318 lines
12 KiB
TeX
318 lines
12 KiB
TeX
\begin{frame}{Propagation Paralèlle \emph{à la} Margolus}
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{Le problème de la dépendance aux cellules voisines}
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\vfill
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\centering
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\begin{tikzpicture}
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\clip (-17mm,-17mm) rectangle (17mm,17mm);
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\draw[xshift=5mm,yshift=5mm] ( -3cm, -3cm) grid ( 3cm, 3cm);
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\node (x) at (0,0) {$x_i$};
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\foreach[count=\n] \p in {(1,0),(1,1),(0,1),(-1,1),(-1,0),(-1,-1),(0,-1),(1,-1)} {
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\node (v\n) at \p {$v_{\n_i}$};
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}
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\begin{scope}[on background layer]
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\clip (-17mm,-17mm) rectangle (17mm,17mm);
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\only<1>{%
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\fill[black!10] (v6.south west) rectangle (v2.north east);
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\fill[white] (v6.north east) rectangle (v2.south west);
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\fill[red!60] (x) circle (3mm);
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}
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\only<2>{%
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\fill[black!10] (v3.north east) rectangle ($(v7.south east)+(-10cm,0)$);
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\fill[white] (v3.south west) rectangle ($(v7.north east)+(-10cm,0)$);
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\fill[red!60] (v5) circle (3mm);
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}
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\end{scope}
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\end{tikzpicture}
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\alt<1>{%
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$$ x_{i,1} = f(x_i , v_{1_i} , v_{2_i} , \ldots , v_{8_i}) $$
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}{%
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$$ v_{5_{i,1}} = f(v_{5_i} , x_i , v_{3_i}, v_{4_i} ,
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\alert{? , ? , ?} , v_{6_i} , v_{7_i}) $$
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}
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\vfill~
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\uncover<2>{Une partie du \structure{contexte} est manquant.}
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\end{frame}
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\begin{frame}{Propagation Paralèlle \emph{à la} Margolus}
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{Le voisinage de margolus}
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\vfill
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\centering
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\begin{tikzpicture}
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\clip (-27mm,-27mm) rectangle (27mm,27mm);
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\draw[xshift=5mm,yshift=5mm] ( -5cm, -5cm) grid ( 5cm, 5cm);
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\fill[red] (0,0) circle (3mm);
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\only<1>{\draw[xshift=5mm,yshift=5mm, step=2cm, very thick]%
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( -5cm, -5cm) grid ( 5cm, 5cm);}
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\only<2>{\draw[xshift=-5mm,yshift=-5mm, step=2cm, very thick]%
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( -5cm, -5cm) grid ( 5cm, 5cm);}
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\begin{scope}[on background layer]
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\only<1>{%
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\fill[red!50,shift={(-5mm,-5mm)}] (-1cm,-1cm) rectangle (1cm,1cm);}
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\only<2>{%
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\fill[red!50,shift={(5mm,5mm)}] (-1cm,-1cm) rectangle (1cm,1cm);}
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\end{scope}
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\end{tikzpicture}
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\vfill~
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\end{frame}
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\begin{frame}{Propagation Paralèlle \emph{à la} Margolus}
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{Mise à jour \emph{indépendante} d'un bloc}
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\vfill
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\centering
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\begin{tikzpicture}[
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cell/.style={black,size=1.5mm,circle,inner sep=0pt,font=\TINY},
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neighbor cell/.style={black,size=1.5mm,circle,inner sep=0pt,font=\small},
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center cell/.style={cell,white,fill=black},
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spy using outlines={circle,red,size=58mm,magnification=4,connect spies}]
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\begin{scope}[scale=.5]
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\clip (-27mm,-27mm) rectangle (27mm,27mm);
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% Background
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\only<1-3>{%
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\fill[blue!50,shift={(5mm,5mm)}] (-1cm,-1cm) rectangle (1cm,1cm);
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\fill[red!50,shift={(-5mm,-5mm)}] (-1cm,-1cm) rectangle (1cm,1cm);
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}
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\only<4->{%
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\fill[red!50,shift={(-5mm,-5mm)}] (-1cm,-1cm) rectangle (1cm,1cm);
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\fill[blue!50,shift={(5mm,5mm)}] (-1cm,-1cm) rectangle (1cm,1cm);
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}
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\begin{scope}
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\clip (-3mm,-3mm) rectangle (3mm,3mm);
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\draw[very thin] (-5mm,-5mm) grid (5mm,5mm);
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\end{scope}
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\only<1-3>{
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\begin{scope}[shift={(-1cm,0)}]
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\clip (-3mm,-3mm) rectangle (3mm,3mm);
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\draw[very thin] (-5mm,-5mm) grid (5mm,5mm);
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\end{scope}
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\begin{scope}[shift={(-1cm,-1cm)}]
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\clip (-3mm,-3mm) rectangle (3mm,3mm);
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\draw[very thin] (-5mm,-5mm) grid (5mm,5mm);
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\end{scope}
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\begin{scope}[shift={(0cm,-1cm)}]
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\clip (-3mm,-3mm) rectangle (3mm,3mm);
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\draw[very thin] (-5mm,-5mm) grid (5mm,5mm);
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\end{scope}
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}
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\only<1>{
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% Voisins
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\node[neighbor cell] at ( 1cm, 0cm) {$v_{A,1}$};
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\node[neighbor cell] at ( 1cm, 1cm) {$v_{A,2}$};
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\node[neighbor cell] at ( 0cm, 1cm) {$v_{A,3}$};
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\node[neighbor cell] at (-1cm, 1cm) {$v_{B,1}$};
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\node[neighbor cell] at (-2cm, 1cm) {$v_{B,2}$};
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\node[neighbor cell] at (-2cm, 0cm) {$v_{B,3}$};
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\node[neighbor cell] at (-2cm,-1cm) {$v_{C,1}$};
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\node[neighbor cell] at (-2cm,-2cm) {$v_{C,2}$};
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\node[neighbor cell] at (-1cm,-2cm) {$v_{C,3}$};
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\node[neighbor cell] at ( 0cm,-2cm) {$v_{D,1}$};
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\node[neighbor cell] at ( 1cm,-2cm) {$v_{D,2}$};
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\node[neighbor cell] at ( 1cm,-1cm) {$v_{D,3}$};
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\begin{scope}[scale=0.5,shift={(-5mm,-5mm)}]
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\node[center cell] at ( -0mm, -0mm) {$A$};
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\node[cell] at (-10mm, -0mm) {$B$};
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\node[cell] at (-10mm,-10mm) {$C$};
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\node[cell] at ( -0mm,-10mm) {$D$};
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\node[cell] at ( 1cm, 0cm) {$v_{A,1}$};
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\node[cell] at ( 1cm, 1cm) {$v_{A,2}$};
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\node[cell] at ( 0cm, 1cm) {$v_{A,3}$};
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\node[cell] at (-1cm, 1cm) {$v_{B,1}$};
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\node[cell] at (-2cm, 1cm) {$v_{B,2}$};
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\node[cell] at (-2cm, 0cm) {$v_{B,3}$};
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\node[cell] at (-2cm,-1cm) {$v_{C,1}$};
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\node[cell] at (-2cm,-2cm) {$v_{C,2}$};
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\node[cell] at (-1cm,-2cm) {$v_{C,3}$};
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\node[cell] at ( 0cm,-2cm) {$v_{D,1}$};
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\node[cell] at ( 1cm,-2cm) {$v_{D,2}$};
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\node[cell] at ( 1cm,-1cm) {$v_{D,3}$};
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\end{scope}
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}
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\only<2>{
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\begin{scope}[scale=0.5,shift={(-5mm,-5mm)}]
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\node[center cell] at ( -0mm, -0mm) {$A'$};
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\node[cell] at (-10mm, -0mm) {$B'$};
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\node[cell] at (-10mm,-10mm) {$C'$};
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\node[cell] at ( -0mm,-10mm) {$D'$};
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\end{scope}
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}
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\only<3>{
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\begin{scope}[scale=0.5,shift={(5mm,5mm)}]
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\node[center cell] at ( -0mm, -0mm) {$A'$};
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\node[cell] at (-10mm, -0mm) {$B'$};
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\node[cell] at (-10mm,-10mm) {$C'$};
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\node[cell] at ( -0mm,-10mm) {$D'$};
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\end{scope}
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\begin{scope}[scale=0.5,shift={(-15mm,5mm)}]
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\node[cell] at ( -0mm, -0mm) {$A'$};
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\node[cell] at (-10mm, -0mm) {$B'$};
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\node[cell] at (-10mm,-10mm) {$C'$};
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\node[cell] at ( -0mm,-10mm) {$D'$};
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\end{scope}
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\begin{scope}[scale=0.5,shift={(-15mm,-15mm)}]
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\node[cell] at ( -0mm, -0mm) {$A'$};
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\node[cell] at (-10mm, -0mm) {$B'$};
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\node[cell] at (-10mm,-10mm) {$C'$};
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\node[cell] at ( -0mm,-10mm) {$D'$};
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\end{scope}
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\begin{scope}[scale=0.5,shift={(5mm,-15mm)}]
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\node[cell] at ( -0mm, -0mm) {$A'$};
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\node[cell] at (-10mm, -0mm) {$B'$};
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\node[cell] at (-10mm,-10mm) {$C'$};
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\node[cell] at ( -0mm,-10mm) {$D'$};
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\end{scope}
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}
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\only<4>{
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\begin{scope}[scale=0.5,shift={(5mm,5mm)}]
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\node[center cell] at ( -0mm, -0mm) {$A'$};
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\node[cell] at (-10mm, -0mm) {$B'$};
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\node[cell] at (-10mm,-10mm) {$C'$};
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\node[cell] at ( -0mm,-10mm) {$D'$};
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\end{scope}
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}
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% Grilles:
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\draw[xshift=5mm,yshift=5mm,thin] ( -5cm, -5cm) grid ( 5cm, 5cm);
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\only<1-3>{\draw[xshift=5mm,yshift=5mm, step=2cm, thick]%
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( -5cm, -5cm) grid ( 5cm, 5cm);}
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\only<4>{\draw[xshift=-5mm,yshift=-5mm, step=2cm, thick]%
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( -5cm, -5cm) grid ( 5cm, 5cm);}
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\only<1-3>{
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\coordinate (spyhook) at (-5mm,-5mm);
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}
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\only<4>{
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\coordinate (spyhook) at (5mm,5mm);
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}
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\end{scope}
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\spy on (spyhook) in node (zoom) at (5cm,0);
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\end{tikzpicture}
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%\only<1-2>{
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%Toute l'information \emph{nécessaire} est disponible pour mettre à jour $A$.
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%$$ A' = f( A, v_{A_1}, v_{A_2}, v_{A_3}, v_{B_1}, B, C, D, v_{D_3} ) $$
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%ainsi que $B$, $C$ et $D$, symétriquement.
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%}
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%\only<3>{
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%Le bloc $(A',B',C',D')$ est répliqué 4 fois.}
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%\only<4>{
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%Au décalage de la grille, le nouveau bloc est prêt pour une mise à jour.
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%}
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\vfill~
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\end{frame}
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%\begin{frame}{Propagation Paralèlle \emph{à la} Margolus}
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% {Mise à jour \emph{indépendante} d'un bloc}
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% \vfill
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%
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% \begin{columns}[c]
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% \column{.4\textwidth}\centering
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% \begin{tikzpicture}[scale=.5]
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% \clip (-27mm,-27mm) rectangle (27mm,27mm);
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% \draw[xshift=5mm,yshift=5mm] ( -5cm, -5cm) grid ( 5cm, 5cm);
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% \fill[red] (0,0) circle (3mm);
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% \only<1-3>{\draw[xshift=5mm,yshift=5mm, step=2cm, very thick]%
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% ( -5cm, -5cm) grid ( 5cm, 5cm);}
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% \only<4->{\draw[xshift=-5mm,yshift=-5mm, step=2cm, very thick]%
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% ( -5cm, -5cm) grid ( 5cm, 5cm);}
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% \begin{scope}[on background layer]
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% \only<1-3>{%
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% \fill[blue!50,shift={(5mm,5mm)}] (-1cm,-1cm) rectangle (1cm,1cm);
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% \fill[red!50,shift={(-5mm,-5mm)}] (-1cm,-1cm) rectangle (1cm,1cm);}
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% \only<4->{%
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% \fill[red!50,shift={(5mm,5mm)}] (-1cm,-1cm) rectangle (1cm,1cm);}
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% \end{scope}
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% \end{tikzpicture}
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% \column{.6\textwidth}\centering
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% \begin{tikzpicture}
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% \only<1-2,4>{%
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% \fill[red!50] (-1cm,-1cm) rectangle (1cm,1cm);}
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% \only<3>{%
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% \fill[red!50, shift={(1cm,1cm)}] (0cm,0cm) rectangle (1cm,1cm);
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% \fill[red!50, shift={(1cm,-2cm)}] (0cm,0cm) rectangle (1cm,1cm);
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% \fill[red!50, shift={(-2cm,1cm)}] (0cm,0cm) rectangle (1cm,1cm);
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% \fill[red!50, shift={(-2cm,-2cm)}] (0cm,0cm) rectangle (1cm,1cm);}
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% \only<1>{%
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% \fill[blue!50] (0cm,1cm) -- (0cm,2cm) -- (2cm,2cm) -- (2cm,0cm) -- (1cm,0cm) -- (1cm,1cm) -- cycle;}
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% \draw[very thin,dashed] (-2,-2) grid (2,2);
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% \draw[step=2cm] (-2,-2) grid (2,2);
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% \draw[step=4cm, very thick, shift={(-2cm,-2cm)}] (-4mm,-4mm) grid (44mm,44mm);
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% \only<1>{%
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% \node [fill=red, minimum size=6mm, inner sep=0, circle] (A) at (5mm,5mm) {A};%
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% \node [draw=red, thick, dashed, minimum size=6mm, inner sep=0, circle] (B) at (-5mm,5mm) {B};%
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% \node [draw=red, thick, dashed, minimum size=6mm, inner sep=0, circle] (C) at (-5mm,-5mm) {C};%
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% \node [draw=red, thick, dashed, minimum size=6mm, inner sep=0, circle] (D) at (5mm,-5mm) {D};%
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% \node (va1) at (15mm,5mm) {$v_{A_1}$};%
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% \node (va2) at (15mm,15mm) {$v_{A_2}$};%
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% \node (va3) at (5mm,15mm) {$v_{A_3}$};%
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% \node (vb1) at (-5mm,15mm) {$v_{B_1}$};%
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% \node (vd3) at (15mm,-5mm) {$v_{D_3}$};%
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% }
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% \only<2>{%
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% \node [fill=red, minimum size=6mm, inner sep=0, circle] (A') at (5mm,5mm) {A'};%
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% \node (B') at (-5mm,5mm) {B'};%
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% \node (C') at (-5mm,-5mm) {C'};%
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% \node (D') at (5mm,-5mm) {D'};%
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% }
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% \only<3>{%
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% \node [fill=red, minimum size=6mm, inner sep=0, circle] (A') at (15mm,15mm) {A'};%
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% \node (B') at ( 5mm,15mm) {B'};%
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% \node (C') at ( 5mm, 5mm) {C'};%
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% \node (D') at (15mm, 5mm) {D'};%
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% \begin{scope}[shift={(-15mm,5mm)}]
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% \node (A') at (10mm,10mm) {A'};%
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% \node (B') at ( 0mm,10mm) {B'};%
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% \node (C') at ( 0mm, 0mm) {C'};%
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% \node (D') at (10mm, 0mm) {D'};%
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% \end{scope}
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% \begin{scope}[shift={(5mm,-15mm)}]
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% \node (A') at (10mm,10mm) {A'};%
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% \node (B') at ( 0mm,10mm) {B'};%
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% \node (C') at ( 0mm, 0mm) {C'};%
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% \node (D') at (10mm, 0mm) {D'};%
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% \end{scope}
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% \begin{scope}[shift={(-15mm,-15mm)}]
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% \node (A') at (10mm,10mm) {A'};%
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% \node (B') at ( 0mm,10mm) {B'};%
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% \node (C') at ( 0mm, 0mm) {C'};%
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% \node (D') at (10mm, 0mm) {D'};%
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% \end{scope}
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% }
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% \only<4>{
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% \begin{scope}[shift={(-15mm,-15mm)}]
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% \node [fill=red, minimum size=6mm, inner sep=0, circle] (A') at (10mm,10mm) {A};%
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% \node (B') at ( 0mm,10mm) {B};%
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% \node (C') at ( 0mm, 0mm) {C};%
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% \node (D') at (10mm, 0mm) {D};%
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% \end{scope}
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% }
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% \end{tikzpicture}
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% \end{columns}
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%
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% \centering
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% \only<1-2>{
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% Toute l'information \emph{nécessaire} est disponible pour mettre à jour $A$.
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% $$ A' = f( A, v_{A_1}, v_{A_2}, v_{A_3}, v_{B_1}, B, C, D, v_{D_3} ) $$
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% ainsi que $B$, $C$ et $D$, symétriquement.
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% }
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% \only<3>{
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% Le bloc $(A',B',C',D')$ est répliqué 4 fois.}
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% \only<4>{
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% Au décalage de la grille, le nouveau bloc est prêt pour une mise à jour.
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% }
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%
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%
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% \vfill~
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%\end{frame}
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