Autodiff function for coefficient [add-ad-coeff] #4256
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This PR defines as helper class that can convert user provided functions in to first order derivatives, that can be used by the various
XXXFunctionCoefficientclasses.The functions need to to be provided as either
void vectorTDFun(const Vector& param, const ADVector& x, ADVector& f)or
void vectorTDFun(const Vector& param, const ADVector& x, const ADFloat t, ADVector& f)where
ADVectoris of typestd:vector<ADFloat>andADFloatis equivalent toreal_twith additional autodiff functionality.A full suite of unit tests is provided. This also gives a usage examples.
Envisioned usages: convergence tests based on norms including derivatives.
Functionality could - in principle -be extended to Hessian, Laplacian and other higher order derivatives.
Credit were credit is due: large inspiration has been taken from the autodiff miniapp.