEBRAIC(:,3) = STATES(:,2)./CONSTANTS(:,10);
ALGEBRAIC(:,4) = STATES(:,1)./CONSTANTS(:,10);
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(:,10) = soln(1);
ALGEBRAIC(:,11) = soln(2);
else
SET_ALGEBRAIC(:,10) = logical(1);
SET_ALGEBRAIC(:,11) = 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(:,10) = soln(1);
TEMP_ALGEBRAIC(:,11) = soln(2);
ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
end
end
end
function resid = residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
ALGEBRAIC(:,10) = algebraicCandidate(1);
ALGEBRAIC(:,11) = algebraicCandidate(2);
resid(1) = ALGEBRAIC(:,10) - (STATES(:,7) - STATES(:,5))./ALGEBRAIC(:,11);
resid(2) = ALGEBRAIC(:,11) - piecewise({ALGEBRAIC(:,10)>=0.00000, CONSTANTS(:,35).*power(STATES(:,1), 2.00000)+ CONSTANTS(:,36).*CONSTANTS(:,39) }, (CONSTANTS(:,37)+ CONSTANTS(:,38).*ALGEBRAIC(:,8))./STATES(:,1));
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