\require{physics}
\def\rn{\mathbb{R}^n}
\def\half{\frac{1}{2}}
\def\dd{\ \!\mathrm{d}}
\def\dvvp#1#2{\frac{\partial #1}{\partial #2}}
\def\dvvpn#1#2#3{\frac{\partial^#3 #1}{\partial #2^#3}}
\def\of#1{\tilde{#1}}
\def\ten#1{\mathsf{#1}}
\def\diag#1{\mathrm{diag}{#1}}
\def\abs#1{\left| #1 \right|}
\def\pdv#1{\frac{\partial}{\partial #1}}
%\def\dv#1{\frac{\dd}{\dd #1}}
\def\ddv#1#2{\frac{\dd #1}{\dd #2}}
\def\vdot{\mathbf{\cdot}}