Create a symbolic function of different length vectors in MATLAB Symbolic Toolbox

1
votes

My overall goal is to use the MATLAB symbolic toolbox to simplify the process of formulating and solving for the sensitivities of solutions to ordinary differential equations with respect to the parameters in the equations. In my case I have an ODE with 2 states and 10 parameters. A smaller, but representative, example would look like 

X = sym('X', [2 1])  % Vector representing state variables
p = sym('p', [3 1]) % Vector representing parameters

% Fitzhugh Nagumo Equations
rhs_1 = symfun(p(3)*(X(1) - X(1)^3/3 + X(2)), [X; p])
rhs_2 = symfun(-(X(1) - p(1) + p(2)*X(2))/p(3), [X; p])

I can then get the partial derivatives, which are used to solve for the sensitivities, of the RHS of the ODE wrt to the parameters using a command like 'gradient(rhs_1, p)'. But then I would like to convert this gradient to a matlab function that is a function of the vectors X and p, not a function of the elements of these vectors. I need these functions to be of this form because otherwise I cannot use the CVODES solver in the sundialsTB toolbox. Is this possible? Is there an easier way to accomplish what I am trying to do?

1
matlabsymbolic-math
So you want something automatic? And I presume that you were not able to get matlabFunction to do this? – horchler

1 Answers

1
votes

Recognizing that a comma-separated list of function inputs is really just a cell array, you can do this by converting your vector inputs to a cell arrays of scalar using mat2cell:

x=1:2;
p=1:3;
v = mat2cell([x(:);p(:)],ones(numel(x)+numel(p),1),1);
y1 = rhs_1(v{:})
y2 = rhs_2(v{:})