From 127356c80404dff3c92c3e38a2b62f2782e301e5 Mon Sep 17 00:00:00 2001
From: Francis Russell <francis@unchartedbackwaters.co.uk>
Date: Thu, 21 Feb 2013 18:40:47 +0000
Subject: [PATCH] Add slide on resampling strategies for integrals_locpot.

---
 Makefile                               |  2 +-
 code/integrals_locpot_resampling_1.txt | 32 ++++++++++++++++++++++++++
 code/integrals_locpot_resampling_2.txt | 32 ++++++++++++++++++++++++++
 presentation.tex                       | 30 ++++++++++++++++++++++--
 4 files changed, 93 insertions(+), 3 deletions(-)
 create mode 100644 code/integrals_locpot_resampling_1.txt
 create mode 100644 code/integrals_locpot_resampling_2.txt

diff --git a/Makefile b/Makefile
index 228e24c..53ccadd 100644
--- a/Makefile
+++ b/Makefile
@@ -7,7 +7,7 @@ SVG_OUTPUTS=${patsubst %.svg,%.pdf,$(SVG_SOURCES)}
 CODE_FOLDER=code
 CODE_F90_TEX_FILES=${patsubst %.F90,%.tex,$(wildcard $(CODE_FOLDER)/*.F90)}
 CODE_UFL_TEX_FILES=${patsubst %.ufl,%.tex,$(wildcard $(CODE_FOLDER)/*.ufl)}
-CODE_RAW_FILES=$(wildcard $(CODE_FOLDER)/*.ofl)
+CODE_RAW_FILES=$(wildcard $(CODE_FOLDER)/*.ofl $(CODE_FOLDER)/*.txt)
 CODE_TEX_FILES=$(CODE_F90_TEX_FILES) $(CODE_UFL_TEX_FILES)
 
 DOT_FOLDER=images-dot
diff --git a/code/integrals_locpot_resampling_1.txt b/code/integrals_locpot_resampling_1.txt
new file mode 100644
index 0000000..894552a
--- /dev/null
+++ b/code/integrals_locpot_resampling_1.txt
@@ -0,0 +1,32 @@
+  integrate((bra[alpha]*(downsample(potential_fine)*ket[beta])))
+
+  integrate((bra[alpha]*downsample((potential_fine*upsample(ket[beta])))))
+
+  integrate(upsample((bra[alpha]*(downsample(potential_fine)*ket[beta]))))
+
+  integrate((upsample(bra[alpha])*(potential_fine*upsample(ket[beta]))))
+
+  integrate(upsample((bra[alpha]*
+            downsample((potential_fine*upsample(ket[beta]))))))
+
+  integrate(downsample((upsample(bra[alpha])*
+                        (potential_fine*upsample(ket[beta])))))
+
+  integrate((upsample(bra[alpha])*
+             upsample((downsample(potential_fine)*ket[beta]))))
+
+  integrate((bra[alpha]*
+             downsample((upsample(downsample(potential_fine))*
+                         upsample(ket[beta])))))
+
+  integrate(upsample(downsample((upsample(bra[alpha])*
+                                 (potential_fine*upsample(ket[beta]))))))
+
+  integrate((upsample(bra[alpha])*
+             upsample(downsample((potential_fine*upsample(ket[beta]))))))
+
+  integrate(downsample((upsample(bra[alpha])*
+            upsample((downsample(potential_fine)*ket[beta])))))
+
+  integrate((upsample(bra[alpha])*
+             (upsample(downsample(potential_fine))*upsample(ket[beta]))))
diff --git a/code/integrals_locpot_resampling_2.txt b/code/integrals_locpot_resampling_2.txt
new file mode 100644
index 0000000..f83c35b
--- /dev/null
+++ b/code/integrals_locpot_resampling_2.txt
@@ -0,0 +1,32 @@
+  integrate(upsample((bra[alpha]*
+                      downsample((upsample(downsample(potential_fine))*
+                                  upsample(ket[beta]))))))
+
+  integrate(downsample((upsample(bra[alpha])*
+                        upsample(downsample((potential_fine*upsample(ket[beta])))))))
+
+  integrate(upsample(downsample((upsample(bra[alpha])*
+                                 upsample((downsample(potential_fine)*ket[beta]))))))
+
+  integrate(downsample((upsample(bra[alpha])*
+                        (upsample(downsample(potential_fine))*upsample(ket[beta])))))
+
+  integrate(upsample(downsample((upsample(bra[alpha])*
+                                 upsample(downsample((potential_fine*
+                                                      upsample(ket[beta]))))))))
+
+  integrate(upsample(downsample((upsample(bra[alpha])*
+                                 (upsample(downsample(potential_fine))*
+                                  upsample(ket[beta]))))))
+
+  integrate((upsample(bra[alpha])*
+             upsample(downsample((upsample(downsample(potential_fine))*
+                                  upsample(ket[beta]))))))
+
+  integrate(downsample((upsample(bra[alpha])*
+                        upsample(downsample((upsample(downsample(potential_fine))*
+                                             upsample(ket[beta])))))))
+
+  integrate(upsample(downsample((upsample(bra[alpha])*
+                                 upsample(downsample((upsample(downsample(potential_fine))*
+                                                      upsample(ket[beta]))))))))
diff --git a/presentation.tex b/presentation.tex
index e58cf59..d95b64e 100644
--- a/presentation.tex
+++ b/presentation.tex
@@ -84,7 +84,8 @@ variational forms developed by the FEniCS project.
 Laplacian as follows:
 
 \begin{equation*}
-a(u,v) = \int_\Omega \nabla u(x) \cdot \nabla v(x)\,dx
+  a(u,v) = 
+  \int_\Omega \nabla u(\mathbf{x}) \cdot \nabla v(\mathbf{x})\,d\mathbf{x}
 \end{equation*}
 
 \item In UFL (specifying physical discretisation) we would write:
@@ -541,7 +542,7 @@ We adopt the following strategy:
 
 \frametitle{Reasoning about correctness: an example}
 
-If we want to evaluate $\int a(x)b(x)dx$ inside a periodic domain, can we use
+If we want to evaluate $\int a(\mathbf{x})b(\mathbf{x})\,d\mathbf{x}$ inside a periodic domain, can we use
 $\sum\limits_{x=0}^{N} a[x]b[x]$?
 
 \centering
@@ -572,6 +573,31 @@ It depends whether we do it on an odd or even number of points.
 
 }
 
+\frame{
+
+\frametitle{Resampling choices for {\tt integrals\_locpot}}
+
+\resizebox{0.48\textwidth}{!}{
+\begin{minipage}{1.2\textwidth}
+\begin{alltt}
+\input{code/integrals_locpot_resampling_1.txt}
+\end{alltt}
+\end{minipage}
+}
+\resizebox{0.48\textwidth}{!}{
+\begin{minipage}{1.2\textwidth}
+\begin{alltt}
+\input{code/integrals_locpot_resampling_1.txt}
+\end{alltt}
+\end{minipage}
+}
+
+\vspace{2em}
+\centering
+We just need to filter out the valid ones!
+
+}
+
 \end{document}
 
 
-- 
2.47.3