automatic differentiation with ode45()

Hi,

I wanted to understand how the package Automatic Differentiation for Matlab worked. So I create a small example. I wish to use the add-in to find for example myFunc(t=3) and grad(myFunc)(t=3). My func is a function that is solution to the differential equation x''(t) = 1. So I created a function

 function ds = doubleIntegrator(t,s)
    ds = zeros(2,1);
    ds(1) = s(2);
    ds(2) = 1;
end

and also the function

 function [t,s] = integrateme(f,st,tspan)
    [t,s] = ode45(f,tspan,st);
end

then I define the function myFunc as :

 K>> myFunc=@(t) integrateme(@doubleIntegrator,[0,0],[0,t])

I than use the instructions of the Automatic Differentiation for Matlab add-in so I do :

 K>>tAD = myAD(3) % because I want to compute de AD in t=3
 K>>myFunc(tAD)

but it returns the error

Error using length Too many input arguments.

Error in myAD/length (line 6) mylength = length(x.values);

Error in odearguments (line 20) if length(tspan) < 2

Error in ode45 (line 115) odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in integrateme (line 2) [t,s] = ode45(f,tspan,st);

Error in myAD/length>@(t)integrateme(@doubleIntegrator,[0,0],[0,t])

[Star Strider]

The File Exchange function appears to do numerical differentiation of a vector (similar to MATLAB gradient), and will not produce the derivative used in the ODE solvers.

The Symbolic Math Toolbox is probably your best option if you want to calculate a symbolic derivative.