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 (1.5,4.3) {$X$};
4 \path[draw=black!30,fill=black!8] (0.55,2.65) rectangle (1.5,3.6);
5 \node[font=\small,align=center,font=\small] at (1.025,3.125) {$1$};
6 \path[draw=black!30,fill=black!8] (1.5,2.65) rectangle (2.45,3.6);
7 \node[font=\small,align=center,font=\small] at (1.975,3.125) {$2$};
8 \path[draw=black!30,fill=black!8] (0.55,1.7) rectangle (1.5,2.65);
9 \node[font=\small,align=center,font=\small] at (1.025,2.175) {$3$};
10 \path[draw=black!30,fill=black!8] (1.5,1.7) rectangle (2.45,2.65);
11 \node[font=\small,align=center,font=\small] at (1.975,2.175) {$4$};
12 \node[font=\small,align=center,font=\small] at (4.46,4.65) {$\operatorname{vec}(X)$};
13 \path[draw=black!30,fill=black!8] (4.1,3.23) rectangle (4.82,3.95);
14 \node[font=\small,align=center,font=\small] at (4.46,3.59) {$1$};
15 \path[draw=black!30,fill=black!8] (4.1,2.51) rectangle (4.82,3.23);
16 \node[font=\small,align=center,font=\small] at (4.46,2.87) {$3$};
17 \path[draw=black!30,fill=black!8] (4.1,1.79) rectangle (4.82,2.51);
18 \node[font=\small,align=center,font=\small] at (4.46,2.15) {$2$};
19 \path[draw=black!30,fill=black!8] (4.1,1.07) rectangle (4.82,1.79);
20 \node[font=\small,align=center,font=\small] at (4.46,1.43) {$4$};
21 \node[font=\small,align=center,font=\small] at (8.7,4.3) {$BXA^T$};
22 \path[draw=black!30,fill=black!8] (7.2,2.7) rectangle (8.7,3.6);
23 \node[font=\small,align=center,font=\small] at (7.95,3.15) {$5 + 8 i$};
24 \path[draw=black!30,fill=black!8] (8.7,2.7) rectangle (10.2,3.6);
25 \node[font=\small,align=center,font=\small] at (9.45,3.15) {$2$};
26 \path[draw=black!30,fill=black!8] (7.2,1.8) rectangle (8.7,2.7);
27 \node[font=\small,align=center,font=\small] at (7.95,2.25) {$9 + 12 i$};
28 \path[draw=black!30,fill=black!8] (8.7,1.8) rectangle (10.2,2.7);
29 \node[font=\small,align=center,font=\small] at (9.45,2.25) {$6$};
30 \node[font=\small,align=center,font=\small] at (12.2,3.25) {$A^T$\\not $A^*$};
31 \node[font=\small,align=center] at (7,0.55) {$(A\otimes B)\operatorname{vec}(X)=\operatorname{vec}(BXA^T)$};
32 \end{tikzpicture}

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