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 =7;
end
% There are a total of 1 entries in each of the rate and state variable arrays.
% There are a total of 19 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_CONSTANTS(:,1) = strpad('L_1 in component contraction (mm)');
LEGEND_CONSTANTS(:,2) = strpad('L_2 in component contraction (mm)');
LEGEND_CONSTANTS(:,3) = strpad('L_3 in component contraction (mm)');
LEGEND_CONSTANTS(:,4) = strpad('L_4 in component contraction (mm)');
LEGEND_CONSTANTS(:,5) = strpad('f_c in component contraction (newton)');
LEGEND_CONSTANTS(:,6) = strpad('v_max in component contraction (mm_per_second)');
LEGEND_CONSTANTS(:,7) = strpad('curv in component contraction (dimensionless)');
LEGEND_CONSTANTS(:,8) = strpad('k_1 in component contraction (newton)');
LEGEND_CONSTANTS(:,9) = strpad('k_2 in component contraction (per_mm)');
LEGEND_CONSTANTS(:,10) = strpad('F_1 in component contraction (newton)');
LEGEND_CONSTANTS(:,11) = strpad('d_LSEC1 in component contraction (mm)');
LEGEND_CONSTANTS(:,12) = strpad('k_sh in component contraction (dimensionless)');
LEGEND_CONSTANTS(:,13) = strpad('L_m in component contraction (mm)');
LEGEND_CONSTANTS(:,14) = strpad('F_im in component contraction (newton)');
LEGEND_CONSTANTS(:,15) = strpad('tau in component contraction (second)');
LEGEND_ALGEBRAIC(:,6) = strpad('v_cc in component contraction (mm_per_second)');
LEGEND_ALGEBRAIC(:,7) = strpad('f_v in component contraction (dimensionless)');
LEGEND_ALGEBRAIC(:,2) = strpad('f_L in component contraction (newton)');
LEGEND_ALGEBRAIC(:,5) = strpad('f_sec in component contraction (newton)');
LEGEND_ALGEBRAIC(:,1) = strpad('f_pec in component contraction (newton)');
LEGEND_ALGEBRAIC(:,4) = strpad('delta_L_sec in component contraction (mm)');
LEGEND_CONSTANTS(:,16) = strpad('delta_L_sec1 in component contraction (mm)');
LEGEND_STATES(:,1) = strpad('delta_L_pec in component contraction (mm)');
LEGEND_CONSTANTS(:,17) = strpad('k in component contraction (newton_per_mm)');
LEGEND_ALGEBRAIC(:,3) = strpad('L_mtc in component contraction (mm)');
LEGEND_CONSTANTS(:,18) = strpad('A in component contraction (dimensionless)');
LEGEND_CONSTANTS(:,19) = strpad('L_mslack in component contraction (mm)');
LEGEND_RATES(:,1) = strpad('d/dt delta_L_pec in component contraction (mm)');
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) = -23;
CONSTANTS(:,2) = -14;
CONSTANTS(:,3) = 2;
CONSTANTS(:,4) = 19;
CONSTANTS(:,5) = 0.49;
CONSTANTS(:,6) = -141;
CONSTANTS(:,7) = 5.8;
CONSTANTS(:,8) = 0.012;
CONSTANTS(:,9) = 0.317;
CONSTANTS(:,10) = 4.1;
CONSTANTS(:,11) = 4.1;
CONSTANTS(:,12) = 3.3;
CONSTANTS(:,13) = 0.3;
CONSTANTS(:,14) = 18.1;
CONSTANTS(:,15) = 0.006;
CONSTANTS(:,16) = 4.1;
STATES(:,1) = 0.2;
CONSTANTS(:,17) = 3.5;
CONSTANTS(:,18) = 1;
CONSTANTS(:,19) = 0.3;
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(:,2) = piecewise({STATES(:,1)>=CONSTANTS(:,1)&STATES(:,1)<=CONSTANTS(:,2), (CONSTANTS(:,5)./(CONSTANTS(:,2) - CONSTANTS(:,1))).*(STATES(:,1) - CONSTANTS(:,1)) , STATES(:,1)>CONSTANTS(:,2)&STATES(:,1)<=0.00000, ((1.00000 - CONSTANTS(:,5))./ - CONSTANTS(:,2)).*(STATES(:,1) - CONSTANTS(:,2)) , STATES(:,1)>0.00000&STATES(:,1)<=CONSTANTS(:,3), 1.00000 , STATES(:,1)>CONSTANTS(:,3)&STATES(:,1)<=CONSTANTS(:,4), ( - 1.00000./(CONSTANTS(:,4) - CONSTANTS(:,3))).*(STATES(:,1) - CONSTANTS(:,3)) }, NaN);
ALGEBRAIC(:,3) = piecewise({VOI<=1.00000, 0.290000 , VOI>1.00000&VOI<5.00000, 0.220000 }, 0.190000);
ALGEBRAIC(:,4) = (ALGEBRAIC(:,3) - STATES(:,1)) - CONSTANTS(:,19);
ALGEBRAIC(:,5) = piecewise({ALGEBRAIC(:,4)>0.00000&ALGEBRAIC(:,4)<CONSTANTS(:,16), (CONSTANTS(:,10)./(exp(CONSTANTS(:,12)) - 1.00000)).*(exp(( CONSTANTS(:,12).*ALGEBRAIC(:,4))./CONSTANTS(:,16)) - 1.00000) , ALGEBRAIC(:,4)<=CONSTANTS(:,16), CONSTANTS(:,10)+ CONSTANTS(:,17).*(ALGEBRAIC(:,4) - CONSTANTS(:,16)) }, NaN);
ALGEBRAIC(:,1) = piecewise({STATES(:,1)>0.00000, CONSTANTS(:,8).*(exp( CONSTANTS(:,9).*STATES(:,1)) - 1.00000) , STATES(:,1)<=0.00000, 0.00000 }, NaN);
[CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS, STATES, ALGEBRAIC);
RATES(:,1) = ALGEBRAIC(:,6);
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(:,2) = piecewise({STATES(:,1)>=CONSTANTS(:,1)&STATES(:,1)<=CONSTANTS(:,2), (CONSTANTS(:,5)./(CONSTANTS(:,2) - CONSTANTS(:,1))).*(STATES(:,1) - CONSTANTS(:,1)) , STATES(:,1)>CONSTANTS(:,2)&STATES(:,1)<=0.00000, ((1.00000 - CONSTANTS(:,5))./ - CONSTANTS(:,2)).*(STATES(:,1) - CONSTANTS(:,2)) , STATES(:,1)>0.00000&STATES(:,1)<=CONSTANTS(:,3), 1.00000 , STATES(:,1)>CONSTANTS(:,3)&STATES(:,1)<=CONSTANTS(:,4), ( - 1.00000./(CONSTANTS(:,4) - CONSTANTS(:,3))).*(STATES(:,1) - CONSTANTS(:,3)) }, NaN);
ALGEBRAIC(:,3) = piecewise({VOI<=1.00000, 0.290000 , VOI>1.00000&VOI<5.00000, 0.220000 }, 0.190000);
ALGEBRAIC(:,4) = (ALGEBRAIC(:,3) - STATES(:,1)) - CONSTANTS(:,19);
ALGEBRAIC(:,5) = piecewise({ALGEBRAIC(:,4)>0.00000&ALGEBRAIC(:,4)<CONSTANTS(:,16), (CONSTANTS(:,10)./(exp(CONSTANTS(:,12)) - 1.00000)).*(exp(( CONSTANTS(:,12).*ALGEBRAIC(:,4))./CONSTANTS(:,16)) - 1.00000) , ALGEBRAIC(:,4)<=CONSTANTS(:,16), CONSTANTS(:,10)+ CONSTANTS(:,17).*(ALGEBRAIC(:,4) - CONSTANTS(:,16)) }, NaN);
ALGEBRAIC(:,1) = piecewise({STATES(:,1)>0.00000, CONSTANTS(:,8).*(exp( CONSTANTS(:,9).*STATES(:,1)) - 1.00000) , STATES(:,1)<=0.00000, 0.00000 }, NaN);
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(:,6) = soln(1);
ALGEBRAIC(:,7) = soln(2);
else
SET_ALGEBRAIC(:,6) = logical(1);
SET_ALGEBRAIC(:,7) = 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(:,6) = soln(1);
TEMP_ALGEBRAIC(:,7) = soln(2);
ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
end
end
end
function resid = residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
ALGEBRAIC(:,6) = algebraicCandidate(1);
ALGEBRAIC(:,7) = algebraicCandidate(2);
resid(1) = ALGEBRAIC(:,6) - (1.00000./ALGEBRAIC(:,7)).*((ALGEBRAIC(:,5) - ALGEBRAIC(:,1))./( CONSTANTS(:,18).*ALGEBRAIC(:,2).*CONSTANTS(:,14)));
resid(2) = ALGEBRAIC(:,7) - (CONSTANTS(:,6) - ALGEBRAIC(:,6))./(CONSTANTS(:,6)+ ALGEBRAIC(:,6).*CONSTANTS(:,7));
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