Vector mode higher order derivatives

[Manushanker]

Hi @MaxSagebaum

May I know if it is possible to compute higher order derivatives using vector mode? I have a function that generates an array of data and I would like to compute higher order derivatives of each array elements.

Thanks,

Manushanker

[MaxSagebaum]

Hi, sorry I missed this.

It is kind of possible. You can have a vector of a CoDiPack type and it works as expected. The problem is when you start to nest this again. Then you have some values that are vectors and some that are not.

using t1v = codi::RealForwardGen<double, codi::Direction<double, 2>>;
using t2v = codi::RealForwardGen<t1v, codi::Direction<t1v, 2>>;

t2v a = 1.0;
a.value().value() = 2.0;  // Is a value
a.value().gradient() = {1.0, 1.0}; // I a vector
a.gradient()[0].value() = 1.0; // First entry of a vector;
a.gradient()[1].value() = 1.0; // First entry of a vector;
a.gradient()[0].gradient() = {1.0, 1.0}; // First vector entry of a vector;
a.gradient()[1].gradient() = {1.0, 1.0}; // First vector entry of a vector;

This should work, but I have not tested it. What kind of vector derivatives do you need?

This is also demonstrated partly in the Tutorials:

• https://www.scicomp.uni-kl.de/codi/d3/db6/Tutorial_06_Higher_order_types_helper_acces.html
• https://www.scicomp.uni-kl.de/codi/d1/d3f/Example_04_Higher_order_types_helper_access_compile_time.html
• https://www.scicomp.uni-kl.de/codi/d1/d6a/Example_05_Higher_order_types_direct_access.html