CoCalc -- convolution-linear.tex

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cocalc-examples / martinthoma-latex-examples / presentations / CNN-Intro / graphics / convolution-linear.tex
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\newcommand{\filtersize}{3}
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\newcommand{\filterx}{8}
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\newcommand{\filtery}{2.2}
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\newcommand{\filteroffset}{1}
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\newcommand{\filterxres}{12}
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\newcommand{\imagesize}{7}
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\newcommand{\imagex}{0}
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\newcommand{\imagey}{0}
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\newcommand{\imageoffset}{2}
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\newcommand{\outx}{16}
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\newcommand{\outy}{0}
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\newcommand{\outoffset}{2}
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\newcommand{\percx}{1}
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\newcommand{\percy}{2}
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\begin{tikzpicture}[scale=0.6]
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    \tikzstyle{point}=[draw=none,inner sep=0pt]
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    % draw perceptive field
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    \node (p1)[point] at (\imagex+\percx,
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                          \imagey+\percy+\percx*\imageoffset/\imagesize) {};
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    \node (p2)[point] at (\imagex+\percx+\filtersize,
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                          \imagey+\percy+\percx*\imageoffset/\imagesize+\filtersize*\imageoffset/\imagesize) {};
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    \node (p3)[point,blue] at (\imagex+\percx+\filtersize,
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                          \imagey+\percy+\filtersize+\percx*\imageoffset/\imagesize+\filtersize*\imageoffset/\imagesize) {};
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    \node (p4)[point] at (\imagex+\percx,
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                          \imagey+\percy+\filtersize+\percx*\imageoffset/\imagesize) {};
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    \draw[fill=gray] (p1.center) -- (p2.center) -- (p3.center) -- (p4.center) -- (p1.center);
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    % draw output point
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    \node (o1)[point] at (\outx+\percx+1,
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                          \outy+\percy+\percx*\outoffset/\imagesize+1+1*\outoffset/\imagesize) {};
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    \node (o2)[point] at (\outx+\percx+2,
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                          \outy+\percy+\percx*\outoffset/\imagesize+1*\outoffset/\imagesize+1+1*\outoffset/\imagesize) {};
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    \node (o3)[point,blue] at (\outx+\percx+2,
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                          \outy+\percy+1+\percx*\outoffset/\imagesize+1*\outoffset/\imagesize+1+1*\outoffset/\imagesize) {};
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    \node (o4)[point] at (\outx+\percx+1,
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                          \outy+\percy+2+\percx*\outoffset/\imagesize+1*\outoffset/\imagesize) {};
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    \draw[fill=gray] (o1.center) -- (o2.center) -- (o3.center) -- (o4.center) -- (o1.center);
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    % draw image
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    \foreach \x in {0,...,\imagesize}
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    {
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    \draw (\imagex+\x, \imagey+\x*\imageoffset/\imagesize) -- (\imagex+\x, \imagey+\imagesize+\x*\imageoffset/\imagesize);
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    \draw (\imagex, \imagey+\x) -- (\imagex+\imagesize, \imagey+\x+\imageoffset);
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    }
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    % draw filter
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    \foreach \x in {0,...,\filtersize}
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    {
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    \draw (\filterx+\x, \filtery+\x*\filteroffset/\filtersize) -- (\filterx+\x, \filtery+\filtersize+\x*\filteroffset/\filtersize);
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    \draw (\filterx, \filtery+\x) -- (\filterx+\filtersize, \filtery+\x+\filteroffset);
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    }
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    % draw filter result
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    \foreach \x in {0,...,\filtersize}
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    {
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    \draw (\filterxres+\x, \filtery+\x*\filteroffset/\filtersize) -- (\filterxres+\x, \filtery+\filtersize+\x*\filteroffset/\filtersize);
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    \draw (\filterxres, \filtery+\x) -- (\filterxres+\filtersize, \filtery+\x+\filteroffset);
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    }
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    % draw out
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    \foreach \x in {0,...,\imagesize}
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    {
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    \draw (\outx+\x, \outy+\x*\outoffset/\imagesize) -- (\outx+\x, \outy+\imagesize+\x*\outoffset/\imagesize);
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    \draw (\outx, \outy+\x) -- (\outx+\imagesize, \outy+\x+\outoffset);
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    }
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    \node at (\imagex + \imagesize/2,\imagey + \imagesize + 2) {\Huge $I \in \mathbb{R}^{\imagesize \times \imagesize}$};
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     \node[text width=4cm, align=center] at (\filterx + \filtersize/2,\filtery + \filtersize - 4) {\large Filter kernel\\$F \in \mathbb{R}^{\filtersize \times \filtersize}$};
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    \node[text width=4cm, align=center] at (\filterx + 4 + \filtersize/2,\filtery + \filtersize - 4) {\large Result of point-wise multiplication};
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    \node at (\outx + \imagesize/2,\outy + \imagesize + 2) {\Huge $I' \in \mathbb{R}^{\imagesize \times \imagesize}$};
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    % Start image (left to right, top to bottom)
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    \node[draw=none] at (0.5, 6.6) {\large 104};
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    \node[draw=none] at (1.5, 6.9) {\large 116};
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    \node[draw=none] at (2.5, 7.2) {\large 116};
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    \node[draw=none] at (3.5, 7.5) {\large 112};
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    \node[draw=none] at (4.5, 7.8) {\large  58};
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    \node[draw=none] at (5.5, 8.1) {\large  47};
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    \node[draw=none] at (6.5, 8.4) {\large  47};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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    \node[draw=none] at (0.5, 5.6) {\large 109};
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    \node[draw=none] at (1.5, 5.9) {\large  97};
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    \node[draw=none] at (2.5, 6.2) {\large 114};
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    \node[draw=none] at (3.5, 6.5) {\large 116};
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    \node[draw=none] at (4.5, 6.8) {\large 105};
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    \node[draw=none] at (5.5, 7.1) {\large 110};
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    \node[draw=none] at (6.5, 7.4) {\large  45};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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    \node[draw=none] at (0.5, 4.6) {\large 116};
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    \node[draw=none] at (1.5, 4.9) {\large 104};
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    \node[draw=none] at (2.5, 5.2) {\large 111};
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    \node[draw=none] at (3.5, 5.5) {\large 109};
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    \node[draw=none] at (4.5, 5.8) {\large  97};
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    \node[draw=none] at (5.5, 6.1) {\large  46};
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    \node[draw=none] at (6.5, 6.4) {\large 100};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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    \node[draw=none] at (0.5, 3.6) {\large 101};
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    \node[draw=none] at (1.5, 3.9) {\large  47};
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    \node[draw=none] at (2.5, 4.2) {\large 109};
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    \node[draw=none] at (3.5, 4.5) {\large  97};
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    \node[draw=none] at (4.5, 4.8) {\large 115};
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    \node[draw=none] at (5.5, 5.1) {\large 116};
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    \node[draw=none] at (6.5, 5.4) {\large 101};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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    \node[draw=none] at (0.5, 2.6) {\large 114};
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    \node[draw=none] at (1.5, 2.9) {\large  47};
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    \node[draw=none] at (2.5, 3.2) {\large  99};
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    \node[draw=none] at (3.5, 3.5) {\large  97};
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    \node[draw=none] at (4.5, 3.8) {\large 116};
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    \node[draw=none] at (5.5, 4.1) {\large  99};
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    \node[draw=none] at (6.5, 4.4) {\large  97};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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    \node[draw=none] at (0.5, 1.6) {\large 116};
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    \node[draw=none] at (1.5, 1.9) {\large  99};
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    \node[draw=none] at (2.5, 2.2) {\large  97};
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    \node[draw=none] at (3.5, 2.5) {\large 116};
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    \node[draw=none] at (4.5, 2.8) {\large  46};
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    \node[draw=none] at (5.5, 3.1) {\large 112};
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    \node[draw=none] at (6.5, 3.4) {\large 104};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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    \node[draw=none] at (0.5, 0.6) {\large 112};
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    \node[draw=none] at (1.5, 0.9) {\large  63};
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    \node[draw=none] at (2.5, 1.2) {\large 118};
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    \node[draw=none] at (3.5, 1.5) {\large  61};
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    \node[draw=none] at (4.5, 1.8) {\large  49};
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    \node[draw=none] at (5.5, 2.1) {\large  46};
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    \node[draw=none] at (6.5, 2.4) {\large  48};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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    % Filter
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    \node[draw=none] at ( 8.5, 4.8) {\large  9};
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    \node[draw=none] at ( 9.5, 5.1) {\large -3};
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    \node[draw=none] at (10.5, 5.4) {\large -1};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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    \node[draw=none] at ( 8.5, 3.8) {\large -6};
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    \node[draw=none] at ( 9.5, 4.1) {\large  5};
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    \node[draw=none] at (10.5, 4.4) {\large  3};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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    \node[draw=none] at ( 8.5, 2.8) {\large  2};
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    \node[draw=none] at ( 9.5, 3.1) {\large -8};
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    \node[draw=none] at (10.5, 3.4) {\large  0};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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    % Result
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    \node[draw=none] at (12.5, 4.8) {\large  936};
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    \node[draw=none] at (13.5, 5.1) {\large -333};
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    \node[draw=none] at (14.5, 5.4) {\large -109};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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    \node[draw=none] at (12.5, 3.8) {\large -282};
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    \node[draw=none] at (13.5, 4.1) {\large  545};
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    \node[draw=none] at (14.5, 4.4) {\large  291};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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    \node[draw=none] at (12.5, 2.8) {\large   94};
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    \node[draw=none] at (13.5, 3.1) {\large -792};
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    \node[draw=none] at (14.5, 3.4) {\large  0};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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    % Result image (left to right, top to bottom)
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    % [[  -4 -254 -498 -662 -849 -642 -187]
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    \node[draw=none] at (16.5, 6.6) {\large -4};
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    \node[draw=none] at (17.5, 6.9) {\large -254};
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    \node[draw=none] at (18.5, 7.2) {\large -498};
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    \node[draw=none] at (19.5, 7.5) {\large -662};
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    \node[draw=none] at (20.5, 7.8) {\large -849};
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    \node[draw=none] at (21.5, 8.1) {\large -642};
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    \node[draw=none] at (22.5, 8.4) {\large 187};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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    %  [-520   45  240  211  388  215 -861]
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    \node[draw=none] at (16.5, 5.6) {\large-520};
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    \node[draw=none] at (17.5, 5.9) {\large  45};
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    \node[draw=none] at (18.5, 6.2) {\large 240};
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    \node[draw=none] at (19.5, 6.5) {\large 211};
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    \node[draw=none] at (20.5, 6.8) {\large 388};
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    \node[draw=none] at (21.5, 7.1) {\large 215};
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    \node[draw=none] at (22.5, 7.4) {\large-861};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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    %  [-340  559 -105  185 -138 -180  503]
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    \node[draw=none] at (16.5, 4.6) {\large -340};
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    \node[draw=none] at (17.5, 4.9) {\large  559};
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    \node[draw=none] at (18.5, 5.2) {\large -105};
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    \node[draw=none] at (19.5, 5.5) {\large  185};
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    \node[draw=none] at (20.5, 5.8) {\large -138};
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    \node[draw=none] at (21.5, 6.1) {\large -180};
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    \node[draw=none] at (22.5, 6.4) {\large  503};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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    %  [-718  429  350  173  251  268 -655]
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    \node[draw=none] at (16.5, 3.6) {\large -718};
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    \node[draw=none] at (17.5, 3.9) {\large  429};
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    \node[draw=none] at (18.5, 4.2) {\large  350};
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    \node[draw=none] at (19.5, 4.5) {\large  173};
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    \node[draw=none] at (20.5, 4.8) {\large  251};
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    \node[draw=none] at (21.5, 5.1) {\large  268};
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    \node[draw=none] at (22.5, 5.4) {\large -655};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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    %  [-567  -53  -75   80  571 -128   24]
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    \node[draw=none] at (16.5, 2.6) {\large -567};
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    \node[draw=none] at (17.5, 2.9) {\large  -53};
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    \node[draw=none] at (18.5, 3.2) {\large  -75};
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    \node[draw=none] at (19.5, 3.5) {\large   80};
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    \node[draw=none] at (20.5, 3.8) {\large  571};
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    \node[draw=none] at (21.5, 4.1) {\large -128};
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    \node[draw=none] at (22.5, 4.4) {\large   24};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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    %  [-408  596 -550  368   26  976  156]
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    \node[draw=none] at (16.5, 1.6) {\large -408};
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    \node[draw=none] at (17.5, 1.9) {\large  596};
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    \node[draw=none] at (18.5, 2.2) {\large -550};
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    \node[draw=none] at (19.5, 2.5) {\large  368};
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    \node[draw=none] at (20.5, 2.8) {\large   26};
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    \node[draw=none] at (21.5, 3.1) {\large  976};
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    \node[draw=none] at (22.5, 3.4) {\large  156};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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    %  [ 302  647  879  223  811   54  660]]
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    \node[draw=none] at (16.5, 0.6) {\large 302};
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    \node[draw=none] at (17.5, 0.9) {\large 647};
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    \node[draw=none] at (18.5, 1.2) {\large 879};
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    \node[draw=none] at (19.5, 1.5) {\large 223};
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    \node[draw=none] at (20.5, 1.8) {\large 811};
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    \node[draw=none] at (21.5, 2.1) {\large  54};
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    \node[draw=none] at (22.5, 2.4) {\large 660};%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\end{tikzpicture}
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