Fvar<var>

[betanalpha]

Fvars

With forward mode only all you can get out are directional derivatives, so you can associate each component with a certain inner product of a derivative with vectors. And at higher-order those inner products mix many different orders of derivatives making things very confusing. For example, consider a many-to-one function, f : R^{N} -> R. Evaluating the function with a fvar<double> will require 2N inputs: the N function inputs, call them x, and the N sensitivities, call them u. The fvar<doub…