expression is too large, symengine can't calculate
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I use symbolic expression to calculate sensitivity equasions of ODEs with 19 ODEs and 42 variables. And the error message is "the expression is too large , symengin can't calculate " when using it to calculate the second order sensitivity equations. I checked the dimension is more than 3 ten thousand and it isn't the sparse matrix. I debug into the symbolic there is no sourcecode, how do I do next?
Part codes like next:
function obj = compute_2nd_order_sensitivity_equations(obj)
M = obj.M;
N = obj.N;
if isempty(obj.S) || isempty(obj.dS) || isempty(obj.S0)
obj = obj.compute_1st_order_sensitivity_equations;
end
[SS,dSS,SS0] = sensitivity_equations_another([obj.x;obj.S(:)], obj.theta, [obj.dx;obj.dS(:)], [obj.x0;obj.S0(:)]);
SS(1:M,:)=[]; dSS(1:M,:)=[]; SS0(1:M,:)=[]; % remove the first order sensitivity equations
obj.SS = reshape(SS,M,N,N) ; % reshape the 2nd order equations
obj.dSS = reshape(dSS,M,N,N);
obj.SS0 = reshape(SS0,M,N,N);
obj.ODE_2nd_order_sensitivity_rhs = matlabFunction(obj.dx,obj.dS(:),obj.dSS(:),'vars', {'t', obj.x,obj.S(:),obj.SS(:), obj.theta}); % define the right hand side of the ODE as a function of time, system states + sensitivity, and parameter
obj.ODE_2nd_order_sensitivity_init = matlabFunction(obj.x0,obj.S0(:),obj.SS0(:),'vars', {obj.theta}); % define the initial condition as a function of parameters
end
symengine give error messages in function of matlabFunction
......
else
body = mup2matcell(funs, opts.Sparse);
body = renameInputs(body,vars,inputs);
g = symengine('makeFhandle',varnames,body);
end
1 Comment
Walter Roberson
on 18 Jan 2020
It would be more common to use odeFunction() instead of matlabFunction in constructing equations ?
Answers (2)
Walter Roberson
on 18 Jan 2020
Edited: Walter Roberson
on 18 Jan 2020
Create
eqns = [obj.dx,obj.dS(:);obj.dSS(:)];
Now break that up into chunks. For example:
At_a_time = 10;
num_eqn = length(eqns);
num_chunks = ceil(num_eqn ./ At_a_time);
fh = cell(num_chunks, 1);
for K = 1 : At_a_time : num_eqn - At_a_time
fn{K} = matlabFunction(eqns(K:K+At_a_time-1), 'vars', {'t', obj.x,obj.S(:),obj.SS(:), obj.theta});
end
if num_chunks * At_a_time ~= num_eqn %you should double-check the boundary conditions here
fn{K+1} = matlabFunction(eqns(K+At_a_time:end), 'vars', {'t', obj.x,obj.S(:),obj.SS(:), obj.theta});
end
And now:
obj.ODE_2nd_order_sensitivity_rhs = @(varargin) cell2mat(cellfun(@(FH) FH(varargin{:}), fn, 'uniform', 0));
which should execute the handles one at a time and form a vector of the results.
Yes, this is a bit of a hack, but if it gets the job done then it gets the job done.
3 Comments
Walter Roberson
on 23 Jan 2020
You use matlabFunction with 'vars' and provide a cell array with five elements. That is going to convert into a function that expects five parameters. However you are only passing three parameters to it. It needs t, x S, SS, and theta parameters.
Wang Hong
on 9 Feb 2020
7 Comments
Walter Roberson
on 24 Feb 2020
You don't do a sensitivity analysis when the number of variables is quite large. Not unless you are only concerned about the change with respect to one variable at a time, not about sensitivity as multiple variables change.
If you only care about one variable at a time then differentiate each equation with respect to each variable. I know that there is a function to do that but the function name is not coming to mind. This would not involve the use of matlabFunction. matlabFunction would only be for numeric work but you want analytic work.
Possibly you would be willing to establish a base numeric point and analyze the effect of changing one variable at a time at that particular numeric point. That would involve looping substituting all the numeric values except that one variable at a time you substitute numeric value plus symbolic delta. In some cases you will get a polynomial output; others might be difficult to analyze, such as if the equations involved the bessel functions.
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