Given a function $f_1:\mathbb R^n\mapsto \mathbb R$, and a fixed vector $v\in \mathbb R^n$ I construct another function $f_2:\mathbb R^n \times \mathbb R^n\mapsto \mathbb R$ such that $f_2(d,v):=f_1(T(v) \cdot d)$ where $T(v)$ is some transformation matrix depending on $v$. I need to compute two quantities which are characteristic of the functions themselves, namely their global sensitivity: $$ S(f_1) = \max\limits_{d,d^\prime} |f_1(d)-f_1(d^\prime)| $$ and for a fixed $v$: $$ S(f_2) = \max\limits_{d,d^\prime} |f_2(d,v)-f_2(d^\prime,v)| $$ where $d$ and $d^\prime$ differ on at most one item.
I am looking for a notation to make clear that $v$ is being held constant when I refer to $S(f_2)/S(f_1)$ (as this is a critical fact to highlight and I refer to that quantity quite a lot in my article). I have came up with several alternatives (dropping the numeric subscript), including $S(f_v)$, $S_d(T(v)\cdot d)$, $S(f(d;v))$ but none of them seems suggestive enough (at least for me).
I am pretty sure someone has met this problem before (the problem of denoting one argument of being fixed and acting upon the other) and if such a notation was notorious (although I haven't heard of it) I'd like to stick to it instead of making up a notation of my own. Hence I am asking this question here.
