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

Download original file

This is the original TeX manuscript source. Use the paper’s PDF for typeset equations.

Read the typeset paper

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 (1.32,4.5) {$U_C$};
4 \path[draw=black!30,fill=black!8] (0.8,3.28) rectangle (1.32,3.8);
5 \node[font=\small,align=center,font=\small] at (1.06,3.54) {$6$};
6 \path[draw=black!30,fill=black!8] (1.32,3.28) rectangle (1.84,3.8);
7 \node[font=\small,align=center,font=\small] at (1.58,3.54) {$1$};
8 \path[draw=black!30,fill=black!8] (0.8,2.76) rectangle (1.32,3.28);
9 \node[font=\small,align=center,font=\small] at (1.06,3.02) {$4$};
10 \path[draw=black!30,fill=black!8] (1.32,2.76) rectangle (1.84,3.28);
11 \node[font=\small,align=center,font=\small] at (1.58,3.02) {$1$};
12 \path[draw=black!30,fill=black!8] (0.8,2.24) rectangle (1.32,2.76);
13 \node[font=\small,align=center,font=\small] at (1.06,2.5) {$6$};
14 \path[draw=black!30,fill=black!8] (1.32,2.24) rectangle (1.84,2.76);
15 \node[font=\small,align=center,font=\small] at (1.58,2.5) {$1$};
16 \path[draw=black!30,fill=black!8] (0.8,1.72) rectangle (1.32,2.24);
17 \node[font=\small,align=center,font=\small] at (1.06,1.98) {$4$};
18 \path[draw=black!30,fill=black!8] (1.32,1.72) rectangle (1.84,2.24);
19 \node[font=\small,align=center,font=\small] at (1.58,1.98) {$1$};
20 \path[draw=black!30,fill=black!8] (0.8,1.2) rectangle (1.32,1.72);
21 \node[font=\small,align=center,font=\small] at (1.06,1.46) {$6$};
22 \path[draw=black!30,fill=black!8] (1.32,1.2) rectangle (1.84,1.72);
23 \node[font=\small,align=center,font=\small] at (1.58,1.46) {$1$};
24 \path[draw=black!30,fill=black!8] (0.8,0.68) rectangle (1.32,1.2);
25 \node[font=\small,align=center,font=\small] at (1.06,0.94) {$4$};
26 \path[draw=black!30,fill=black!8] (1.32,0.68) rectangle (1.84,1.2);
27 \node[font=\small,align=center,font=\small] at (1.58,0.94) {$1$};
28 \node[font=\small,align=center,font=\small] at (5.62,4.5) {$V_C$};
29 \path[draw=black!30,fill=white] (5.1,3.28) rectangle (5.62,3.8);
30 \node[font=\small,align=center,font=\small] at (5.36,3.54) {$0$};
31 \path[draw=black!30,fill=black!8] (5.62,3.28) rectangle (6.14,3.8);
32 \node[font=\small,align=center,font=\small] at (5.88,3.54) {$1$};
33 \path[draw=black!30,fill=black!8] (5.1,2.76) rectangle (5.62,3.28);
34 \node[font=\small,align=center,font=\small] at (5.36,3.02) {$1$};
35 \path[draw=black!30,fill=black!8] (5.62,2.76) rectangle (6.14,3.28);
36 \node[font=\small,align=center,font=\small] at (5.88,3.02) {$2$};
37 \path[draw=black!30,fill=white] (5.1,2.24) rectangle (5.62,2.76);
38 \node[font=\small,align=center,font=\small] at (5.36,2.5) {$0$};
39 \path[draw=black!30,fill=black!8] (5.62,2.24) rectangle (6.14,2.76);
40 \node[font=\small,align=center,font=\small] at (5.88,2.5) {$3$};
41 \path[draw=black!30,fill=black!8] (5.1,1.72) rectangle (5.62,2.24);
42 \node[font=\small,align=center,font=\small] at (5.36,1.98) {$1$};
43 \path[draw=black!30,fill=black!8] (5.62,1.72) rectangle (6.14,2.24);
44 \node[font=\small,align=center,font=\small] at (5.88,1.98) {$4$};
45 \path[draw=black!30,fill=white] (5.1,1.2) rectangle (5.62,1.72);
46 \node[font=\small,align=center,font=\small] at (5.36,1.46) {$0$};
47 \path[draw=black!30,fill=black!8] (5.62,1.2) rectangle (6.14,1.72);
48 \node[font=\small,align=center,font=\small] at (5.88,1.46) {$5$};
49 \path[draw=black!30,fill=black!8] (5.1,0.68) rectangle (5.62,1.2);
50 \node[font=\small,align=center,font=\small] at (5.36,0.94) {$1$};
51 \path[draw=black!30,fill=black!8] (5.62,0.68) rectangle (6.14,1.2);
52 \node[font=\small,align=center,font=\small] at (5.88,0.94) {$6$};
53 \node[font=\small,align=center] at (10.3,3.45) {$AB=D_AD_B+U_CV_C^T$};
54 \node[font=\small,align=center] at (10.3,2.15) {$U_A(V_A^TU_B)V_B^T$};
55 \node[font=\small,align=center,font=\small] at (10.3,1.35) {must be retained};
56 \node[font=\small,align=center,font=\scriptsize] at (7,0.1) {Two input rank-one corrections produce at most rank two, not three.};
57 \end{tikzpicture}

Back to source controls

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