Add slides on variability in ONTEP.

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@@ -316,6 +316,103 @@ generate code subject to the various constraints.
 \end{minipage}
 }
 
+}
+
+\frame{
+
+\frametitle{Variability in ONETEP}
+
+At the ONETEP masterclass, I got assistance in transcribing the calculations
+that form the bulk of ONETEP's computations. We worked out DSL descriptions for
+the following ONETEP methods:
+
+\begin{itemize}
+
+\item {\tt density\_on\_dbl\_grid}
+\item {\tt integrals\_grad}
+\item {\tt integrals\_kinetic}
+\item {\tt integrals\_locpot}
+\item {\tt integrals\_pos}
+
+\end{itemize}
+
+Although ONETEP is sometimes required to compute other quantities, it is
+apparent that the structure of ONETEP's calculations fall into a couple
+of distinct patterns.
+
+}
+
+\frame{
+
+\frametitle{Variability in ONETEP}
+
+Calculations in ONETEP typically computer either:
+
+\begin{enumerate}
+
+\item Matrices for quantities described using ``bra-ket'' notation.
+
+\item Dense representations of some quantity defined over the entire
+simulation cell.
+
+\end{enumerate}
+
+Naturally, the ONETEP developers have spent a large amount of effort 
+optimising the implementation of these computation patterns. It is unclear
+how any automated code generator might be able to improve upon these.
+
+}
+
+\frame{
+
+\frametitle{Cross-component Optimisation}
+
+
+\begin{itemize}
+
+\item ONETEP makes extensive use of Fast Fourier Transforms (FFTs) to convert
+between position and momentum representation of fields. 
+
+\item Each of the ONETEP calculations uses combinations of FFTs in different
+ways. These include:
+
+\begin{itemize}
+
+\item Up-sampling fields.
+\item Down-sampling fields.
+\item Computing gradients operations in momentum space.
+
+\end{itemize}
+
+\item Can we generate synthesised code that exploits how these transforms are
+  composed in order to reduce computation?
+
+\end{itemize}
+}
+
+\frame{
+
+\frametitle{What might we be able to exploit?}
+
+\begin{itemize}
+
+\item Up-sampling involves performing an inverse-FFT on data-set padded with
+  zeros (new zero-amplitude frequency components).
+
+\item Down-sampling involves discarding parts of the frequency decomposition
+  returned by an FFT (the high-frequency components). 
+
+\item Often, the region being transformed by an FFT is filled with mostly zeros.
+
+\end{itemize}
+
+\centering
+%\resizebox{0.5\linewidth}{!}{\includegraphics{images/fftbox}}
+
+\footnote{Skylaris, Mostofi, Haynes, Pickard \& Payne, 2001, "Accurate kinetic
+energy evaluation in electronic structure calculations with localized functions
+on a real space grid".}
+
 }
 \end{document}