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 6 entries in each of the rate and state variable arrays.
% There are a total of 13 entries in the constant variable array.
%
function [VOI, STATES, ALGEBRAIC, CONSTANTS] = solveModel()
% Create ALGEBRAIC of correct size
global algebraicVariableCount; algebraicVariableCount = getAlgebraicVariableCount();
% Initialise constants and state variables
[INIT_STATES, CONSTANTS] = initConsts;
% Set timespan to solve over
tspan = [0, 10];
% Set numerical accuracy options for ODE solver
options = odeset('RelTol', 1e-06, 'AbsTol', 1e-06, 'MaxStep', 1);
% Solve model with ODE solver
[VOI, STATES] = ode15s(@(VOI, STATES)computeRates(VOI, STATES, CONSTANTS), tspan, INIT_STATES, options);
% Compute algebraic variables
[RATES, ALGEBRAIC] = computeRates(VOI, STATES, CONSTANTS);
ALGEBRAIC = computeAlgebraic(ALGEBRAIC, CONSTANTS, STATES, VOI);
% Plot state variables against variable of integration
[LEGEND_STATES, LEGEND_ALGEBRAIC, LEGEND_VOI, LEGEND_CONSTANTS] = createLegends();
figure();
plot(VOI, STATES);
xlabel(LEGEND_VOI);
l = legend(LEGEND_STATES);
set(l,'Interpreter','none');
end
function [LEGEND_STATES, LEGEND_ALGEBRAIC, LEGEND_VOI, LEGEND_CONSTANTS] = createLegends()
LEGEND_STATES = ''; LEGEND_ALGEBRAIC = ''; LEGEND_VOI = ''; LEGEND_CONSTANTS = '';
LEGEND_VOI = strpad('time in component environment (second)');
LEGEND_STATES(:,1) = strpad('D in component equations (dimensionless)');
LEGEND_STATES(:,2) = strpad('A_1 in component equations (dimensionless)');
LEGEND_STATES(:,3) = strpad('A_2 in component equations (dimensionless)');
LEGEND_ALGEBRAIC(:,1) = strpad('R_off in component equations (dimensionless)');
LEGEND_CONSTANTS(:,1) = strpad('x_0 in component equations (dimensionless)');
LEGEND_STATES(:,4) = strpad('x_1 in component equations (dimensionless)');
LEGEND_STATES(:,5) = strpad('x_2 in component equations (dimensionless)');
LEGEND_ALGEBRAIC(:,8) = strpad('g in component equations (per_second)');
LEGEND_ALGEBRAIC(:,12) = strpad('f in component equations (per_second)');
LEGEND_ALGEBRAIC(:,9) = strpad('h in component equations (per_second)');
LEGEND_ALGEBRAIC(:,4) = strpad('lambda_A1 in component equations (dimensionless)');
LEGEND_ALGEBRAIC(:,6) = strpad('lambda_A2 in component equations (dimensionless)');
LEGEND_ALGEBRAIC(:,5) = strpad('F_t in component equations (dimensionless)');
LEGEND_ALGEBRAIC(:,2) = strpad('E_1 in component equations (dimensionless)');
LEGEND_ALGEBRAIC(:,3) = strpad('E_2 in component equations (dimensionless)');
LEGEND_ALGEBRAIC(:,13) = strpad('dSL_dt in component equations (per_second)');
LEGEND_STATES(:,6) = strpad('SL in component equations (dimensionless)');
LEGEND_CONSTANTS(:,2) = strpad('k_on in component equations (per_second)');
LEGEND_CONSTANTS(:,3) = strpad('k_off in component equations (per_second)');
LEGEND_CONSTANTS(:,4) = strpad('f_r in component equations (per_second)');
LEGEND_ALGEBRAIC(:,10) = strpad('f_prime in component equations (per_second)');
LEGEND_CONSTANTS(:,5) = strpad('f_prime_0 in component equations (per_second)');
LEGEND_CONSTANTS(:,6) = strpad('h_0 in component equations (per_second)');
LEGEND_ALGEBRAIC(:,11) = strpad('h_prime in component equations (per_second)');
LEGEND_CONSTANTS(:,7) = strpad('h_prime_0 in component equations (per_second)');
LEGEND_CONSTANTS(:,8) = strpad('g_0 in component equations (per_second)');
LEGEND_CONSTANTS(:,9) = strpad('nu in component equations (dimensionless)');
LEGEND_ALGEBRAIC(:,7) = strpad('sigma in component equations (dimensionless)');
LEGEND_CONSTANTS(:,10) = strpad('sigma_minus in component equations (dimensionless)');
LEGEND_CONSTANTS(:,11) = strpad('sigma_plus in component equations (dimensionless)');
LEGEND_CONSTANTS(:,12) = strpad('R_T in component equations (dimensionless)');
LEGEND_CONSTANTS(:,13) = strpad('e_cb in component equations (dimensionless)');
LEGEND_RATES(:,1) = strpad('d/dt D in component equations (dimensionless)');
LEGEND_RATES(:,2) = strpad('d/dt A_1 in component equations (dimensionless)');
LEGEND_RATES(:,3) = strpad('d/dt A_2 in component equations (dimensionless)');
LEGEND_RATES(:,5) = strpad('d/dt x_2 in component equations (dimensionless)');
LEGEND_RATES(:,4) = strpad('d/dt x_1 in component equations (dimensionless)');
LEGEND_RATES(:,6) = strpad('d/dt SL in component equations (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) = 0.005;
STATES(:,2) = 0.005;
STATES(:,3) = 0.005;
CONSTANTS(:,1) = 1e-16;
STATES(:,4) = 1e-16;
STATES(:,5) = 1e-16;
STATES(:,6) = 2;
CONSTANTS(:,2) = 120;
CONSTANTS(:,3) = 50;
CONSTANTS(:,4) = 50;
CONSTANTS(:,5) = 400;
CONSTANTS(:,6) = 8;
CONSTANTS(:,7) = 6;
CONSTANTS(:,8) = 4;
CONSTANTS(:,9) = 3;
CONSTANTS(:,10) = 1;
CONSTANTS(:,11) = 8;
CONSTANTS(:,12) = 1;
CONSTANTS(:,13) = 1.5;
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(:,7) = piecewise({STATES(:,5)>CONSTANTS(:,1), CONSTANTS(:,11) , STATES(:,5)<CONSTANTS(:,1), CONSTANTS(:,10) }, 0.00000);
ALGEBRAIC(:,8) = CONSTANTS(:,8).*exp( ALGEBRAIC(:,7).*power(STATES(:,5) - CONSTANTS(:,1), 2.00000));
ALGEBRAIC(:,9) = CONSTANTS(:,6).*exp( ALGEBRAIC(:,7).*power(STATES(:,4), 2.00000));
ALGEBRAIC(:,11) = CONSTANTS(:,7).*exp( ALGEBRAIC(:,7).*(power(STATES(:,5), 2.00000) - power(STATES(:,4), 2.00000)));
RATES(:,3) = ALGEBRAIC(:,9).*STATES(:,2) - (ALGEBRAIC(:,11)+ALGEBRAIC(:,8)).*STATES(:,3);
ALGEBRAIC(:,1) = ((CONSTANTS(:,12) - STATES(:,1)) - STATES(:,2)) - STATES(:,3);
ALGEBRAIC(:,4) = STATES(:,2)./CONSTANTS(:,12);
ALGEBRAIC(:,6) = STATES(:,3)./CONSTANTS(:,12);
ALGEBRAIC(:,12) = CONSTANTS(:,4).*power(1.00000+ ALGEBRAIC(:,4).*(exp( (STATES(:,4)./CONSTANTS(:,1)).*(CONSTANTS(:,9) - 1.00000)) - 1.00000)+ ALGEBRAIC(:,6).*(exp( (STATES(:,5)./CONSTANTS(:,1)).*(CONSTANTS(:,9) - 1.00000)) - 1.00000), 2.00000);
ALGEBRAIC(:,10) = CONSTANTS(:,5).*exp( ALGEBRAIC(:,7).*power(STATES(:,4), 2.00000));
RATES(:,1) = ( CONSTANTS(:,2).*ALGEBRAIC(:,1)+ ALGEBRAIC(:,10).*STATES(:,2)+ ALGEBRAIC(:,8).*STATES(:,3)) - (CONSTANTS(:,3)+ALGEBRAIC(:,12)).*STATES(:,1);
RATES(:,2) = ( ALGEBRAIC(:,12).*STATES(:,1)+ ALGEBRAIC(:,11).*STATES(:,3)) - (ALGEBRAIC(:,10)+ALGEBRAIC(:,9)).*STATES(:,2);
ALGEBRAIC(:,13) = piecewise({VOI>0.00100000&VOI<0.00200000, 21.2000 }, 0.00000);
RATES(:,5) = piecewise({STATES(:,3)==0.00000, ALGEBRAIC(:,13) }, (( - ALGEBRAIC(:,9).*STATES(:,2))./STATES(:,3)).*(STATES(:,5) - CONSTANTS(:,1))+ALGEBRAIC(:,13));
RATES(:,4) = piecewise({STATES(:,2)==0.00000, ALGEBRAIC(:,13) }, - (( ALGEBRAIC(:,12).*STATES(:,1))./STATES(:,2)+( ALGEBRAIC(:,11).*STATES(:,3))./STATES(:,2)).*STATES(:,4)+ALGEBRAIC(:,13));
RATES(:,6) = ALGEBRAIC(:,13);
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(:,7) = piecewise({STATES(:,5)>CONSTANTS(:,1), CONSTANTS(:,11) , STATES(:,5)<CONSTANTS(:,1), CONSTANTS(:,10) }, 0.00000);
ALGEBRAIC(:,8) = CONSTANTS(:,8).*exp( ALGEBRAIC(:,7).*power(STATES(:,5) - CONSTANTS(:,1), 2.00000));
ALGEBRAIC(:,9) = CONSTANTS(:,6).*exp( ALGEBRAIC(:,7).*power(STATES(:,4), 2.00000));
ALGEBRAIC(:,11) = CONSTANTS(:,7).*exp( ALGEBRAIC(:,7).*(power(STATES(:,5), 2.00000) - power(STATES(:,4), 2.00000)));
ALGEBRAIC(:,1) = ((CONSTANTS(:,12) - STATES(:,1)) - STATES(:,2)) - STATES(:,3);
ALGEBRAIC(:,4) = STATES(:,2)./CONSTANTS(:,12);
ALGEBRAIC(:,6) = STATES(:,3)./CONSTANTS(:,12);
ALGEBRAIC(:,12) = CONSTANTS(:,4).*power(1.00000+ ALGEBRAIC(:,4).*(exp( (STATES(:,4)./CONSTANTS(:,1)).*(CONSTANTS(:,9) - 1.00000)) - 1.00000)+ ALGEBRAIC(:,6).*(exp( (STATES(:,5)./CONSTANTS(:,1)).*(CONSTANTS(:,9) - 1.00000)) - 1.00000), 2.00000);
ALGEBRAIC(:,10) = CONSTANTS(:,5).*exp( ALGEBRAIC(:,7).*power(STATES(:,4), 2.00000));
ALGEBRAIC(:,13) = piecewise({VOI>0.00100000&VOI<0.00200000, 21.2000 }, 0.00000);
ALGEBRAIC(:,2) = CONSTANTS(:,13).*STATES(:,2);
ALGEBRAIC(:,3) = CONSTANTS(:,13).*STATES(:,3);
ALGEBRAIC(:,5) = ALGEBRAIC(:,2).*STATES(:,4)+ ALGEBRAIC(:,3).*STATES(:,5);
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