How to Covert a Symbolic Jacobian to a Numerical Matrix that can be Used by ODE15s-- the Jacobian Contains Fewer Variables than the Original System

I am currently working with a system of 27 ODE's. I am attempting to solve the system using ode15s and because of the nature of this problem I need to include the precalculated Jacobian.

I have written a MATLAB function to calculate the symbolic Jacobian of the system, but am having trouble with the conversion of the symbolic matrix into a numeric structure that can be used by ode15s.

The problem I am having is that although the original system contains 27 state variables, the Jacobian only contains 8. Thus I cannot input a vector of the dependent variables into the Jacobian as is necessary for ode15s.

Here is a minimal code that describes what I am trying to do:

function Jacob = Jacobian

syms  x y z
w = [x, y, z];

wp(1) = 2*x + y + z;

wp(2) = x^2 -4*y;

wp(3) = z^3 -x;

SymJacob = jacobian(wp',w);
Jacob = matlabFunction(SymJacob);
end

If I call this in the command window using

>> J = Jacobian

The output is:

@(x,z)reshape([2.0,conj(x).*2.0,-1.0,1.0,-4.0,0.0,1.0,0.0,conj(z).^2.*3.0],[3,3])

i.e. the Jacobian is a function of x and z but not y.

I need to somehow make the Jacobian a function of y so that I can input the entire vector of variables (J(x,y,z)).

Any help would be greatly appreciated!

Laura

Answer 1

[Walter Roberson]

Jacob = matlabFunction(SymJacob, 'vars', [x, y, z]);