Changeset 139

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• docs/trunk/omega-test-slides/omega-test.tex

  r138	r139
  375	375	\end{frame}
  376	376
  377	\begin{frame}(削除) (削除ここまで)[fragile]
  377	\begin{frame}(追記) <1-2> (追記ここまで)[fragile]
  378	378	\frametitle{Variable Elimination}
  379	Pick a variable to eliminate (for illustration, $x_n$) and rephrase the set of inequalities 0ドル \leq \displaystyle\sum_{i=0}^n a_i x_i$ as:
  380
  381	%TODO this slide is quite dense and a little confusing.
  382	%Would be really cool to animate the equations. Otherwise at least split i = 0 to n out into
  383	% i = 0 to n - 1, plus the case for n
  384
  385	\begin{tabular}{cll}
  386	$a_n$ & Rephrase & Bound\\ \hline
  387	0 & \textit{$x_n$ already eliminated} & \\ \hline
  388	Pos & $\displaystyle\sum_{i=0}^{n-1} -a_i x_i \leq a x_n$ where $a = a_n$ & Lower\\ \hline
  389	Neg & $b x_n \leq \displaystyle\sum_{i=0}^{n-1} a_i x_i$ where $b = -a_n$ & Upper\\ \hline
  390
  379	Pick a variable to eliminate (for illustration, $x_n$)
  380
  381	\only<1>{ \[ 0 \leq \displaystyle\sum_{i=0}^n a_i x_i \] }
  382
  383	\only<1>{ \[ 0 \leq \displaystyle\sum_{i=0}^{n-1} a_i x_i + a_n x_n \] }
  384	\only<2>{
  385	\begin{tabular}{lcr}
  386	& 0ドル \leq \displaystyle\sum_{i=0}^{n-1} a_i x_i + a_n x_n$ & \\
  387	$\displaystyle\sum_{i=0}^{n-1} -a_i x_i \leq a_n x_n$ & & $-a_n x_n \leq \displaystyle\sum_{i=0}^{n-1} a_i x_i$ \\
  388	$a_n$ positive; $a = a_n$ & & $a_n$ negative; $b = -a_n$ \\
  389	& N.B. $a > 0,ドル $b > 0$ & \\
  391	390	\end{tabular}
  392
  393	N.B. $a > 0,ドル $b > 0$
  394
  395	\end{frame}
  396
  397	\begin{frame}[fragile]
  398	\frametitle{Final Flow Chart}
  391	}
  392	%\begin{tabular}{l|l|l}
  393	% & 0ドル \leq \displaystyle\sum_{i=0}^{n-1} a_i x_i + a_n x_n$ \\
  394	%$a_n$ Positive & $\displaystyle\sum_{i=0}^{n-1} -a_i x_i \leq a x_n$ where $a = a_n$ & Lower\\
  395	%$a_n$ Negative & $b x_n \leq \displaystyle\sum_{i=0}^{n-1} a_i x_i$ where $b = -a_n$ & Upper\\
  396	%\end{tabular}
  397
  398	%N.B. $a > 0,ドル $b > 0$
  399
  400	\end{frame}
  401
  402	\begin{frame}[fragile]
  403	\frametitle{Flow Chart}
  399	404	\biggraph{Omega-Flowchart-M2}
  400	405	\end{frame}

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