block_error.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 (2.26,4.5) {$100E$: twelve omitted entries};
4 \path[draw=black!30,fill=white] (0.7,3.02) rectangle (1.48,3.8);
5 \node[font=\small,align=center,font=\small] at (1.09,3.41) {$0$};
6 \path[draw=black!30,fill=black!8] (1.48,3.02) rectangle (2.26,3.8);
7 \node[font=\small,align=center,font=\small] at (1.87,3.41) {$1$};
8 \path[draw=black!30,fill=black!8] (2.26,3.02) rectangle (3.04,3.8);
9 \node[font=\small,align=center,font=\small] at (2.65,3.41) {$1$};
10 \path[draw=black!30,fill=black!8] (3.04,3.02) rectangle (3.82,3.8);
11 \node[font=\small,align=center,font=\small] at (3.43,3.41) {$1$};
12 \path[draw=black!30,fill=black!8] (0.7,2.24) rectangle (1.48,3.02);
13 \node[font=\small,align=center,font=\small] at (1.09,2.63) {$1$};
14 \path[draw=black!30,fill=white] (1.48,2.24) rectangle (2.26,3.02);
15 \node[font=\small,align=center,font=\small] at (1.87,2.63) {$0$};
16 \path[draw=black!30,fill=black!8] (2.26,2.24) rectangle (3.04,3.02);
17 \node[font=\small,align=center,font=\small] at (2.65,2.63) {$1$};
18 \path[draw=black!30,fill=black!8] (3.04,2.24) rectangle (3.82,3.02);
19 \node[font=\small,align=center,font=\small] at (3.43,2.63) {$1$};
20 \path[draw=black!30,fill=black!8] (0.7,1.46) rectangle (1.48,2.24);
21 \node[font=\small,align=center,font=\small] at (1.09,1.85) {$1$};
22 \path[draw=black!30,fill=black!8] (1.48,1.46) rectangle (2.26,2.24);
23 \node[font=\small,align=center,font=\small] at (1.87,1.85) {$1$};
24 \path[draw=black!30,fill=white] (2.26,1.46) rectangle (3.04,2.24);
25 \node[font=\small,align=center,font=\small] at (2.65,1.85) {$0$};
26 \path[draw=black!30,fill=black!8] (3.04,1.46) rectangle (3.82,2.24);
27 \node[font=\small,align=center,font=\small] at (3.43,1.85) {$1$};
28 \path[draw=black!30,fill=black!8] (0.7,0.68) rectangle (1.48,1.46);
29 \node[font=\small,align=center,font=\small] at (1.09,1.07) {$1$};
30 \path[draw=black!30,fill=black!8] (1.48,0.68) rectangle (2.26,1.46);
31 \node[font=\small,align=center,font=\small] at (1.87,1.07) {$1$};
32 \path[draw=black!30,fill=black!8] (2.26,0.68) rectangle (3.04,1.46);
33 \node[font=\small,align=center,font=\small] at (2.65,1.07) {$1$};
34 \path[draw=black!30,fill=white] (3.04,0.68) rectangle (3.82,1.46);
35 \node[font=\small,align=center,font=\small] at (3.43,1.07) {$0$};
36 \draw[line width=.6pt] (7.35,0.85) -- (12.85,0.85);
37 \node[font=\small,align=center] at (10.1,4.25) {error norms, in units of $1/100$};
38 \path[draw=black,fill=black!12,line width=.6pt] (7.79,0.85) rectangle (8.743333,1.5125);
39 \node[font=\small,align=center,font=\scriptsize] at (8.266667,0.55) {one block};
40 \node[font=\small,align=center,font=\scriptsize] at (8.266667,1.7325) {$1$};
41 \path[draw=black,fill=black!12,line width=.6pt] (9.623333,0.85) rectangle (10.576667,2.8375);
42 \node[font=\small,align=center,font=\scriptsize] at (10.1,0.55) {spectral};
43 \node[font=\small,align=center,font=\scriptsize] at (10.1,3.0575) {$3$};
44 \path[draw=black,fill=black!12,line width=.6pt] (11.456667,0.85) rectangle (12.41,3.144967);
45 \node[font=\small,align=center,font=\scriptsize] at (11.933333,0.55) {Frobenius};
46 \node[font=\small,align=center,font=\scriptsize] at (11.933333,3.364967) {$2 \sqrt{3}$};
47 \node[font=\small,align=center,font=\scriptsize] at (7,0.1) {$\|E\|_F^2=12/10^4$, while $E\mathbf1=(3/100)\mathbf1$.};
48 \end{tikzpicture}

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