% Equations for clamp-kernel-v1
\section{Equations: clamp-kernel-v1}

\subsection{clamp}
\label{eq:clamp}

\begin{equation}
  y_i = min(max(x_i, lo), hi)
\end{equation}

\textbf{Domain:} $x \in \mathbb{R}^n, lo \leq hi$

\textbf{Codomain:} $y \in [lo, hi]^n$

\textbf{Invariants:}
\begin{itemize}
  \item $lo \leq y_i \leq hi for all i$
  \item $clamp(clamp(x)) = clamp(x)$
  \item $x_i \leq x_j \to y_i \leq y_j$
\end{itemize}

