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 =9;
end
% There are a total of 2 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('t in component main (second)');
LEGEND_CONSTANTS(:,1) = strpad('V_m in component main (J_per_C)');
LEGEND_CONSTANTS(:,2) = strpad('RTF in component main (J_per_C)');
LEGEND_CONSTANTS(:,11) = strpad('epsilon in component main (dimensionless)');
LEGEND_STATES(:,1) = strpad('TA_i in component main (mol_per_m3)');
LEGEND_ALGEBRAIC(:,1) = strpad('CO2_o in component main (mol_per_m3)');
LEGEND_ALGEBRAIC(:,6) = strpad('CO2_i in component main (mol_per_m3)');
LEGEND_ALGEBRAIC(:,8) = strpad('HCO3_i in component main (mol_per_m3)');
LEGEND_ALGEBRAIC(:,2) = strpad('HCO3_o in component main (mol_per_m3)');
LEGEND_STATES(:,2) = strpad('H_i in component main (mol_per_m3)');
LEGEND_CONSTANTS(:,3) = strpad('H_o in component main (mol_per_m3)');
LEGEND_CONSTANTS(:,4) = strpad('H_Lim in component main (mol_per_m3)');
LEGEND_ALGEBRAIC(:,7) = strpad('M_CO2 in component main (mol_per_m2_s)');
LEGEND_ALGEBRAIC(:,9) = strpad('M_HCO3 in component main (mol_per_m2_s)');
LEGEND_ALGEBRAIC(:,4) = strpad('M_H in component main (mol_per_m2_s)');
LEGEND_ALGEBRAIC(:,3) = strpad('pH_i in component main (dimensionless)');
LEGEND_CONSTANTS(:,12) = strpad('pH_o in component main (dimensionless)');
LEGEND_CONSTANTS(:,13) = strpad('pH_Lim in component main (dimensionless)');
LEGEND_CONSTANTS(:,5) = strpad('P_CO2 in component main (m_per_s)');
LEGEND_CONSTANTS(:,6) = strpad('P_HCO3 in component main (m_per_s)');
LEGEND_CONSTANTS(:,7) = strpad('k in component main (m_per_s)');
LEGEND_CONSTANTS(:,8) = strpad('K_A in component main (mol_per_m3)');
LEGEND_CONSTANTS(:,9) = strpad('rho in component main (per_m)');
LEGEND_ALGEBRAIC(:,5) = strpad('alpha_i in component main (dimensionless)');
LEGEND_CONSTANTS(:,10) = strpad('beta in component main (mol_per_m3)');
LEGEND_RATES(:,1) = strpad('d/dt TA_i in component main (mol_per_m3)');
LEGEND_RATES(:,2) = strpad('d/dt H_i in component main (mol_per_m3)');
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) = -0.057;
CONSTANTS(:,2) = 0.0256796;
STATES(:,1) = 0.0;
STATES(:,2) = 3.981071705534970e-05;
CONSTANTS(:,3) = 1.995262314968879e-05;
CONSTANTS(:,4) = 3.981071705534970e-05;
CONSTANTS(:,5) = 6e-5;
CONSTANTS(:,6) = 5e-9;
CONSTANTS(:,7) = 0.0375;
CONSTANTS(:,8) = 1e-3;
CONSTANTS(:,9) = 8000;
CONSTANTS(:,10) = -26;
CONSTANTS(:,11) = exp( - CONSTANTS(:,1)./CONSTANTS(:,2));
CONSTANTS(:,12) = - arbitrary_log( 0.00100000.*CONSTANTS(:,3), 10);
CONSTANTS(:,13) = - arbitrary_log( 0.00100000.*CONSTANTS(:,4), 10);
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(:,1) = piecewise({VOI<100.000, 0.00000 , VOI<2800.00, 1.18770 }, 0.00000);
ALGEBRAIC(:,5) = STATES(:,2)./(STATES(:,2)+CONSTANTS(:,8));
ALGEBRAIC(:,6) = ALGEBRAIC(:,5).*STATES(:,1);
ALGEBRAIC(:,7) = CONSTANTS(:,5).*(ALGEBRAIC(:,1) - ALGEBRAIC(:,6));
ALGEBRAIC(:,8) = (1.00000 - ALGEBRAIC(:,5)).*STATES(:,1);
ALGEBRAIC(:,2) = ( CONSTANTS(:,8).*ALGEBRAIC(:,1))./CONSTANTS(:,3);
ALGEBRAIC(:,9) = ( (( CONSTANTS(:,6).*CONSTANTS(:,1))./CONSTANTS(:,2)).*(ALGEBRAIC(:,2) - ALGEBRAIC(:,8).*CONSTANTS(:,11)))./(1.00000 - CONSTANTS(:,11));
RATES(:,1) = CONSTANTS(:,9).*(ALGEBRAIC(:,7)+ALGEBRAIC(:,9));
ALGEBRAIC(:,3) = - arbitrary_log( 0.00100000.*STATES(:,2), 10);
ALGEBRAIC(:,4) = piecewise({ALGEBRAIC(:,3)<CONSTANTS(:,13), CONSTANTS(:,7).*(STATES(:,2) - CONSTANTS(:,4)) }, 0.00000);
RATES(:,2) = (( - 2.30300.*STATES(:,2))./CONSTANTS(:,10)).*CONSTANTS(:,9).*(( (1.00000 - ALGEBRAIC(:,5)).*ALGEBRAIC(:,7) - ALGEBRAIC(:,5).*ALGEBRAIC(:,9)) - ALGEBRAIC(:,4));
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<100.000, 0.00000 , VOI<2800.00, 1.18770 }, 0.00000);
ALGEBRAIC(:,5) = STATES(:,2)./(STATES(:,2)+CONSTANTS(:,8));
ALGEBRAIC(:,6) = ALGEBRAIC(:,5).*STATES(:,1);
ALGEBRAIC(:,7) = CONSTANTS(:,5).*(ALGEBRAIC(:,1) - ALGEBRAIC(:,6));
ALGEBRAIC(:,8) = (1.00000 - ALGEBRAIC(:,5)).*STATES(:,1);
ALGEBRAIC(:,2) = ( CONSTANTS(:,8).*ALGEBRAIC(:,1))./CONSTANTS(:,3);
ALGEBRAIC(:,9) = ( (( CONSTANTS(:,6).*CONSTANTS(:,1))./CONSTANTS(:,2)).*(ALGEBRAIC(:,2) - ALGEBRAIC(:,8).*CONSTANTS(:,11)))./(1.00000 - CONSTANTS(:,11));
ALGEBRAIC(:,3) = - arbitrary_log( 0.00100000.*STATES(:,2), 10);
ALGEBRAIC(:,4) = piecewise({ALGEBRAIC(:,3)<CONSTANTS(:,13), CONSTANTS(:,7).*(STATES(:,2) - CONSTANTS(:,4)) }, 0.00000);
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
% Compute a logarithm to any base" +
function x = arbitrary_log(a, base)
x = log(a) ./ log(base);
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