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 =15;
end
% There are a total of 3 entries in each of the rate and state variable arrays.
% There are a total of 21 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 environment (second)');
LEGEND_ALGEBRAIC(:,8) = strpad('Pi in component TempCDa (UnitP)');
LEGEND_ALGEBRAIC(:,12) = strpad('Pi in component TempR (UnitP)');
LEGEND_ALGEBRAIC(:,11) = strpad('Qo in component TempRC (UnitQ)');
LEGEND_ALGEBRAIC(:,13) = strpad('Qo in component TempCDv (UnitQ)');
LEGEND_ALGEBRAIC(:,4) = strpad('Pi in component TempCDv (UnitP)');
LEGEND_ALGEBRAIC(:,10) = strpad('Qo in component TempCDa (UnitQ)');
LEGEND_CONSTANTS(:,1) = strpad('CVao in component ParaLeftHeart (UnitCV)');
LEGEND_ALGEBRAIC(:,3) = strpad('E in component EVentricle (UnitE)');
LEGEND_STATES(:,1) = strpad('V in component TempCDv (UnitV)');
LEGEND_CONSTANTS(:,2) = strpad('PlvIni in component ParaLeftHeart (UnitP)');
LEGEND_CONSTANTS(:,3) = strpad('VlvIni in component ParaLeftHeart (UnitV)');
LEGEND_ALGEBRAIC(:,14) = strpad('Tao in component TempCDv (dimensionless)');
LEGEND_CONSTANTS(:,4) = strpad('Vlv0 in component ParaLeftHeart (UnitV)');
LEGEND_CONSTANTS(:,5) = strpad('CVmi in component ParaLeftHeart (UnitCV)');
LEGEND_ALGEBRAIC(:,7) = strpad('E in component EAtrium (UnitE)');
LEGEND_STATES(:,2) = strpad('V in component TempCDa (UnitV)');
LEGEND_CONSTANTS(:,6) = strpad('PlaIni in component ParaLeftHeart (UnitP)');
LEGEND_CONSTANTS(:,7) = strpad('VlaIni in component ParaLeftHeart (UnitV)');
LEGEND_ALGEBRAIC(:,9) = strpad('Tao in component TempCDa (dimensionless)');
LEGEND_CONSTANTS(:,8) = strpad('Vla0 in component ParaLeftHeart (UnitV)');
LEGEND_CONSTANTS(:,9) = strpad('ElvMax in component ParaLeftHeart (UnitE)');
LEGEND_CONSTANTS(:,10) = strpad('ElvMin in component ParaLeftHeart (UnitE)');
LEGEND_CONSTANTS(:,11) = strpad('T in component ParaLeftHeart (second)');
LEGEND_CONSTANTS(:,12) = strpad('Ts1 in component ParaLeftHeart (dimensionless)');
LEGEND_CONSTANTS(:,13) = strpad('Ts2 in component ParaLeftHeart (dimensionless)');
LEGEND_ALGEBRAIC(:,1) = strpad('mt in component EVentricle (second)');
LEGEND_ALGEBRAIC(:,2) = strpad('et in component EVentricle (dimensionless)');
LEGEND_CONSTANTS(:,14) = strpad('ElaMax in component ParaLeftHeart (UnitE)');
LEGEND_CONSTANTS(:,15) = strpad('ElaMin in component ParaLeftHeart (UnitE)');
LEGEND_CONSTANTS(:,16) = strpad('Tpwb in component ParaLeftHeart (dimensionless)');
LEGEND_CONSTANTS(:,17) = strpad('Tpww in component ParaLeftHeart (dimensionless)');
LEGEND_ALGEBRAIC(:,5) = strpad('mt in component EAtrium (second)');
LEGEND_ALGEBRAIC(:,6) = strpad('et in component EAtrium (dimensionless)');
LEGEND_STATES(:,3) = strpad('Pi in component TempRC (UnitP)');
LEGEND_ALGEBRAIC(:,15) = strpad('Qo in component TempR (UnitQ)');
LEGEND_CONSTANTS(:,18) = strpad('Rc in component ParaWestkessel (UnitR)');
LEGEND_CONSTANTS(:,19) = strpad('Rv in component ParaWestkessel (UnitR)');
LEGEND_CONSTANTS(:,20) = strpad('Cv in component ParaWestkessel (UnitC)');
LEGEND_CONSTANTS(:,21) = strpad('P0v in component ParaWestkessel (UnitP)');
LEGEND_RATES(:,1) = strpad('d/dt V in component TempCDv (UnitV)');
LEGEND_RATES(:,2) = strpad('d/dt V in component TempCDa (UnitV)');
LEGEND_RATES(:,3) = strpad('d/dt Pi in component TempRC (UnitP)');
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) = 350.;
CONSTANTS(:,2) = 1.0;
CONSTANTS(:,3) = 5.0;
CONSTANTS(:,4) = 500;
CONSTANTS(:,5) = 400.;
CONSTANTS(:,6) = 1.0;
CONSTANTS(:,7) = 4.0;
CONSTANTS(:,8) = 20;
CONSTANTS(:,9) = 2.5;
CONSTANTS(:,10) = 0.1;
CONSTANTS(:,11) = 1.0;
CONSTANTS(:,12) = 0.3;
CONSTANTS(:,13) = 0.45;
CONSTANTS(:,14) = 0.25;
CONSTANTS(:,15) = 0.15;
CONSTANTS(:,16) = 0.92;
CONSTANTS(:,17) = 0.09;
CONSTANTS(:,18) = 0.005;
CONSTANTS(:,19) = 0.65;
CONSTANTS(:,20) = 2.6;
CONSTANTS(:,21) = 0.;
STATES(:,1) = CONSTANTS(:,4);
STATES(:,2) = CONSTANTS(:,8);
STATES(:,3) = CONSTANTS(:,21);
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) = VOI - CONSTANTS(:,11).*floor(VOI./CONSTANTS(:,11));
ALGEBRAIC(:,6) = piecewise({ALGEBRAIC(:,5)>=0.00000&ALGEBRAIC(:,5)<= ((CONSTANTS(:,16)+CONSTANTS(:,17)) - 1.00000).*CONSTANTS(:,11), 1.00000 - cos(( 2.00000.*3.14159.*(ALGEBRAIC(:,5) - (CONSTANTS(:,16) - 1.00000).*CONSTANTS(:,11)))./( CONSTANTS(:,17).*CONSTANTS(:,11))) , ALGEBRAIC(:,5)> ((CONSTANTS(:,16)+CONSTANTS(:,17)) - 1.00000).*CONSTANTS(:,11)&ALGEBRAIC(:,5)<= CONSTANTS(:,16).*CONSTANTS(:,11), 0.00000 , ALGEBRAIC(:,5)> CONSTANTS(:,16).*CONSTANTS(:,11)&ALGEBRAIC(:,5)<=CONSTANTS(:,11), 1.00000 - cos(( 2.00000.*3.14159.*(ALGEBRAIC(:,5) - CONSTANTS(:,16).*CONSTANTS(:,11)))./( CONSTANTS(:,17).*CONSTANTS(:,11))) }, NaN);
ALGEBRAIC(:,7) = CONSTANTS(:,15)+( ALGEBRAIC(:,6).*(CONSTANTS(:,14) - CONSTANTS(:,15)))./2.00000;
ALGEBRAIC(:,8) = CONSTANTS(:,6)+ ALGEBRAIC(:,7).*(STATES(:,2) - CONSTANTS(:,7));
ALGEBRAIC(:,11) = (STATES(:,3) - ALGEBRAIC(:,8))./CONSTANTS(:,19);
ALGEBRAIC(:,1) = VOI - CONSTANTS(:,11).*floor(VOI./CONSTANTS(:,11));
ALGEBRAIC(:,2) = piecewise({ALGEBRAIC(:,1)>=0.00000&ALGEBRAIC(:,1)<= CONSTANTS(:,12).*CONSTANTS(:,11), 1.00000 - cos(( 3.14159.*ALGEBRAIC(:,1))./( CONSTANTS(:,12).*CONSTANTS(:,11))) , ALGEBRAIC(:,1)> CONSTANTS(:,12).*CONSTANTS(:,11)&ALGEBRAIC(:,1)<= CONSTANTS(:,13).*CONSTANTS(:,11), 1.00000+cos(( 3.14159.*(ALGEBRAIC(:,1) - CONSTANTS(:,12).*CONSTANTS(:,11)))./( (CONSTANTS(:,13) - CONSTANTS(:,12)).*CONSTANTS(:,11))) , ALGEBRAIC(:,1)> CONSTANTS(:,13).*CONSTANTS(:,11)&ALGEBRAIC(:,1)<CONSTANTS(:,11), 0.00000 }, NaN);
ALGEBRAIC(:,3) = CONSTANTS(:,10)+( ALGEBRAIC(:,2).*(CONSTANTS(:,9) - CONSTANTS(:,10)))./2.00000;
ALGEBRAIC(:,4) = CONSTANTS(:,2)+ ALGEBRAIC(:,3).*(STATES(:,1) - CONSTANTS(:,3));
ALGEBRAIC(:,9) = piecewise({ALGEBRAIC(:,8)>=ALGEBRAIC(:,4), 1.00000 , ALGEBRAIC(:,8)<ALGEBRAIC(:,4), 0.00000 }, NaN);
ALGEBRAIC(:,10) = piecewise({ALGEBRAIC(:,8)>=ALGEBRAIC(:,4), CONSTANTS(:,5).*ALGEBRAIC(:,9).*power(abs(ALGEBRAIC(:,8) - ALGEBRAIC(:,4)), 0.500000) , ALGEBRAIC(:,8)<ALGEBRAIC(:,4), -1.00000.*CONSTANTS(:,5).*ALGEBRAIC(:,9).*power(abs(ALGEBRAIC(:,4) - ALGEBRAIC(:,8)), 0.500000) }, NaN);
RATES(:,2) = ALGEBRAIC(:,11) - ALGEBRAIC(:,10);
[CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS, STATES, ALGEBRAIC);
RATES(:,1) = ALGEBRAIC(:,10) - ALGEBRAIC(:,13);
ALGEBRAIC(:,15) = ALGEBRAIC(:,13);
RATES(:,3) = (ALGEBRAIC(:,15) - ALGEBRAIC(:,11))./CONSTANTS(:,20);
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) = VOI - CONSTANTS(:,11).*floor(VOI./CONSTANTS(:,11));
ALGEBRAIC(:,6) = piecewise({ALGEBRAIC(:,5)>=0.00000&ALGEBRAIC(:,5)<= ((CONSTANTS(:,16)+CONSTANTS(:,17)) - 1.00000).*CONSTANTS(:,11), 1.00000 - cos(( 2.00000.*3.14159.*(ALGEBRAIC(:,5) - (CONSTANTS(:,16) - 1.00000).*CONSTANTS(:,11)))./( CONSTANTS(:,17).*CONSTANTS(:,11))) , ALGEBRAIC(:,5)> ((CONSTANTS(:,16)+CONSTANTS(:,17)) - 1.00000).*CONSTANTS(:,11)&ALGEBRAIC(:,5)<= CONSTANTS(:,16).*CONSTANTS(:,11), 0.00000 , ALGEBRAIC(:,5)> CONSTANTS(:,16).*CONSTANTS(:,11)&ALGEBRAIC(:,5)<=CONSTANTS(:,11), 1.00000 - cos(( 2.00000.*3.14159.*(ALGEBRAIC(:,5) - CONSTANTS(:,16).*CONSTANTS(:,11)))./( CONSTANTS(:,17).*CONSTANTS(:,11))) }, NaN);
ALGEBRAIC(:,7) = CONSTANTS(:,15)+( ALGEBRAIC(:,6).*(CONSTANTS(:,14) - CONSTANTS(:,15)))./2.00000;
ALGEBRAIC(:,8) = CONSTANTS(:,6)+ ALGEBRAIC(:,7).*(STATES(:,2) - CONSTANTS(:,7));
ALGEBRAIC(:,11) = (STATES(:,3) - ALGEBRAIC(:,8))./CONSTANTS(:,19);
ALGEBRAIC(:,1) = VOI - CONSTANTS(:,11).*floor(VOI./CONSTANTS(:,11));
ALGEBRAIC(:,2) = piecewise({ALGEBRAIC(:,1)>=0.00000&ALGEBRAIC(:,1)<= CONSTANTS(:,12).*CONSTANTS(:,11), 1.00000 - cos(( 3.14159.*ALGEBRAIC(:,1))./( CONSTANTS(:,12).*CONSTANTS(:,11))) , ALGEBRAIC(:,1)> CONSTANTS(:,12).*CONSTANTS(:,11)&ALGEBRAIC(:,1)<= CONSTANTS(:,13).*CONSTANTS(:,11), 1.00000+cos(( 3.14159.*(ALGEBRAIC(:,1) - CONSTANTS(:,12).*CONSTANTS(:,11)))./( (CONSTANTS(:,13) - CONSTANTS(:,12)).*CONSTANTS(:,11))) , ALGEBRAIC(:,1)> CONSTANTS(:,13).*CONSTANTS(:,11)&ALGEBRAIC(:,1)<CONSTANTS(:,11), 0.00000 }, NaN);
ALGEBRAIC(:,3) = CONSTANTS(:,10)+( ALGEBRAIC(:,2).*(CONSTANTS(:,9) - CONSTANTS(:,10)))./2.00000;
ALGEBRAIC(:,4) = CONSTANTS(:,2)+ ALGEBRAIC(:,3).*(STATES(:,1) - CONSTANTS(:,3));
ALGEBRAIC(:,9) = piecewise({ALGEBRAIC(:,8)>=ALGEBRAIC(:,4), 1.00000 , ALGEBRAIC(:,8)<ALGEBRAIC(:,4), 0.00000 }, NaN);
ALGEBRAIC(:,10) = piecewise({ALGEBRAIC(:,8)>=ALGEBRAIC(:,4), CONSTANTS(:,5).*ALGEBRAIC(:,9).*power(abs(ALGEBRAIC(:,8) - ALGEBRAIC(:,4)), 0.500000) , ALGEBRAIC(:,8)<ALGEBRAIC(:,4), -1.00000.*CONSTANTS(:,5).*ALGEBRAIC(:,9).*power(abs(ALGEBRAIC(:,4) - ALGEBRAIC(:,8)), 0.500000) }, NaN);
ALGEBRAIC(:,15) = ALGEBRAIC(:,13);
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) ~= 3), initialGuess_0 = [0.1,0.1,0.1];, 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(:,12) = soln(1);
ALGEBRAIC(:,13) = soln(2);
ALGEBRAIC(:,14) = soln(3);
else
SET_ALGEBRAIC(:,12) = logical(1);
SET_ALGEBRAIC(:,13) = logical(1);
SET_ALGEBRAIC(:,14) = 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(:,12) = soln(1);
TEMP_ALGEBRAIC(:,13) = soln(2);
TEMP_ALGEBRAIC(:,14) = soln(3);
ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
end
end
end
function resid = residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
ALGEBRAIC(:,12) = algebraicCandidate(1);
ALGEBRAIC(:,13) = algebraicCandidate(2);
ALGEBRAIC(:,14) = algebraicCandidate(3);
resid(1) = ALGEBRAIC(:,14) - piecewise({ALGEBRAIC(:,4)>=ALGEBRAIC(:,12), 1.00000 , ALGEBRAIC(:,4)<ALGEBRAIC(:,12), 0.00000 }, NaN);
resid(2) = ALGEBRAIC(:,13) - piecewise({ALGEBRAIC(:,4)>=ALGEBRAIC(:,12), CONSTANTS(:,1).*ALGEBRAIC(:,14).*power(abs(ALGEBRAIC(:,4) - ALGEBRAIC(:,12)), 0.500000) , ALGEBRAIC(:,4)<ALGEBRAIC(:,12), -1.00000.*CONSTANTS(:,1).*ALGEBRAIC(:,14).*power(abs(ALGEBRAIC(:,12) - ALGEBRAIC(:,4)), 0.500000) }, NaN);
resid(3) = ALGEBRAIC(:,12) - (STATES(:,3)+ CONSTANTS(:,18).*ALGEBRAIC(:,13));
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