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authorReto <reto.fritsche@ost.ch>2021-08-31 23:42:02 +0200
committerReto <reto.fritsche@ost.ch>2021-08-31 23:42:02 +0200
commit2657b49e75509661039bd8b35fdf9a23d4807b1b (patch)
tree5cb374246353de7357435d9abc09efa9172ef63f /buch/papers/multiplikation/images
parentadded syndrome table (diff)
parentKapitel 3 (diff)
downloadSeminarMatrizen-2657b49e75509661039bd8b35fdf9a23d4807b1b.tar.gz
SeminarMatrizen-2657b49e75509661039bd8b35fdf9a23d4807b1b.zip
Merge remote-tracking branch 'upstream/master' into mceliece
Diffstat (limited to '')
-rw-r--r--buch/papers/multiplikation/images/algo_tab.pdfbin0 -> 34251 bytes
-rw-r--r--buch/papers/multiplikation/images/algo_tab.tex122
-rw-r--r--buch/papers/multiplikation/images/bigo.pdfbin28372 -> 28312 bytes
-rw-r--r--buch/papers/multiplikation/images/bigo.tex1
-rw-r--r--buch/papers/multiplikation/images/meas_c.pdfbin23161 -> 23887 bytes
-rw-r--r--buch/papers/multiplikation/images/meas_c.tex129
-rw-r--r--buch/papers/multiplikation/images/meas_python.pdfbin21700 -> 22337 bytes
-rw-r--r--buch/papers/multiplikation/images/meas_python.tex60
-rw-r--r--buch/papers/multiplikation/images/strassen.pdfbin19970 -> 22262 bytes
-rw-r--r--buch/papers/multiplikation/images/strassen.tex149
10 files changed, 345 insertions, 116 deletions
diff --git a/buch/papers/multiplikation/images/algo_tab.pdf b/buch/papers/multiplikation/images/algo_tab.pdf
new file mode 100644
index 0000000..7f2bb4f
--- /dev/null
+++ b/buch/papers/multiplikation/images/algo_tab.pdf
Binary files differ
diff --git a/buch/papers/multiplikation/images/algo_tab.tex b/buch/papers/multiplikation/images/algo_tab.tex
new file mode 100644
index 0000000..50ce392
--- /dev/null
+++ b/buch/papers/multiplikation/images/algo_tab.tex
@@ -0,0 +1,122 @@
+\documentclass{article}
+\usepackage[left=25mm,right=25mm,top=25mm,bottom=25mm]{geometry}
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{times}
+\usepackage{geometry}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{algorithm}
+\usepackage{algpseudocode}
+\usepackage{mathrsfs}
+\usepackage{amsfonts}
+\usepackage{amsthm}
+\usepackage{lipsum}
+\usepackage{amscd}
+\usepackage{graphicx}
+\usepackage{fancyhdr}
+\usepackage{textcomp}
+\usepackage{pgfplots}
+\usepackage{txfonts}
+\usepackage[all]{xy}
+\usepackage{paralist}
+\usepackage[colorlinks=true]{hyperref}
+\usepackage{array}
+\usepackage{tikz}
+\usepackage{slashed}
+\usepackage{pdfpages}
+\usepackage{multicol}
+\usepackage{cite}
+\usepackage{url}
+\usepackage{amsmath,amsfonts,amssymb}
+\usepackage{tikz}
+\usetikzlibrary{arrows,matrix,positioning}
+\usetikzlibrary{overlay-beamer-styles}
+\usetikzlibrary{matrix.skeleton}
+\usetikzlibrary{automata,positioning}
+\usetikzlibrary{decorations.text}
+\usepackage{listings}
+\usepackage{multirow}
+\usepackage{color}
+
+\begin{document}
+
+
+
+\begin{table}[t]
+ \begin{tabular}{ll}
+ \begin{minipage}{0.4\textwidth}
+ \begin{algorithm}[H]\footnotesize\caption{}
+ \label{multiplikation:alg:b1}
+ \setlength{\lineskip}{7pt}
+ \begin{algorithmic}
+ \Function{B1}{$a, b$}
+ \State \textbf{return} $a+b$
+ \EndFunction
+ \State
+ \State
+ \end{algorithmic}
+ \end{algorithm}
+ \end{minipage}
+ &
+ \begin{minipage}{0.4\textwidth}
+ \begin{algorithm}[H]\footnotesize\caption{}
+ \label{multiplikation:alg:b2}
+ \setlength{\lineskip}{7pt}
+ \begin{algorithmic}
+ \Function{B2}{$a, b$}
+ \State $ x \gets a+b $
+ \State $ y \gets a \cdot b $
+ \State \textbf{return} $x+y$
+ \EndFunction
+ \end{algorithmic}
+\end{algorithm}
+
+ \end{minipage}
+ \end{tabular}
+\end{table}
+
+\begin{table}
+ \begin{tabular}[t]{ll}
+ \begin{minipage}{0.4\textwidth}
+ \begin{algorithm}[H]\footnotesize\caption{}
+ \setlength{\lineskip}{7pt}
+ \begin{algorithmic}
+ \label{multiplikation:alg:linear}
+ \Function{L}{$\mathbf{a}, \mathbf{b}$,n}
+ \State $ sum \gets 0$
+ \For{$i = 0,1,2 \dots,n$}
+ \State $ sum \gets sum + A[i] \cdot B[i] $
+ \EndFor
+
+ \State \textbf{return} $sum$
+
+ \EndFunction
+ \State
+ \State
+ \end{algorithmic}
+ \end{algorithm}
+ \end{minipage}
+ &
+ \begin{minipage}{0.4\textwidth}
+ \begin{algorithm}[H]\footnotesize\caption{}
+ \label{multiplikation:alg:q1}
+ \setlength{\lineskip}{7pt}
+ \begin{algorithmic}
+ \Function{Q}{$\mathbf{A}, \mathbf{B}$,n}
+ \State $ sum \gets 0$
+ \For{$i = 0,1,2 \dots,n$}
+ \For{$j = 0,1,2 \dots,n$}
+ \State $ sum \gets sum + A[i] \cdot B[j] $
+ \EndFor
+ \EndFor
+ \State \textbf{return} $sum$
+ \EndFunction
+ \end{algorithmic}
+ \end{algorithm}
+ \end{minipage}
+ \end{tabular}
+\end{table}
+
+dhdfh
+\end{document}
diff --git a/buch/papers/multiplikation/images/bigo.pdf b/buch/papers/multiplikation/images/bigo.pdf
index 8a53398..2519553 100644
--- a/buch/papers/multiplikation/images/bigo.pdf
+++ b/buch/papers/multiplikation/images/bigo.pdf
Binary files differ
diff --git a/buch/papers/multiplikation/images/bigo.tex b/buch/papers/multiplikation/images/bigo.tex
index 9ee3a68..63fd0fd 100644
--- a/buch/papers/multiplikation/images/bigo.tex
+++ b/buch/papers/multiplikation/images/bigo.tex
@@ -54,6 +54,7 @@
xticklabels=\empty,
scale only axis=true,
width=12cm, height=8cm,
+ legend cell align={left}
]
\addplot [
domain= 1:5000,
diff --git a/buch/papers/multiplikation/images/meas_c.pdf b/buch/papers/multiplikation/images/meas_c.pdf
index 3a4cfd8..521151e 100644
--- a/buch/papers/multiplikation/images/meas_c.pdf
+++ b/buch/papers/multiplikation/images/meas_c.pdf
Binary files differ
diff --git a/buch/papers/multiplikation/images/meas_c.tex b/buch/papers/multiplikation/images/meas_c.tex
index 818a7e6..12d3527 100644
--- a/buch/papers/multiplikation/images/meas_c.tex
+++ b/buch/papers/multiplikation/images/meas_c.tex
@@ -43,99 +43,106 @@
\begin{tikzpicture}
\begin{axis}[
xmode=log, ymode=log,
-xmin=60, xmax=5000,
-ymin=1e-4, ymax=2e3,
+xmin=30, xmax=10000,
+ymin=1e-5, ymax=2e4,
grid=both,
major grid style={black!50},
-xlabel = data Input ($n$),
+xlabel = data input ($n$),
ylabel = {time ($s$)},
legend pos=north west,
very thick,
scale only axis=true,
width=12cm, height=8cm,
- log basis x={10}
+ log basis x={10},
+ legend cell align={left}
]
\addlegendentry{Winograd}
-\addplot[ color=purple,
+\addplot[ color=blue,
+ error bars/.cd, y dir=both, y explicit,
] coordinates {
-% (2, 0.000001)
-% (4, 0.000001)
-% (8, 0.000002)
-% (16, 0.000011)
-% (32, 0.000100)
-(64, 0.000654)
-(128, 0.005229)
-(256, 0.057440)
-(512, 0.517850)
-(1024,4.539413)
-(2048,130.627663)
+%(2,1e-07)
+%(4,5e-07)
+%(8,2.0000000000000003e-06)
+%(16,1.1999999999999999e-05)
+(32,8.329999999999999e-05)
+(64,0.0006479)
+(128,0.0052873)
+(256,0.052674599999999995)
+(512,0.5249752000000001)
+(1024,4.671161)
+(2048,136.6769777)
(4096,1179.261048)
+(8192,10071.512655)
};
\addlegendentry{Strassen}
\addplot [ color=black,
]coordinates {
- % (2,0.000001 )
- % (4,0.000003 )
- % (8,0.000010 )
- % (16,0.000066 )
- % (32,0.000470 )
- (64,0.003368 )
- (128,0.024232 )
- (256,0.172000 )
- (512,1.209262 )
-(1024,8.457472 )
-(2048,59.267256)
+%(2,1e-07)
+%(4,2.1e-06)
+%(8,1.13e-05)
+%(16,7.07e-05)
+(32,0.0005041)
+(64,0.003596)
+(128,0.0254481)
+(256,0.1781817)
+(512,1.2555)
+(1024,8.8302371)
+(2048,61.9018691)
(4096,414.648901)
+(8192,3014.235467)
};
\addlegendentry{MM div and conq}
\addplot[ color=green,
] coordinates {
- % (2,0.000003 )
- % (4,0.000002 )
- % (8,0.000010 )
- % (16,0.000068 )
- % (32,0.000594 )
- (64,0.004264 )
- (128,0.036289 )
- (256,0.324645 )
- (512,2.612010 )
-(1024,19.928951 )
-(2048,159.333884 )
+%(2,3e-07)
+%(4,1.1e-06)
+%(8,8.6e-06)
+%(16,7.819999999999999e-05)
+(32,0.0005940000000000001)
+(64,0.0044339)
+(128,0.0348443)
+(256,0.29484730000000003)
+(512,2.2228507)
+(1024,17.659234500000004)
+(2048,141.6103936)
(4096,1147.106865)
+(8192,9606.402522)
};
\addlegendentry{MM}
\addplot [ color=red,
]coordinates {
- % (2,0.000001 )
- % (4,0.000001 )
- % (8,0.000001 )
- % (16,0.000010 )
- % (32,0.000081 )
- (64,0.000654 )
- (128,0.005556 )
- (256,0.054253 )
- (512,0.487317 )
-(1024,4.162845 )
-(2048,125.909034 )
+%(2,0.0)
+%(4,3e-07)
+%(8,1.8000000000000001e-06)
+%(16,1.1999999999999999e-05)
+(32,8.93e-05)
+(64,0.0006923)
+(128,0.0056842)
+(256,0.051771500000000005)
+(512,0.5062468000000001)
+(1024,4.5048086)
+(2048,129.2894619)
(4096,1111.312696)
+(8192,9376.173434)
};
\addlegendentry{BLAS}
-\addplot[ color=blue,
+\addplot[ color=purple,
] coordinates {
- % (2,0.000001 )
- % (4,0.000001 )
- % (8,0.000001 )
- % (16,0.000003 )
- % (32,0.000022 )
- (64,0.000179 )
- (128,0.001278 )
- (256,0.010165 )
- (512,0.074739 )
-(1024,0.704748 )
-(2048,6.845095 )
+%(2,1e-07)
+%(4,0.0)
+%(8,1e-07)
+%(16,3.9e-06)
+(32,2.1000000000000002e-05)
+(64,0.00018580000000000002)
+(128,0.0012649)
+(256,0.0096489)
+(512,0.0773765)
+(1024,0.7643868)
+(2048,7.6320993999999995)
(4096,55.845038)
+(8192,478.429957)
};
\end{axis}
\end{tikzpicture}
diff --git a/buch/papers/multiplikation/images/meas_python.pdf b/buch/papers/multiplikation/images/meas_python.pdf
index cea2232..fe89773 100644
--- a/buch/papers/multiplikation/images/meas_python.pdf
+++ b/buch/papers/multiplikation/images/meas_python.pdf
Binary files differ
diff --git a/buch/papers/multiplikation/images/meas_python.tex b/buch/papers/multiplikation/images/meas_python.tex
index ee4db43..ad43cf6 100644
--- a/buch/papers/multiplikation/images/meas_python.tex
+++ b/buch/papers/multiplikation/images/meas_python.tex
@@ -43,8 +43,8 @@
\begin{tikzpicture}
\begin{axis}[
xmode=log, ymode=log,
-xmin=30, xmax=1050,
-ymin=0.01, ymax=900,
+xmin=30, xmax=4200,
+ymin=0.01, ymax=70000,
grid=both,
major grid style={black!50},
xlabel = data input ($n$),
@@ -53,10 +53,11 @@ legend pos=north west,
very thick,
scale only axis=true,
width=12cm, height=8cm,
- log basis x={10}
+ log basis x={10},
+ legend cell align={left}
]
\addlegendentry{Winograd}
-\addplot[ color=purple,
+\addplot[ color=blue,
] coordinates {
% (2, 2.7895e-05 )
% (4, 0.000104904)
@@ -68,7 +69,8 @@ width=12cm, height=8cm,
(256, 8.29899 )
(512, 68.3699 )
(1024,537.374 )
-
+(2046,4884.61)
+(4096,43597.1)
};
\addlegendentry{Strassen}
\addplot [ color=black,
@@ -79,10 +81,12 @@ width=12cm, height=8cm,
% (16,0.00475407 )
(32,0.0485256 )
(64,0.220414 )
- (128,1.44718 2 )
- (256,9.93866 0 )
- (512,63.961 2 )
-(1024,461.494 2 )
+ (128,1.44718 )
+ (256,9.93866 )
+ (512,63.961 )
+(1024,461.494 )
+(2046,3860.57)
+(4096,22904.3)
};
\addlegendentry{MM div and conq}
@@ -98,6 +102,8 @@ width=12cm, height=8cm,
(256,13.27 )
(512,105.397 )
(1024,847.321 )
+(2046,7375.93)
+(4096,58466)
};
\addlegendentry{MM}
@@ -113,25 +119,27 @@ width=12cm, height=8cm,
(256, 11.0062 )
(512, 85.4768)
(1024,750.757 )
+(2046,6154.18)
+(4096,46813.3)
};
-% \addlegendentry{NumPy}
-% \addplot[ color=blue,
-% ] coordinates {
-% (2,1.83582e-05 )
-% (4,7.86781e-06)
-% (8,1.00136e-05)
-% (16,5.4121e-05 )
-% (32,4.26769e-05)
-% (64,0.000118494)
-% (128,0.000244141 )
-% (256,0.000695705 )
-% (512,0.00221705 )
-% (1024,0.0188088 )
-% };
+% \addlegendentry{NumPy}
+% \addplot[ color=blue,
+% ] coordinates {
+% % (2,1.83582e-05 )
+% % (4,7.86781e-06)
+% % (8,1.00136e-05)
+% % (16,5.4121e-05 )
+% (32,4.26769e-05)
+% (64,0.000118494)
+% (128,0.000244141 )
+% (256,0.000695705 )
+% (512,0.00221705 )
+% (1024,0.0188088 )
+% (2046,0.215739)
+% (4096,1.49159)
+% };
+
\end{axis}
\end{tikzpicture}
\end{document}
-
-
-
diff --git a/buch/papers/multiplikation/images/strassen.pdf b/buch/papers/multiplikation/images/strassen.pdf
index a30fdaa..d150125 100644
--- a/buch/papers/multiplikation/images/strassen.pdf
+++ b/buch/papers/multiplikation/images/strassen.pdf
Binary files differ
diff --git a/buch/papers/multiplikation/images/strassen.tex b/buch/papers/multiplikation/images/strassen.tex
index 5cf39b4..b51a9d5 100644
--- a/buch/papers/multiplikation/images/strassen.tex
+++ b/buch/papers/multiplikation/images/strassen.tex
@@ -56,7 +56,7 @@
A_{11}B_{11} \& A_{12}B_{12} \& A_{21}B_{12} \& A_{22}B_{12} \\
A_{11}B_{22} \& A_{12}B_{22} \& A_{21}B_{22} \& A_{22}B_{22} \\
};}
-
+
\foreach \j in {1,...,7}
{
\matrix(M\i\j)[matrix of math nodes,nodes in empty cells,
@@ -76,18 +76,18 @@
}
\huge{
- \node at (-3,-20) {$C_{22}=$};
- \node at (-3,-15) {$C_{21}=$} ;
- \node at (-3,-10) {$C_{12}=$} ;
- \node at (-3,-5) {$C_{11}=$} ;
-
- \node at (5,-2) {P};
- \node at (10,-2) {Q};
- \node at (15,-2) {R};
- \node at (20,-2) {S};
- \node at (25,-2) {T};
- \node at (30,-2) {U};
- \node at (35,-2) {V};
+ \node at (-3,-20) {$\mathbf{C}_{22}=$};
+ \node at (-3,-15) {$\mathbf{C}_{21}=$} ;
+ \node at (-3,-10) {$\mathbf{C}_{12}=$} ;
+ \node at (-3,-5) {$\mathbf{C}_{11}=$} ;
+
+ \node at (5,-2) {$\mathbf{P}$};
+ \node at (10,-2) {$\mathbf{Q}$};
+ \node at (15,-2) {$\mathbf{R}$};
+ \node at (20,-2) {$\mathbf{S}$};
+ \node at (25,-2) {$\mathbf{T}$};
+ \node at (30,-2) {$\mathbf{U}$};
+ \node at (35,-2) {$\mathbf{V}$};
}
@@ -100,41 +100,132 @@
\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X4-3-3)] {};
\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(X4-4-4)] {};
+% P
\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M11-4-1)] {};
\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M11-1-4)] {};
\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M11-4-4)] {};
\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M11-1-1)] {};
-\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M14-1-4)] {};
-\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M14-2-4)] {};
-\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M15-4-1)] {};
-\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M15-4-2)] {};
-\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M17-2-4)] {};
-\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M17-4-4)] {};
-\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M17-2-2)] {};
-\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M17-4-2)] {};
-\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M23-3-1)] {};
-\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M23-4-1)] {};
-\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M25-4-1)] {};
-\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M25-4-2)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M21-4-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M21-1-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M21-4-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M21-1-1)] {};
-\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M32-1-4)] {};
-\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M32-1-3)] {};
-\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M34-1-4)] {};
-\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M34-2-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M31-4-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M31-1-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M31-4-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M31-1-1)] {};
\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M41-4-1)] {};
\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M41-1-4)] {};
\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M41-4-4)] {};
\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M41-1-1)] {};
+
+% Q
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M12-1-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M12-1-3)] {};
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M22-1-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M22-1-3)] {};
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M32-1-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M32-1-3)] {};
+
\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M42-1-4)] {};
\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M42-1-3)] {};
+
+% R
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M13-3-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M13-4-1)] {};
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M23-3-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M23-4-1)] {};
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M33-3-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M33-4-1)] {};
+
\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M43-3-1)] {};
\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M43-4-1)] {};
+
+% S
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M14-1-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M14-2-4)] {};
+
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M24-1-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M24-2-4)] {};
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M34-1-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M34-2-4)] {};
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M44-1-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M44-2-4)] {};
+
+%T
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M15-4-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M15-4-2)] {};
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M25-4-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M25-4-2)] {};
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M35-4-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M35-4-2)] {};
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M45-4-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M45-4-2)] {};
+
+% U
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M16-1-3)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M16-1-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M16-3-3)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M16-3-1)] {};
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M26-1-3)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M26-1-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M26-3-3)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M26-3-1)] {};
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M36-1-3)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M36-1-1)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M36-3-3)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M36-3-1)] {};
+
\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M46-1-3)] {};
\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M46-1-1)] {};
\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M46-3-3)] {};
\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M46-3-1)] {};
+
+%V
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M17-2-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=red, fit=(M17-4-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M17-2-2)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=green, fit=(M17-4-2)] {};
+
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M27-2-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M27-4-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M27-2-2)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M27-4-2)] {};
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M37-2-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M37-4-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M37-2-2)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M37-4-2)] {};
+
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M47-2-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M47-4-4)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M47-2-2)] {};
+\node[opacity=0.5, rounded corners=0pt, inner sep=-1pt, fill=gray, fit=(M47-4-2)] {};
+
+
+
+
+
\end{tikzpicture}
\end{document}