How to add self defined functions to AD<Base>?

[xuruilong100]

I am trying to add Gamma function in this way:

template <class Base>
inline AD<Base> gamma(const AD<Base> &x)
{   
    return x.gamma_me();
}

How to implement it? Which parts of source codes should I modify?

[bradbell]

Does the following work for you ?

template <class Float>
Float gamma(const Float& x)
{
    // your C++ code for the gamma function
    ...
   return result;
}

[xuruilong100]

In fact, there are a lot of 'if-else' branches in the numerical algorithm of Gamma function, see boost's implement

https://www.boost.org/doc/libs/1_78_0/boost/math/special_functions/gamma.hpp

I am worried about that the code may be non-differentiable.

[bradbell]

The operation sequence will depend on the results of all the if branches in your program; see https://coin-or.github.io/CppAD/doc/compare_change.htm

It is more complicated to create a gamma function where you never have to retape. For an example see the atan2 example https://coin-or.github.io/CppAD/doc/condexp.htm#Atan2

It is even more complicated, but more efficient, to create an atomic gamma function; see https://coin-or.github.io/CppAD/doc/atomic_four_get_started.cpp.htm Note that to use this in derivative calculations, you will have to define the derivatives of the gamma function.

[xuruilong100]

Great, thank you very much. I have to say I need more tutorials about atomic_four function.

[bradbell]

The important thing is to only implement the virtual functions that you need. For more examples see; https://coin-or.github.io/CppAD/doc/atomic_four_example.htm

[xuruilong100]

Really helpful! And can you tell me what do the args mean, for instance select_y and call_id.

[bradbell]

See the documentation for the particular function below https://coin-or.github.io/CppAD/doc/atomic_four_define.htm

[bradbell]

If you are satisfied with this answer, would you please close this issue.