toeplitz.tex

Paper VIII: Packet Operator Algorithms, Exact Compilation, and GPU Realization

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Stealth,line cap=round,line join=round]
2 \path[use as bounding box] (0,-.6) rectangle (14,4.8);
3 \node[font=\small,align=center,font=\small] at (1.52,4.5) {$T$};
4 \path[draw=black!30,fill=black!8] (0.35,3.02) rectangle (1.13,3.8);
5 \node[font=\small,align=center,font=\small] at (0.74,3.41) {$2$};
6 \path[draw=black!30,fill=black!8] (1.13,3.02) rectangle (1.91,3.8);
7 \node[font=\small,align=center,font=\small] at (1.52,3.41) {$-1$};
8 \path[draw=black!30,fill=black!8] (1.91,3.02) rectangle (2.69,3.8);
9 \node[font=\small,align=center,font=\small] at (2.3,3.41) {$5$};
10 \path[draw=black!30,fill=black!8] (0.35,2.24) rectangle (1.13,3.02);
11 \node[font=\small,align=center,font=\small] at (0.74,2.63) {$3$};
12 \path[draw=black!30,fill=black!8] (1.13,2.24) rectangle (1.91,3.02);
13 \node[font=\small,align=center,font=\small] at (1.52,2.63) {$2$};
14 \path[draw=black!30,fill=black!8] (1.91,2.24) rectangle (2.69,3.02);
15 \node[font=\small,align=center,font=\small] at (2.3,2.63) {$-1$};
16 \path[draw=black!30,fill=black!8] (0.35,1.46) rectangle (1.13,2.24);
17 \node[font=\small,align=center,font=\small] at (0.74,1.85) {$4$};
18 \path[draw=black!30,fill=black!8] (1.13,1.46) rectangle (1.91,2.24);
19 \node[font=\small,align=center,font=\small] at (1.52,1.85) {$3$};
20 \path[draw=black!30,fill=black!8] (1.91,1.46) rectangle (2.69,2.24);
21 \node[font=\small,align=center,font=\small] at (2.3,1.85) {$2$};
22 \node[font=\small,align=center,font=\small] at (4.355,4.5) {circulant column $g$};
23 \path[draw=black!30,fill=black!8] (4.1,3.29) rectangle (4.61,3.8);
24 \node[font=\small,align=center,font=\small] at (4.355,3.545) {$2$};
25 \path[draw=black!30,fill=black!8] (4.1,2.78) rectangle (4.61,3.29);
26 \node[font=\small,align=center,font=\small] at (4.355,3.035) {$3$};
27 \path[draw=black!30,fill=black!8] (4.1,2.27) rectangle (4.61,2.78);
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31 \path[draw=black!30,fill=black!8] (4.1,1.25) rectangle (4.61,1.76);
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33 \path[draw=black!30,fill=black!8] (4.1,0.74) rectangle (4.61,1.25);
34 \node[font=\small,align=center,font=\small] at (4.355,0.995) {$-1$};
35 \node[font=\small,align=center,font=\small] at (7.355,4.5) {padded input};
36 \path[draw=black!30,fill=black!8] (7.1,3.29) rectangle (7.61,3.8);
37 \node[font=\small,align=center,font=\small] at (7.355,3.545) {$1$};
38 \path[draw=black!30,fill=black!8] (7.1,2.78) rectangle (7.61,3.29);
39 \node[font=\small,align=center,font=\small] at (7.355,3.035) {$2$};
40 \path[draw=black!30,fill=black!8] (7.1,2.27) rectangle (7.61,2.78);
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44 \path[draw=black!30,fill=white] (7.1,1.25) rectangle (7.61,1.76);
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47 \node[font=\small,align=center,font=\small] at (7.355,0.995) {$0$};
48 \node[font=\small,align=center,font=\small] at (10.855,4.5) {six outputs};
49 \path[draw=black!30,fill=black!8] (10.6,3.29) rectangle (11.11,3.8);
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51 \path[draw=black!30,fill=black!8] (10.6,2.78) rectangle (11.11,3.29);
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53 \path[draw=black!30,fill=black!8] (10.6,2.27) rectangle (11.11,2.78);
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55 \path[draw=black!30,fill=black!8] (10.6,1.76) rectangle (11.11,2.27);
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57 \path[draw=black!30,fill=black!8] (10.6,1.25) rectangle (11.11,1.76);
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59 \path[draw=black!30,fill=black!8] (10.6,0.74) rectangle (11.11,1.25);
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61 \path[draw,line width=1.2pt] (10.6,2.27) rectangle (11.11,3.8);
62 \node[font=\small,align=center,font=\scriptsize] at (12.5,2.95) {keep\\first three};
63 \node[font=\small,align=center,font=\scriptsize] at (7,0.05) {Padding is part of the operator identity, not optional workspace.};
64 \end{tikzpicture}

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