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 3 entries in each of the rate and state variable arrays.
% There are a total of 3 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_STATES(:,1) = strpad('q_C in component main (coulomb)');
LEGEND_ALGEBRAIC(:,3) = strpad('v_C in component main (C_per_s)');
LEGEND_ALGEBRAIC(:,1) = strpad('v_R in component main (C_per_s)');
LEGEND_STATES(:,2) = strpad('v_L in component main (C_per_s)');
LEGEND_ALGEBRAIC(:,9) = strpad('a_L in component main (C_per_s2)');
LEGEND_ALGEBRAIC(:,5) = strpad('u_C in component main (J_per_C)');
LEGEND_ALGEBRAIC(:,7) = strpad('u_R in component main (J_per_C)');
LEGEND_ALGEBRAIC(:,8) = strpad('u_L in component main (J_per_C)');
LEGEND_CONSTANTS(:,1) = strpad('C in component main (C2_per_J)');
LEGEND_CONSTANTS(:,2) = strpad('R in component main (Js_per_C2)');
LEGEND_CONSTANTS(:,3) = strpad('L in component main (Js2_per_C2)');
LEGEND_ALGEBRAIC(:,10) = strpad('P_C in component main (watt)');
LEGEND_ALGEBRAIC(:,11) = strpad('P_R in component main (watt)');
LEGEND_ALGEBRAIC(:,12) = strpad('P_L in component main (watt)');
LEGEND_ALGEBRAIC(:,13) = strpad('P_tot in component main (watt)');
LEGEND_ALGEBRAIC(:,2) = strpad('E_C in component main (joule)');
LEGEND_STATES(:,3) = strpad('E_R in component main (joule)');
LEGEND_ALGEBRAIC(:,4) = strpad('E_L in component main (joule)');
LEGEND_ALGEBRAIC(:,6) = strpad('E_tot in component main (joule)');
LEGEND_RATES(:,2) = strpad('d/dt v_L in component main (C_per_s)');
LEGEND_RATES(:,1) = strpad('d/dt q_C in component main (coulomb)');
LEGEND_RATES(:,3) = strpad('d/dt E_R in component main (joule)');
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) = 1;
STATES(:,2) = 0;
CONSTANTS(:,1) = 20;
CONSTANTS(:,2) = 2;
CONSTANTS(:,3) = 10;
STATES(:,3) = 0;
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) = STATES(:,2);
ALGEBRAIC(:,3) = - ALGEBRAIC(:,1);
RATES(:,1) = ALGEBRAIC(:,3);
ALGEBRAIC(:,5) = STATES(:,1)./CONSTANTS(:,1);
ALGEBRAIC(:,7) = ALGEBRAIC(:,1).*CONSTANTS(:,2);
[CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS, STATES, ALGEBRAIC);
[CONSTANTS, STATES, ALGEBRAIC] = rootfind_1(VOI, CONSTANTS, STATES, ALGEBRAIC);
RATES(:,2) = ALGEBRAIC(:,9);
ALGEBRAIC(:,11) = ALGEBRAIC(:,7).*ALGEBRAIC(:,1);
RATES(:,3) = ALGEBRAIC(:,11);
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) = STATES(:,2);
ALGEBRAIC(:,3) = - ALGEBRAIC(:,1);
ALGEBRAIC(:,5) = STATES(:,1)./CONSTANTS(:,1);
ALGEBRAIC(:,7) = ALGEBRAIC(:,1).*CONSTANTS(:,2);
ALGEBRAIC(:,11) = ALGEBRAIC(:,7).*ALGEBRAIC(:,1);
ALGEBRAIC(:,2) = (( 0.500000.*1.00000)./CONSTANTS(:,1)).*power(STATES(:,1), 2.00000);
ALGEBRAIC(:,4) = 0.500000.*CONSTANTS(:,3).*power(STATES(:,2), 2.00000);
ALGEBRAIC(:,6) = ALGEBRAIC(:,2)+ALGEBRAIC(:,4)+STATES(:,3);
ALGEBRAIC(:,10) = ALGEBRAIC(:,5).*ALGEBRAIC(:,3);
ALGEBRAIC(:,12) = ALGEBRAIC(:,8).*STATES(:,2);
ALGEBRAIC(:,13) = ALGEBRAIC(:,10)+ALGEBRAIC(:,11)+ALGEBRAIC(:,12);
end
% Functions required for solving differential algebraic equation
function [CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS_IN, STATES_IN, ALGEBRAIC_IN)
CONSTANTS = CONSTANTS_IN;
STATES = STATES_IN;
ALGEBRAIC = ALGEBRAIC_IN;
global initialGuess_0;
if (length(initialGuess_0) ~= 1), initialGuess_0 = 0.1;, end
options = optimset('Display', 'off', 'TolX', 1E-6);
if length(VOI) == 1
residualfn = @(algebraicCandidate)residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES);
ALGEBRAIC(:,8) = fsolve(residualfn, initialGuess_0, options);
initialGuess_0 = ALGEBRAIC(:,8);
else
SET_ALGEBRAIC(:,8) = logical(1);
for i=1:length(VOI)
residualfn = @(algebraicCandidate)residualSN_0(algebraicCandidate, ALGEBRAIC(i,:), VOI(i), CONSTANTS, STATES(i,:));
TEMP_ALGEBRAIC(:,8) = fsolve(residualfn, initialGuess_0, options);
ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
initialGuess_0 = TEMP_ALGEBRAIC(:,8);
end
end
end
function resid = residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
ALGEBRAIC(:,8) = algebraicCandidate;
resid = (ALGEBRAIC(:,5)) - (ALGEBRAIC(:,7)+ALGEBRAIC(:,8));
end
% Functions required for solving differential algebraic equation
function [CONSTANTS, STATES, ALGEBRAIC] = rootfind_1(VOI, CONSTANTS_IN, STATES_IN, ALGEBRAIC_IN)
CONSTANTS = CONSTANTS_IN;
STATES = STATES_IN;
ALGEBRAIC = ALGEBRAIC_IN;
global initialGuess_1;
if (length(initialGuess_1) ~= 1), initialGuess_1 = 0.1;, end
options = optimset('Display', 'off', 'TolX', 1E-6);
if length(VOI) == 1
residualfn = @(algebraicCandidate)residualSN_1(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES);
ALGEBRAIC(:,9) = fsolve(residualfn, initialGuess_1, options);
initialGuess_1 = ALGEBRAIC(:,9);
else
SET_ALGEBRAIC(:,9) = logical(1);
for i=1:length(VOI)
residualfn = @(algebraicCandidate)residualSN_1(algebraicCandidate, ALGEBRAIC(i,:), VOI(i), CONSTANTS, STATES(i,:));
TEMP_ALGEBRAIC(:,9) = fsolve(residualfn, initialGuess_1, options);
ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
initialGuess_1 = TEMP_ALGEBRAIC(:,9);
end
end
end
function resid = residualSN_1(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
ALGEBRAIC(:,9) = algebraicCandidate;
resid = (ALGEBRAIC(:,8)) - ( ALGEBRAIC(:,9).*CONSTANTS(:,3));
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