Illustrationen Markov-Ketten

10 files changed, 397 insertions, 1 deletions

diff --git a/buch/chapters/80-wahrscheinlichkeit/images/Makefile b/buch/chapters/80-wahrscheinlichkeit/images/Makefile
index 24c0631..b04f6ff 100644
--- a/buch/chapters/80-wahrscheinlichkeit/images/Makefile
+++ b/buch/chapters/80-wahrscheinlichkeit/images/Makefile
@@ -5,7 +5,7 @@
 #
 all:	dreieck.pdf trenn.pdf vergleich.pdf vergleich.jpg \
 	positiv.pdf positiv.jpg diffusion.png diffusion.pdf \
-	konvex.pdf
+	konvex.pdf internet.pdf markov.pdf markov2.pdf markov3.pdf
 
 # Visualisierung diffusion in einer primitiven Matrix
 diffusion.pdf:	diffusion.tex diffusion.jpg
@@ -58,3 +58,16 @@ drei.inc:	dreieck.m
 # Konvex
 konvex.pdf:	konvex.tex
 	pdflatex konvex.tex
+
+internet.pdf:	internet.tex
+	pdflatex internet.tex
+
+markov.pdf:	markov.tex
+	pdflatex markov.tex
+
+markov2.pdf:	markov2.tex
+	pdflatex markov2.tex
+
+markov3.pdf:	markov3.tex
+	pdflatex markov3.tex
+
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/internet.pdf b/buch/chapters/80-wahrscheinlichkeit/images/internet.pdf
new file mode 100644
index 0000000..12eaf1e
--- /dev/null
+++ b/buch/chapters/80-wahrscheinlichkeit/images/internet.pdf
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/internet.tex b/buch/chapters/80-wahrscheinlichkeit/images/internet.tex
new file mode 100644
index 0000000..1b384ad
--- /dev/null
+++ b/buch/chapters/80-wahrscheinlichkeit/images/internet.tex
@@ -0,0 +1,58 @@
+%
+% internet.tex -- Modellinternet
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\foreach \x in {0,3,6,9}{
+	\foreach \y in {0,3}{
+		\fill[color=white] ({\x},{\y}) circle[radius=0.3];
+		\draw ({\x},{\y}) circle[radius=0.3];
+	}
+}
+\node at (0,3) {$1$};
+\node at (0,0) {$2$};
+\node at (3,3) {$3$};
+\node at (3,0) {$4$};
+\node at (6,3) {$5$};
+\node at (6,0) {$6$};
+\node at (9,3) {$7$};
+\node at (9,0) {$8$};
+% 1
+\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (0,3) -- (3,3);
+\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (0,3) -- (0,0);
+% 2
+\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (0,0) to[out=-20,in=-160] (3,0);
+% 3
+\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (3,3) -- (6,3);
+\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (3,3) -- (0,0);
+% 4
+\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (3,0) -- (6,3);
+\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (3,0) -- (6,0);
+\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (3,0) to[out=160,in=20] (0,0);
+% 5
+\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (6,3) -- (9,3);
+\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (6,3) -- (9,0);
+\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (6,3) -- (6,0);
+% 6
+\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (6,0) to[out=20,in=160] (9,0);
+% 7
+\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (9,3) .. controls (7.5,4) .. (6,4) -- (3,4) .. controls (1.5,4) .. (0,3);
+\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (9,3) to[out=-110,in=110] (9,0);
+% 8
+\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (9,0) to[out=-160,in=-20] (6,0);
+\draw[->,shorten >= 0.3cm, shorten <= 0.3cm] (9,0) to[out=70,in=-70] (9,3);
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/markov.pdf b/buch/chapters/80-wahrscheinlichkeit/images/markov.pdf
new file mode 100644
index 0000000..fba9489
--- /dev/null
+++ b/buch/chapters/80-wahrscheinlichkeit/images/markov.pdf
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/markov.tex b/buch/chapters/80-wahrscheinlichkeit/images/markov.tex
new file mode 100644
index 0000000..72f3b85
--- /dev/null
+++ b/buch/chapters/80-wahrscheinlichkeit/images/markov.tex
@@ -0,0 +1,99 @@
+%
+% markov2.tex -- template for standalon tikz images
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\def\punkt#1#2#3{
+	\fill[color=white] #1 circle[radius=0.10];
+	\fill[color=#2] #1 circle[radius=0.13];
+	\node[color=white] at #1 {$\scriptstyle #3$};
+}
+
+\def\xs{2.5}
+\def\ys{1}
+
+\foreach \x in {0,...,5}{
+	\draw[color=red,line width=0.5pt] 
+		({\x*\xs},{-0.7*\ys}) -- ({\x*\xs},{-6.5*\ys});
+}
+
+\def\dotradius{0.04}
+
+\def\dotrow#1#2{
+	\punkt{({#1*\xs},{-1*\ys})}{#2}{1}
+	\punkt{({#1*\xs},{-2*\ys})}{#2}{2}
+	\punkt{({#1*\xs},{-3*\ys})}{#2}{3}
+	\punkt{({#1*\xs},{-4*\ys})}{#2}{4}
+	\fill[color=#2] ({#1*\xs},{-5*\ys-0.3}) circle[radius=\dotradius];
+	\fill[color=#2] ({#1*\xs},{-5*\ys-0.15}) circle[radius=\dotradius];
+	\fill[color=#2] ({#1*\xs},{-5*\ys}) circle[radius=\dotradius];
+	\fill[color=#2] ({#1*\xs},{-5*\ys+0.15}) circle[radius=\dotradius];
+	\fill[color=#2] ({#1*\xs},{-5*\ys+0.3}) circle[radius=\dotradius];
+	\punkt{({#1*\xs},{-6*\ys})}{#2}{s}
+}
+
+\def\fan#1#2{
+	\foreach \x in {1,2,3,4,6}{
+		\foreach \y in {1,2,3,4,6}{
+			\draw[->,shorten >= 2mm,shorten <= 2mm,color=#2]
+				({#1*\xs},{-\x*\ys})
+				--
+				({(#1+1)*\xs},{-\y*\ys});
+		}
+	}
+}
+
+\begin{scope}
+\clip (-0.5,{-6.5*\ys}) rectangle ({5*\xs+0.5},-0.5);
+\fan{-1}{gray}
+\fan{0}{gray}
+\fan{1}{gray}
+\fan{2}{black}
+\fan{3}{gray}
+\fan{4}{gray}
+\fan{5}{gray}
+\end{scope}
+
+\dotrow{0}{gray}
+\dotrow{1}{gray}
+\dotrow{2}{black}
+\dotrow{3}{black}
+\dotrow{4}{gray}
+\dotrow{5}{gray}
+
+\def\ty{-0.5}
+\node[color=gray] at ({0.5*\xs},{\ty*\ys}) {$T(n-1,n-2)$};
+\node[color=gray] at ({1.5*\xs},{\ty*\ys}) {$T(n,n-1)$};
+\node[color=black] at ({2.5*\xs},{\ty*\ys}) {$T(n+1,n)$};
+\node[color=gray] at ({3.5*\xs},{\ty*\ys}) {$T(n+2,n+1)$};
+\node[color=gray] at ({4.5*\xs},{\ty*\ys}) {$T(n+3,n+2)$};
+
+\draw[->,color=red] (-0.7,{-6.5*\ys}) -- ({5*\xs+0.7},{-6.5*\ys}) coordinate[label={$t$}];
+
+\foreach \x in {0,...,5}{
+	\draw[color=red]
+		({\x*\xs},{-6.5*\ys-0.05})
+		--
+		({\x*\xs},{-6.5*\ys+0.05});
+}
+\node[color=red] at ({0*\xs},{-6.5*\ys}) [below] {$n-2\mathstrut$};
+\node[color=red] at ({1*\xs},{-6.5*\ys}) [below] {$n-1\mathstrut$};
+\node[color=red] at ({2*\xs},{-6.5*\ys}) [below] {$n\mathstrut$};
+\node[color=red] at ({3*\xs},{-6.5*\ys}) [below] {$n+1\mathstrut$};
+\node[color=red] at ({4*\xs},{-6.5*\ys}) [below] {$n+2\mathstrut$};
+\node[color=red] at ({5*\xs},{-6.5*\ys}) [below] {$n+3\mathstrut$};
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/markov2.pdf b/buch/chapters/80-wahrscheinlichkeit/images/markov2.pdf
new file mode 100644
index 0000000..d534c8f
--- /dev/null
+++ b/buch/chapters/80-wahrscheinlichkeit/images/markov2.pdf
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/markov2.tex b/buch/chapters/80-wahrscheinlichkeit/images/markov2.tex
new file mode 100644
index 0000000..c2fab2e
--- /dev/null
+++ b/buch/chapters/80-wahrscheinlichkeit/images/markov2.tex
@@ -0,0 +1,113 @@
+%
+% markov.tex -- Illustration markov-Kette
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\def\punkt#1#2#3{
+	\fill[color=white] #1 circle[radius=0.10];
+	\fill[color=#2] #1 circle[radius=0.13];
+	\node[color=white] at #1 {$\scriptstyle #3$};
+}
+
+\def\xs{2.5}
+\def\ys{1}
+
+\foreach \x in {0,...,5}{
+	\draw[color=red,line width=0.5pt] 
+		({\x*\xs},{-0.7*\ys}) -- ({\x*\xs},{-8.5*\ys});
+}
+
+\def\dotradius{0.04}
+
+\def\dotrow#1#2{
+	\punkt{({#1*\xs},{-1*\ys})}{#2}{1}
+	\punkt{({#1*\xs},{-2*\ys})}{#2}{2}
+	\fill[color=#2] ({#1*\xs},{-3*\ys-0.3}) circle[radius=\dotradius];
+	\fill[color=#2] ({#1*\xs},{-3*\ys-0.15}) circle[radius=\dotradius];
+	\fill[color=#2] ({#1*\xs},{-3*\ys}) circle[radius=\dotradius];
+	\fill[color=#2] ({#1*\xs},{-3*\ys+0.15}) circle[radius=\dotradius];
+	\fill[color=#2] ({#1*\xs},{-3*\ys+0.3}) circle[radius=\dotradius];
+	\punkt{({#1*\xs},{-4*\ys})}{#2}{7}
+	\punkt{({#1*\xs},{-5*\ys})}{#2}{8}
+	\punkt{({#1*\xs},{-6*\ys})}{#2}{9}
+	\fill[color=#2] ({#1*\xs},{-7*\ys-0.3}) circle[radius=\dotradius];
+	\fill[color=#2] ({#1*\xs},{-7*\ys-0.15}) circle[radius=\dotradius];
+	\fill[color=#2] ({#1*\xs},{-7*\ys}) circle[radius=\dotradius];
+	\fill[color=#2] ({#1*\xs},{-7*\ys+0.15}) circle[radius=\dotradius];
+	\fill[color=#2] ({#1*\xs},{-7*\ys+0.3}) circle[radius=\dotradius];
+	\punkt{({#1*\xs},{-8*\ys})}{#2}{s}
+}
+
+\def\fan#1#2{
+	\foreach \x in {1,2,4}{
+		\foreach \y in {1,2,4}{
+			\draw[->,shorten >= 2mm,shorten <= 2mm,color=#2]
+				({#1*\xs},{-\x*\ys})
+				--
+				({(#1+1)*\xs},{-\y*\ys});
+		}
+	}
+	\foreach \x in {5,6,8}{
+		\foreach \y in {5,6,8}{
+			\draw[->,shorten >= 2mm,shorten <= 2mm,color=#2]
+				({#1*\xs},{-\x*\ys})
+				--
+				({(#1+1)*\xs},{-\y*\ys});
+		}
+	}
+}
+
+\begin{scope}
+\clip (-0.5,{-8.5*\ys}) rectangle ({5*\xs+0.5},-0.5);
+\fan{-1}{gray}
+\fan{0}{gray}
+\fan{1}{gray}
+\fan{2}{black}
+\fan{3}{gray}
+\fan{4}{gray}
+\fan{5}{gray}
+\end{scope}
+
+\dotrow{0}{gray}
+\dotrow{1}{gray}
+\dotrow{2}{black}
+\dotrow{3}{black}
+\dotrow{4}{gray}
+\dotrow{5}{gray}
+
+\def\ty{-0.5}
+\node[color=gray] at ({0.5*\xs},{\ty*\ys}) {$T(n-1,n-2)$};
+\node[color=gray] at ({1.5*\xs},{\ty*\ys}) {$T(n,n-1)$};
+\node[color=black] at ({2.5*\xs},{\ty*\ys}) {$T(n+1,n)$};
+\node[color=gray] at ({3.5*\xs},{\ty*\ys}) {$T(n+2,n+1)$};
+\node[color=gray] at ({4.5*\xs},{\ty*\ys}) {$T(n+3,n+2)$};
+
+\draw[->,color=red] (-0.7,{-8.5*\ys}) -- ({5*\xs+0.7},{-8.5*\ys}) coordinate[label={$t$}];
+
+\foreach \x in {0,...,5}{
+	\draw[color=red]
+		({\x*\xs},{-8.5*\ys-0.05})
+		--
+		({\x*\xs},{-8.5*\ys+0.05});
+}
+\node[color=red] at ({0*\xs},{-8.5*\ys}) [below] {$n-2\mathstrut$};
+\node[color=red] at ({1*\xs},{-8.5*\ys}) [below] {$n-1\mathstrut$};
+\node[color=red] at ({2*\xs},{-8.5*\ys}) [below] {$n\mathstrut$};
+\node[color=red] at ({3*\xs},{-8.5*\ys}) [below] {$n+1\mathstrut$};
+\node[color=red] at ({4*\xs},{-8.5*\ys}) [below] {$n+2\mathstrut$};
+\node[color=red] at ({5*\xs},{-8.5*\ys}) [below] {$n+3\mathstrut$};
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/markov3.pdf b/buch/chapters/80-wahrscheinlichkeit/images/markov3.pdf
new file mode 100644
index 0000000..61f4fe7
--- /dev/null
+++ b/buch/chapters/80-wahrscheinlichkeit/images/markov3.pdf
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/markov3.tex b/buch/chapters/80-wahrscheinlichkeit/images/markov3.tex
new file mode 100644
index 0000000..0b99ef3
--- /dev/null
+++ b/buch/chapters/80-wahrscheinlichkeit/images/markov3.tex
@@ -0,0 +1,113 @@
+%
+% markov2.tex -- template for standalon tikz images
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\def\punkt#1#2#3{
+	\fill[color=white] #1 circle[radius=0.10];
+	\fill[color=#2] #1 circle[radius=0.13];
+	\node[color=white] at #1 {$\scriptstyle #3$};
+}
+
+\def\xs{2.5}
+\def\ys{1}
+
+\fill[color=blue!20]
+	(-0.5,{-3.3*\ys}) rectangle ({5*\xs+0.5},{-0.7*\ys});
+
+\foreach \x in {0,...,5}{
+	\draw[color=red,line width=0.5pt] 
+		({\x*\xs},{-0.7*\ys}) -- ({\x*\xs},{-7.5*\ys});
+}
+
+\def\dotradius{0.04}
+
+\def\dotrow#1#2{
+	\punkt{({#1*\xs},{-1*\ys})}{#2}{1}
+	\fill[color=#2] ({#1*\xs},{-2*\ys-0.3}) circle[radius=\dotradius];
+	\fill[color=#2] ({#1*\xs},{-2*\ys-0.15}) circle[radius=\dotradius];
+	\fill[color=#2] ({#1*\xs},{-2*\ys}) circle[radius=\dotradius];
+	\fill[color=#2] ({#1*\xs},{-2*\ys+0.15}) circle[radius=\dotradius];
+	\fill[color=#2] ({#1*\xs},{-2*\ys+0.3}) circle[radius=\dotradius];
+	\punkt{({#1*\xs},{-3*\ys})}{#2}{7}
+	\punkt{({#1*\xs},{-4*\ys})}{#2}{8}
+	\punkt{({#1*\xs},{-5*\ys})}{#2}{9}
+	\fill[color=#2] ({#1*\xs},{-6*\ys-0.3}) circle[radius=\dotradius];
+	\fill[color=#2] ({#1*\xs},{-6*\ys-0.15}) circle[radius=\dotradius];
+	\fill[color=#2] ({#1*\xs},{-6*\ys}) circle[radius=\dotradius];
+	\fill[color=#2] ({#1*\xs},{-6*\ys+0.15}) circle[radius=\dotradius];
+	\fill[color=#2] ({#1*\xs},{-6*\ys+0.3}) circle[radius=\dotradius];
+	\punkt{({#1*\xs},{-7*\ys})}{#2}{s}
+}
+
+\def\fan#1#2{
+	\foreach \x in {1,3}{
+		\draw[->,shorten >= 2mm,shorten <= 2mm,color=#2,line width=2pt]
+			({#1*\xs},{-\x*\ys})
+			--
+			({(#1+1)*\xs},{-\x*\ys});
+	}
+	\foreach \x in {4,5,7}{
+		\foreach \y in {1,3,4,5,7}{
+			\draw[->,shorten >= 2mm,shorten <= 2mm,color=#2]
+				({#1*\xs},{-\x*\ys})
+				--
+				({(#1+1)*\xs},{-\y*\ys});
+		}
+	}
+}
+
+\begin{scope}
+\clip (-0.5,{-7.5*\ys}) rectangle ({5*\xs+0.5},-0.5);
+\fan{-1}{gray}
+\fan{0}{gray}
+\fan{1}{gray}
+\fan{2}{black}
+\fan{3}{gray}
+\fan{4}{gray}
+\fan{5}{gray}
+\end{scope}
+
+\dotrow{0}{gray}
+\dotrow{1}{gray}
+\dotrow{2}{black}
+\dotrow{3}{black}
+\dotrow{4}{gray}
+\dotrow{5}{gray}
+
+\def\ty{-0.5}
+\node[color=gray] at ({0.5*\xs},{\ty*\ys}) {$T(n-1,n-2)$};
+\node[color=gray] at ({1.5*\xs},{\ty*\ys}) {$T(n,n-1)$};
+\node[color=black] at ({2.5*\xs},{\ty*\ys}) {$T(n+1,n)$};
+\node[color=gray] at ({3.5*\xs},{\ty*\ys}) {$T(n+2,n+1)$};
+\node[color=gray] at ({4.5*\xs},{\ty*\ys}) {$T(n+3,n+2)$};
+
+\draw[->,color=red] (-0.7,{-7.5*\ys}) -- ({5*\xs+0.7},{-7.5*\ys}) coordinate[label={$t$}];
+
+\foreach \x in {0,...,5}{
+	\draw[color=red]
+		({\x*\xs},{-7.5*\ys-0.05})
+		--
+		({\x*\xs},{-7.5*\ys+0.05});
+}
+\node[color=red] at ({0*\xs},{-7.5*\ys}) [below] {$n-2\mathstrut$};
+\node[color=red] at ({1*\xs},{-7.5*\ys}) [below] {$n-1\mathstrut$};
+\node[color=red] at ({2*\xs},{-7.5*\ys}) [below] {$n\mathstrut$};
+\node[color=red] at ({3*\xs},{-7.5*\ys}) [below] {$n+1\mathstrut$};
+\node[color=red] at ({4*\xs},{-7.5*\ys}) [below] {$n+2\mathstrut$};
+\node[color=red] at ({5*\xs},{-7.5*\ys}) [below] {$n+3\mathstrut$};
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdf b/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdf
index f065f76..c6173ce 100644
--- a/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdf
+++ b/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdf