Initial work on Scala implementation slides.

diff --git a/.gitignore b/.gitignore
index 411f5399091e31e31b5b1281324d40be1d7a2822..8ae8e9d52eeeb99da021908bb6593d27a74e3897 100644 (file)
--- a/.gitignore
+++ b/.gitignore
@@ -11,3 +11,4 @@
 /*.snm
 /*.toc
 /code/*.tex
+/images-dot/*.tex

diff --git a/Makefile b/Makefile
index 5d5d19902d35f76e0be58881e34e72e7afff45a2..bbbf133b915d18032e2524065c47226367c79824 100644 (file)
--- a/Makefile
+++ b/Makefile
@@ -9,6 +9,9 @@ CODE_F90_TEX_FILES=${patsubst %.F90,%.tex,$(wildcard $(CODE_FOLDER)/*.F90)}
 CODE_UFL_TEX_FILES=${patsubst %.ufl,%.tex,$(wildcard $(CODE_FOLDER)/*.ufl)}
 CODE_TEX_FILES=$(CODE_F90_TEX_FILES) $(CODE_UFL_TEX_FILES)
 
+DOT_FOLDER=images-dot
+DOT_TEX_FILES=${patsubst %.dot,%.tex,$(wildcard $(DOT_FOLDER)/*.dot)}
+
 
 PDFLATEX_OUTPUT_LOG=pdflatex_output.log
 
@@ -25,7 +28,7 @@ display-4up: presentation-4up.pdf
 presentation-4up.pdf: presentation.pdf
        pdfnup --nup 2x2 --a4paper --scale 0.95 --frame true presentation.pdf -o presentation-4up.pdf
 
-presentation.pdf: $(IMAGE_FILES) $(SVG_OUTPUTS) $(CODE_TEX_FILES) $(wildcard *.tex *.sty) pygments.sty
+presentation.pdf: $(IMAGE_FILES) $(SVG_OUTPUTS) $(CODE_TEX_FILES) $(DOT_TEX_FILES) $(wildcard *.tex *.sty) pygments.sty
        pdflatex -draftmode presentation &&\
        while(pdflatex presentation | tee $(PDFLATEX_OUTPUT_LOG) && grep "Rerun to get cross-references right" $(PDFLATEX_OUTPUT_LOG)); do true; done &&\
        rm -f $(PDFLATEX_OUTPUT_LOG)
@@ -36,6 +39,7 @@ clean:
         $(BASIS_FUNCTIONS_FOLDER)/*.pdf \
         $(BASIS_FUNCTIONS_BUILD_STAMP) \
         $(CODE_TEX_FILES) \
+       $(DOT_FOLDER)/*.tex \
         pygments.sty
 
 upload: presentation.pdf
@@ -53,4 +57,7 @@ pygments.sty:
 %.tex: %.ufl
        pygmentize -f latex -l python -o $@ $<
 
+%.tex: %.dot
+       dot2tex --codeonly --usepdflatex -f tikz $< -o $@
+
 .PHONY: all display clean upload 4up display-4up

diff --git a/images-dot/index_propagation_dag.dot b/images-dot/index_propagation_dag.dot
new file mode 100644 (file)
index 0000000..c339469
--- /dev/null
+++ b/images-dot/index_propagation_dag.dot
@@ -0,0 +1,22 @@
+digraph discrete_expression_dag
+{
+  size="6x9";
+  ratio="compress";
+
+  // Expression DAG
+  node[shape=box, style=filled, texmode="raw", height=0.3,
+    style="thick,draw=blue!75,fill=blue!20,rounded corners=1pt"
+  ];
+
+  "multiply" [label="$\times$"];
+  "dot" [label="$\\begin{matrix} \\cdot \\\\ \\{x_b=x''_k, y_b=y''_k, z_b=z''_k\\} \\end{matrix}$", height=1.0];
+
+  edge[texmode="raw"];
+  "dot" -> "bra[alpha]" [label="$\\{func_b,x_b,y_b,z_b\\}$"];
+  "fft" -> "ket[beta]" [label="$\\{func_k,x_k,y_k,z_k\\}$"];
+  "laplacian" -> "fft" [label="$\\{func_k,x'_k,y'_k,z'_k\\}$"];
+  "ifft" -> "laplacian" [label="$\\{func_k,x'_k,y'_k,z'_k\\}$"];
+  "dot" -> "ifft" [label="$\\{func_k,x''_k,y''_k,z''_k\\}$"];
+  "multiply" -> "dot" [label="$\\{func_b,func_k\\}$"];
+  "multiply" -> "-0.5" [label="$\\emptyset$"];
+}

diff --git a/presentation.tex b/presentation.tex
index b569399d947ed519f1549efcffa4a2c47df72cc3..c61195d23aaccfca043487c3a8d2222c5aca53bc 100644 (file)
--- a/presentation.tex
+++ b/presentation.tex
@@ -5,6 +5,7 @@
 \usepackage{graphicx}
 \usepackage{verbatim}
 \usepackage{fancyvrb}
+\usepackage{tikz}
 \usepackage{ucs}
 \usepackage{alltt}
 \usepackage[utf8x]{inputenc}
@@ -154,16 +155,119 @@ variability in the implementation through otherwise inaccessible techniques.
 
 }
 
-\frame{
+\frame[containsverbatim]{
 
 \frametitle{The Domain of Variability in ONETEP}
 
+Our initial approach consisted of designing a DSL similar in style to
+UFL since the operations and notation were similar.
+
+\vspace{1em}
+
+As an example, the kinetic energy integral in mathematical notation:
+
+\vspace{1em}
+
+\begin{equation*}
+T_{\alpha\beta} = - \frac{1}{2}
+\phi_{\alpha}^{*}(\mathbf{r})\nabla^2\phi_{\beta}(\mathbf{r})\;d\mathbf{r}
+\end{equation*}
+
+\vspace{1em}
+
+and written as an expression in the DSL (omitting declarations and other
+additional details):
+
+\vspace{1em}
+
+\begin{verbatim}
+kinet[alpha, beta] = 
+  inner(bra[alpha], laplacian(ket[beta])*-0.5)
+\end{verbatim}
+
+}
+
+\frame{
+
+\frametitle{Our initial design}
+
+\begin{itemize}
+
+\item The fields used by ONETEP are stored in a blocked space format
+called \emph{PPD representation}.
+
+\item PPD representation involves storing a field using fixed-size blocks
+of co-efficients only for locations in the cell where data is not
+zero-valued.
+
+\item This representation is not dissimilar to that used by some formats
+of sparse matrix storage.
+
+\item In addition, the presence of indices into sparse matrices,
+multi-dimensional arrays and reduction operators suggests a system that
+generates code that implements tensor contractions between large, distributed,
+possibly sparse multi-dimensional objects. 
+
+\end{itemize}
+
+}
+
+
+\frame{
+
+\frametitle{Relational algebra to the rescue?}
+
+\begin{itemize}
+
+\item Efficiently implementing contractions between
+  multi-dimensional arrays stored in representations is similar to
+  the problem faced by databases implementing joins.
+
+\item We looked at work by Kotlyar on generating efficient code that handles
+  accessing multi-dimensional data stored using user-defined data structures.
+
+\item The system uses a ``hierarchy of indices'' that describe
+  properties such as dependencies between indices, whether random access is
+  possible, the nature of overlaps between data.
+
+\end{itemize}
+
 \centering
-\scalebox{15.0}{
-$\emptyset$
+{
+\footnotesize
+\begin{tabular}{rl}
+\hline
+\textbf{Name} & \textbf{Type} \\
+\hline
+CRS & $T_{CRS} = I \succ J \succ V $ \\
+CCS & $T_{CCS} = J \succ I \succ V $ \\
+Co-ordinate & $T_{coord} = (I, J) \succ V $ \\
+Dense & $T_{dense} = I \times J \succ V $ \\
+inode & $T_{inode} = INODE \succ_{\not \cap} (I \times J) \succ V $ \\
+Finite element & $T_{FE} = E \succ_{+} (I \times J) \succ V $ \\
+Permutation & $T_{perm} = (I \succ I') \cup (I' \succ I)$ \\
+\hline
+\end{tabular}
+}
+
 }
 
+\frame{
+
+\frametitle{Our initial implementation}
+
+We developed an code generator in Scala that attempted to reason
+abstractly about the indices involved in the computation.
+
+\centering
+\resizebox{!}{0.5\textheight}{
+\begin{tikzpicture}[scale=0.5, minimum size=2em, thick]
+\input{images-dot/index_propagation_dag}
+\end{tikzpicture}
 }
 
+}
 
 \end{document}
+
+