Perron-Frobenius Theorie

5 files changed, 98 insertions, 0 deletions

diff --git a/buch/chapters/80-wahrscheinlichkeit/images/Makefile b/buch/chapters/80-wahrscheinlichkeit/images/Makefile
new file mode 100644
index 0000000..3c6a7f9
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+++ b/buch/chapters/80-wahrscheinlichkeit/images/Makefile
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+#
+# Makefile
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschulen
+#
+all:	diffusion.png diffusion.pdf
+
+diffusion.pdf:	diffusion.tex diffusion.jpg
+	pdflatex diffusion.tex
+
+diffusion.png:	diffusion.pov vektoren.inc
+	povray +A0.1 +W1920 +H1080 -Odiffusion.png diffusion.pov
+
+diffusion.jpg:	diffusion.png
+	convert diffusion.png -density 300 -units PixelsPerInch diffusion.jpg
+
+vektoren.inc:	diffusion.m
+	octave diffusion.m
+
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/diffusion.jpg b/buch/chapters/80-wahrscheinlichkeit/images/diffusion.jpg
new file mode 100644
index 0000000..b79b07b
--- /dev/null
+++ b/buch/chapters/80-wahrscheinlichkeit/images/diffusion.jpg
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/diffusion.m b/buch/chapters/80-wahrscheinlichkeit/images/diffusion.m
new file mode 100644
index 0000000..ad56fe5
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+++ b/buch/chapters/80-wahrscheinlichkeit/images/diffusion.m
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+#
+# diffusion.m
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+e1 = [ 1; 0; 0; 0; 0; 0 ];
+A = 0.8*eye(6) + 0.1*shift(eye(6),1) + 0.1*shift(eye(6),-1);
+A(1,1) = 0.9;
+A(6,6) = 0.9;
+A(1,6) = 0;
+A(6,1) = 0;
+
+N = 30;
+b = zeros(6,N);
+b(:,1) = e1;
+for i = (2:N)
+	b(:,i) = A * b(:,i-1);
+end
+b
+
+f = fopen("vektoren.inc", "w");
+for i = (1:N)
+	fprintf(f, "vektor(%d,%.4f,%.4f,%.4f,%.4f,%.4f,%.4f)\n", i,
+		b(1,i), b(2,i), b(3,i), b(4,i), b(5,i), b(6,i))
+end
+fclose(f);
+
+A1=A
+A2=A*A
+A3=A*A2
+A4=A*A3
+A5=A*A4
+A6=A*A5
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/diffusion.pdf b/buch/chapters/80-wahrscheinlichkeit/images/diffusion.pdf
new file mode 100644
index 0000000..ac4c0ff
--- /dev/null
+++ b/buch/chapters/80-wahrscheinlichkeit/images/diffusion.pdf
diff --git a/buch/chapters/80-wahrscheinlichkeit/images/diffusion.tex b/buch/chapters/80-wahrscheinlichkeit/images/diffusion.tex
new file mode 100644
index 0000000..ff58659
--- /dev/null
+++ b/buch/chapters/80-wahrscheinlichkeit/images/diffusion.tex
@@ -0,0 +1,46 @@
+%
+% diffusion.tex -- Diffusion unter der Wirkung der Matrix 
+%
+% (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]
+
+\node at (0,0) {\includegraphics[width=12cm]{diffusion.jpg}};
+
+\node at (-6.3,-1.2) [rotate=-10] {$k=6$};
+\node at (-5.15,-0.7) [rotate=-10] {$k=1$};
+
+\node at (5.8,-3.25) [rotate=-10] {$k=6$};
+\node at (6.3,-2.5) [rotate=-10] {$k=1$};
+
+\node at (-6.2,-1.7) [rotate=26] {$n=1$};
+\node at (4.8,-3.7) [rotate=53] {$n=30$};
+
+%\foreach \x in {-6,-5.9,...,6.01}{
+%	\draw[line width=0.1pt] (\x,-3.5) -- (\x,3.5);
+%}
+%\foreach \x in {-6,...,6}{
+%	\draw[line width=0.5pt] (\x,-3.5) -- (\x,3.5);
+%	\node at (\x,-3.5) [below] {$\x$};
+%}
+%\foreach \y in {-3.5,-3.4,...,3.51}{
+%	\draw[line width=0.1pt] (-6,\y) -- (6,\y);
+%}
+%\foreach \y in {-3,...,3}{
+%	\draw[line width=0.5pt] (-6,\y) -- (6,\y);
+%	\node at (-6,\y) [left] {$\y$};
+%}
+%\fill (0,0) circle[radius=0.05];
+
+\end{tikzpicture}
+\end{document}
+