[CppAD] Multiple Levels of AD

[Mathias Wagner]

Hi,

I just started using algorithmic differentiation. I wonder wether it  
is possible to get the derivative of a function as an ADFun object of  
the same level.
I have looked into the mul_level example, but this is not enough for  
my purpose.


I would like to use it for solving a differential equation

d/dk f_k(x) = 1/(1+f_k''(x))

f_k''(x) denotes the second derivative w.r.t. to x. The value of is  
not changed during the iteration.

f_0 is given analytically.

So for example I can start with

f_1(x) = f_0(x) + 1/(1+f''_0(x)) as a first step.

Using the approach described in mul_level I can define f_0 using  
ADDDouble and get f_0(x) as ADDouble so I can differentiate f''_0(x).

In the next steps in the iteration I end up with

f_2(x) = f_1(x) + 1/(1+f''_1(x))

which I can calculate because I can calculate the derivatives of f_1(x).

But this value will then be a double and I cannot differentiate it.

I hope you can understand my problem.

Is there any way to get this done using AD? I expect it to be very  
slow, because it probably requires to keep the full history of the  
iteration of f_k, but this should be acceptable.

Mathias



-- 
// ***************************************************************
// ** Mathias Wagner                                            **
// ** Institut fuer Kernphysik, TU Darmstadt                    **
// ** Schlossgartenstr. 9, 64289 Darmstadt, Germany             **
// **                                                           **
// ** email: mathias.wagner at physik.tu-darmstadt.de              **
// ** www  : http://crunch.ikp.physik.tu-darmstadt.de/~wagner   **
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