diff options
Diffstat (limited to 'buch/chapters/80-wahrscheinlichkeit/images')
37 files changed, 1469 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..8d34217 --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/Makefile @@ -0,0 +1,79 @@ +# +# Makefile +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschulen +# +all: dreieck.pdf trenn.pdf vergleich.pdf vergleich.jpg \ + positiv.pdf positiv.jpg diffusion.png diffusion.pdf \ + konvex.pdf internet.pdf markov.pdf markov2.pdf markov3.pdf \ + spielB.pdf spielBtilde.pdf + +# Visualisierung diffusion in einer primitiven Matrix +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 + +# Visualizierung positive Matrix +positiv.pdf: positiv.tex positiv.jpg + pdflatex positiv.tex + +positiv.png: positiv.pov quadrant.inc + povray +A0.1 +W1920 +H1080 -Opositiv.png positiv.pov + +positiv.jpg: positiv.png + convert positiv.png -density 300 -units PixelsPerInch positiv.jpg + +quadrant.inc: positiv.m + octave positiv.m + +# Visualiziserung Vergleichstrick +vergleich.png: vergleich.pov + povray +A0.1 +W1920 +H1080 -Overgleich.png vergleich.pov + +vergleich.jpg: vergleich.png Makefile + convert -extract 1110x1080+180+0 vergleich.png \ + -density 300 -units PixelsPerInch vergleich.jpg + +vergleich.pdf: vergleich.tex vergleich.jpg + pdflatex vergleich.tex + +# Darstellung zum Trenntrick +trenn.pdf: trenn.tex + pdflatex trenn.tex + +# Darstellung zur Dreiecksungleichung +dreieck.pdf: dreieck.tex drei.inc + pdflatex dreieck.tex + +drei.inc: dreieck.m + octave 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 + +spielB.pdf: spielB.tex + pdflatex spielB.tex + +spielBtilde.pdf: spielBtilde.tex + pdflatex spielBtilde.tex diff --git a/buch/chapters/80-wahrscheinlichkeit/images/diffusion.jpg b/buch/chapters/80-wahrscheinlichkeit/images/diffusion.jpg Binary files differnew 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 --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/diffusion.m @@ -0,0 +1,33 @@ +# +# 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 Binary files differnew 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.png b/buch/chapters/80-wahrscheinlichkeit/images/diffusion.png Binary files differnew file mode 100644 index 0000000..f4c6294 --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/diffusion.png diff --git a/buch/chapters/80-wahrscheinlichkeit/images/diffusion.pov b/buch/chapters/80-wahrscheinlichkeit/images/diffusion.pov new file mode 100644 index 0000000..9b385da --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/diffusion.pov @@ -0,0 +1,87 @@ +// +// diffusion.pov +// +// (c) 2021 Prof Dr Andreas Müller, OST Ostscheizer Fachhochschule +// +#version 3.7; +#include "colors.inc" + +global_settings { + assumed_gamma 1 +} + +#declare imagescale = 0.270; +#declare N = 30; +#declare vscale = 10; +#declare r = 0.08; + +camera { + location <43, 20, -50> + look_at <N/2+2, vscale*0.49, 3> + right 16/9 * x * imagescale + up y * imagescale +} + +light_source { + <-4, 20, -50> color White + area_light <1,0,0> <0,0,1>, 10, 10 + adaptive 1 + jitter +} + +sky_sphere { + pigment { + color rgb<1,1,1> + } +} + +#macro saeule(xx,yy,h) +box { <xx+0.1,0,yy+0.1>, <xx+0.9,vscale*h,yy+0.9> } +#end + +#macro vektor(xx,a,b,c,d,e,f) + saeule(xx,5,a) + saeule(xx,4,b) + saeule(xx,3,c) + saeule(xx,2,d) + saeule(xx,1,e) + saeule(xx,0,f) +#end + +union { +#include "vektoren.inc" + pigment { + color rgb<0.8,1,1>*0.6 + } + finish { + specular 0.9 + metallic + } +} + +union { +#declare xx = 1; +#while (xx <= N+1) + cylinder { <xx, 0, 0>, <xx, 0, 6>, r } + #declare xx = xx + 1; +#end +#declare yy = 0; +#while (yy <= 6) + cylinder { <1, 0, yy>, <N+1, 0, yy>, r } + #declare yy = yy + 1; +#end + sphere { <1,0,0>, r } + sphere { <1,0,6>, r } + sphere { <N+1,0,0>, r } + sphere { <N+1,0,6>, r } + cylinder { <1,0,6>, <1,1.1*vscale,6>, r } + cylinder { <1,vscale-r/2,6>, <1,vscale+r/2,6>, 2*r } + cone { <1,1.1*vscale,6>, 2*r, <1,1.15*vscale,6>, 0 } + pigment { + color rgb<1,0.6,1>*0.6 + } + finish { + specular 0.9 + metallic + } +} 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} + diff --git a/buch/chapters/80-wahrscheinlichkeit/images/dreieck.m b/buch/chapters/80-wahrscheinlichkeit/images/dreieck.m new file mode 100644 index 0000000..cc9661b --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/dreieck.m @@ -0,0 +1,41 @@ +# +# dreieck.m +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +w = 12 +N = 10 + +rand("seed", 1); + +angles = 80 * rand(1,N) +radii = 2 * rand(1,N) + 0.4 +angle = 20 + +radii = radii * w / (cosd(angle) * sum(radii)) +radius = sum(radii) +radius * cosd(angle) + +points = zeros(2,N); +ray = zeros(2,N); + +p = [ 0; 0 ]; +for i = (1:N) + p = p + radii(1,i) * [ cosd(angles(1,i)); sind(angles(1,i)) ]; + points(:, i) = p; + ray(:, i) = sum(radii(1,1:i)) * [ cosd(angle); sind(angle) ]; +end + +points + +ray + +fn = fopen("drei.inc", "w"); +for i = (1:N) + fprintf(fn, "\\coordinate (A%d) at (%.4f,%.4f);\n", i, + points(1,i), points(2,i)); + fprintf(fn, "\\coordinate (B%d) at (%.4f,%.4f);\n", i, + ray(1,i), ray(2,i)); +end +fprintf(fn, "\\def\\r{%.4f}\n", radius); +fclose(fn); diff --git a/buch/chapters/80-wahrscheinlichkeit/images/dreieck.pdf b/buch/chapters/80-wahrscheinlichkeit/images/dreieck.pdf Binary files differnew file mode 100644 index 0000000..0cca2e1 --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/dreieck.pdf diff --git a/buch/chapters/80-wahrscheinlichkeit/images/dreieck.tex b/buch/chapters/80-wahrscheinlichkeit/images/dreieck.tex new file mode 100644 index 0000000..0935992 --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/dreieck.tex @@ -0,0 +1,90 @@ +% +% dreieck.tex -- verallgemeinerte Dreiecksungleichung +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usepackage{pgf} +\usetikzlibrary{arrows,intersections,math,calc,hobby} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\coordinate (O) at (0,0); + +\input{drei.inc} + +\begin{scope} +\clip (O) rectangle (12.3,8); +\draw[color=red!40] (O) circle[radius=\r]; +\end{scope} + +\draw[->] (-0.1,0) -- (12.3,0) coordinate[label={$\Re z$}]; +\draw[->] (0,-0.1) -- (0,8.3) coordinate[label={right:$\Im z$}]; + +\fill[color=blue] (A1) circle[radius=0.05]; +\fill[color=blue] (A2) circle[radius=0.05]; +\fill[color=blue] (A3) circle[radius=0.05]; +\fill[color=blue] (A4) circle[radius=0.05]; +\fill[color=blue] (A5) circle[radius=0.05]; +\fill[color=blue] (A6) circle[radius=0.05]; +\fill[color=blue] (A7) circle[radius=0.05]; +\fill[color=blue] (A8) circle[radius=0.05]; +\fill[color=blue] (A9) circle[radius=0.05]; +\fill[color=blue] (A10) circle[radius=0.05]; +\draw[color=blue] (O) -- (A1); +\draw[color=blue] (A1) -- (A2); +\draw[color=blue] (A2) -- (A3); +\draw[color=blue] (A3) -- (A4); +\draw[color=blue] (A4) -- (A5); +\draw[color=blue] (A5) -- (A6); +\draw[color=blue] (A6) -- (A7); +\draw[color=blue] (A7) -- (A8); +\draw[color=blue] (A8) -- (A9); +\draw[color=blue] (A9) -- (A10); +\draw[->,color=blue!40] (O) -- (A10); +\node[color=blue] at ($0.5*(A1)$) [left] {$z_1$}; +\node[color=blue] at ($0.5*(A1)+0.5*(A2)$) [left] {$z_2$}; +\node[color=blue] at ($0.5*(A2)+0.5*(A3)$) [above] {$z_3$}; +\node[color=blue] at ($0.5*(A3)+0.5*(A4)$) [above] {$z_4$}; +\node[color=blue] at ($0.5*(A4)+0.5*(A5)$) [below right] {$z_5$}; +\node[color=blue] at ($0.5*(A5)+0.5*(A6)$) [left] {$z_6$}; +\node[color=blue] at ($0.5*(A6)+0.5*(A7)$) [left] {$z_7$}; +\node[color=blue] at ($0.5*(A7)+0.5*(A8)$) [above] {$z_8$}; +\node[color=blue] at ($0.5*(A8)+0.5*(A9)$) [left] {$z_9$}; +\node[color=blue] at ($0.5*(A9)+0.5*(A10)$) [above] {$z_{10}$}; +\node[color=blue] at ($0.8*(A10)$) [rotate=35,below] {$\displaystyle\sum_{i=1}^n z_i$}; + +\draw[->,color=red] (O) -- (B10); +\fill[color=red] (B1) circle[radius=0.05]; +\fill[color=red] (B2) circle[radius=0.05]; +\fill[color=red] (B3) circle[radius=0.05]; +\fill[color=red] (B4) circle[radius=0.05]; +\fill[color=red] (B5) circle[radius=0.05]; +\fill[color=red] (B6) circle[radius=0.05]; +\fill[color=red] (B7) circle[radius=0.05]; +\fill[color=red] (B8) circle[radius=0.05]; +\fill[color=red] (B9) circle[radius=0.05]; +\fill[color=red] (B10) circle[radius=0.05]; + +\node[color=red] at ($0.5*(B1)$) [above] {$|z_1|c$}; +\node[color=red] at ($0.5*(B1)+0.5*(B2)$) [above] {$|z_2|c$}; +\node[color=red] at ($0.5*(B2)+0.5*(B3)$) [above] {$|z_3|c$}; +\node[color=red] at ($0.5*(B3)+0.5*(B4)$) [above] {$|z_4|c$}; +\node[color=red] at ($0.5*(B4)+0.5*(B5)$) [above] {$|z_5|c$}; +\node[color=red] at ($0.5*(B5)+0.5*(B6)$) [above] {$|z_6|c$}; +\node[color=red] at ($0.5*(B6)+0.5*(B7)$) [above] {$|z_7|c$}; +\node[color=red] at ($0.5*(B7)+0.5*(B8)$) [above] {$|z_8|c$}; +\node[color=red] at ($0.5*(B8)+0.5*(B9)$) [above] {$|z_9|c$}; +\node[color=red] at ($0.5*(B9)+0.5*(B10)$) [above] {$|z_{10}|c$}; + +\node[color=red] at ($0.8*(B10)$) [rotate=20,below] {$\displaystyle c\sum_{i=1}^n |z_i|$}; + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/80-wahrscheinlichkeit/images/internet.pdf b/buch/chapters/80-wahrscheinlichkeit/images/internet.pdf Binary files differnew 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/konvex.pdf b/buch/chapters/80-wahrscheinlichkeit/images/konvex.pdf Binary files differnew file mode 100644 index 0000000..f77cc62 --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/konvex.pdf diff --git a/buch/chapters/80-wahrscheinlichkeit/images/konvex.tex b/buch/chapters/80-wahrscheinlichkeit/images/konvex.tex new file mode 100644 index 0000000..05bbc60 --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/konvex.tex @@ -0,0 +1,75 @@ +% +% konvex.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,calc,hobby} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\def\punkt#1{ + \fill[color=white] #1 circle[radius=0.05]; + \draw #1 circle[radius=0.05]; +} + +\begin{scope}[xshift=-3cm] +\coordinate (O) at (0,0); +\coordinate (A) at (-1,5); +\coordinate (B) at (3,2); +\draw[->] (O) -- (A); +\draw[->] (O) -- (B); +\begin{scope} +\clip (-2,0) rectangle (4,6); +\draw[color=red!40,line width=0.4pt] ($2*(B)-(A)$) -- ($2*(A)-(B)$); +\end{scope} +\draw[color=red,line width=1.5pt] (A) -- (B); +\punkt{(O)} +\punkt{(A)} +\punkt{(B)} +\node at (O) [below left] {$O$}; +\node at (A) [above right] {$A$}; +\node at (B) [above right] {$B$}; +\node at ($0.5*(A)$) [left] {$\vec{a}$}; +\node at ($0.5*(B)$) [below right] {$\vec{b}$}; +\fill[color=white] ($0.6*(A)+0.4*(B)$) circle[radius=0.05]; +\draw[color=red] ($0.6*(A)+0.4*(B)$) circle[radius=0.05]; +\node[color=red] at ($0.6*(A)+0.4*(B)$) [above right] {$t\vec{a}+(1-t)\vec{b}$}; +\end{scope} + +\begin{scope}[xshift=4cm] +\coordinate (O) at (0,0); +\coordinate (A) at (-1,3); +\coordinate (B) at (2,5); +\coordinate (C) at (4,1); +\draw[->] (O) -- (A); +\draw[->] (O) -- (B); +\draw[->] (O) -- (C); +\fill[color=red!50,opacity=0.5] (A) -- (B) -- (C) -- cycle; +\draw[color=red,line width=1.5pt,opacity=0.7] (A) -- (B) -- (C) -- cycle; +\punkt{(O)} +\punkt{(A)} +\punkt{(B)} +\punkt{(C)} +\node at (O) [below left] {$O$}; +\node at (A) [left] {$P_1$}; +\node at (B) [above] {$P_2$}; +\node at (C) [right] {$P_3$}; +\node at ($0.5*(A)$) [left] {$\vec{p}_1$}; +\node at ($0.3*(B)$) [right] {$\vec{p}_2$}; +\node at ($0.5*(C)$) [below] {$\vec{p}_3$}; +\fill[color=white] ($0.5*(C)+0.3*(A)+0.2*(B)$) circle[radius=0.05]; +\draw[color=red] ($0.5*(C)+0.3*(A)+0.2*(B)$) circle[radius=0.05]; +\node[color=red] at ($0.5*(C)+0.3*(A)+0.2*(B)$) [above] {$\displaystyle\sum_{t=1}^3 t_i\vec{p}_i$}; +\end{scope} + + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/80-wahrscheinlichkeit/images/markov.pdf b/buch/chapters/80-wahrscheinlichkeit/images/markov.pdf Binary files differnew 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 Binary files differnew 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 Binary files differnew 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/positiv.jpg b/buch/chapters/80-wahrscheinlichkeit/images/positiv.jpg Binary files differnew file mode 100644 index 0000000..53544cb --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/positiv.jpg diff --git a/buch/chapters/80-wahrscheinlichkeit/images/positiv.m b/buch/chapters/80-wahrscheinlichkeit/images/positiv.m new file mode 100644 index 0000000..4dca950 --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/positiv.m @@ -0,0 +1,36 @@ +# +# positiv.m +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +N = 10; +p = 0.2; + +A = eye(3) + p * rand(3,3); +A = [ + 1, 0.2, 0.2; + 0.1, 1, 0.1; + 0.05, 0.05, 1 +]; +B = eye(3); + +function retval = punkt(x) + retval = sprintf("<%.4f,%.4f,%.4f>", x(1), x(3), x(2)); +end + +fn = fopen("quadrant.inc", "w"); +for i = (1:N) + fprintf(fn, "quadrant(%s,%s,%s)\n", + punkt(B(:,1)), punkt(B(:,2)), punkt(B(:,3))) + B = B * A; +end + +x = [ 1; 1; 1 ]; +for i = (1:100) + x = A * x; + x = x / norm(x); +end +fprintf(fn, "eigenvektor(<%.4f, %.4f, %.4f>)\n", x(1), x(3), x(2)); + + +fclose(fn); diff --git a/buch/chapters/80-wahrscheinlichkeit/images/positiv.pdf b/buch/chapters/80-wahrscheinlichkeit/images/positiv.pdf Binary files differnew file mode 100644 index 0000000..39aa3cd --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/positiv.pdf diff --git a/buch/chapters/80-wahrscheinlichkeit/images/positiv.png b/buch/chapters/80-wahrscheinlichkeit/images/positiv.png Binary files differnew file mode 100644 index 0000000..a2bd9bf --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/positiv.png diff --git a/buch/chapters/80-wahrscheinlichkeit/images/positiv.pov b/buch/chapters/80-wahrscheinlichkeit/images/positiv.pov new file mode 100644 index 0000000..9197498 --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/positiv.pov @@ -0,0 +1,137 @@ +// +// diffusion.pov +// +// (c) 2021 Prof Dr Andreas Müller, OST Ostscheizer Fachhochschule +// +#version 3.7; +#include "colors.inc" + +global_settings { + assumed_gamma 1 +} + +#declare imagescale = 0.077; +#declare N = 30; +#declare vscale = 10; +#declare r = 0.04; + +camera { + location <43, 20, -20> + look_at <1, 0.83, 2.5> + right 16/9 * x * imagescale + up y * imagescale +} + +light_source { + <40, 20, -10> color White + area_light <1,0,0> <0,0,1>, 10, 10 + adaptive 1 + jitter +} + +sky_sphere { + pigment { + color rgb<1,1,1> + } +} + +// +// draw an arrow from <from> to <to> with thickness <arrowthickness> with +// color <c> +// +#macro arrow(from, to, arrowthickness, c) +#declare arrowdirection = vnormalize(to - from); +#declare arrowlength = vlength(to - from); +union { + sphere { + from, 1.1 * arrowthickness + } + cylinder { + from, + from + (arrowlength - 5 * arrowthickness) * arrowdirection, + arrowthickness + } + cone { + from + (arrowlength - 5 * arrowthickness) * arrowdirection, + 2 * arrowthickness, + to, + 0 + } + pigment { + color c + } + finish { + specular 0.9 + metallic + } +} +#end + +arrow(<0,0,0>, <3,0,0>, r, White) +arrow(<0,0,0>, <0,3,0>, r, White) +arrow(<0,0,0>, <0,0,3>, r, White) + +#macro quadrant(A, B, C) +intersection { + sphere { <0, 0, 0>, 1 + matrix <A.x, A.y, A.z, + B.x, B.y, B.z, + C.x, C.y, C.z, + 0, 0, 0 > + } + plane { vnormalize(vcross(A, B)), 0 } + plane { vnormalize(vcross(B, C)), 0 } + plane { vnormalize(vcross(C, A)), 0 } + pigment { + //color rgbf<0.8,1,1,0.7> + color rgb<0.8,1,1> + } + finish { + specular 0.9 + metallic + } +} +#end + +#macro eigenvektor(E) +union { + cylinder { -E, 8 * E, r } + #declare r0 = 0.7 * r; + + sphere { 3 * < 0, E.y, E.z >, r0 } + sphere { 3 * < E.x, 0, E.z >, r0 } + sphere { 3 * < E.x, E.y, 0 >, r0 } + sphere { 3 * E, r0 } + + cylinder { 3*< E.x, 0, 0 >, 3*< E.x, 0, E.z >, r0 } + cylinder { 3*< E.x, 0, 0 >, 3*< E.x, E.y, 0 >, r0 } + cylinder { 3*< 0, E.y, 0 >, 3*< E.x, E.y, 0 >, r0 } + cylinder { 3*< 0, E.y, 0 >, 3*< 0, E.y, E.z >, r0 } + cylinder { 3*< 0, 0, E.z >, 3*< 0, E.y, E.z >, r0 } + cylinder { 3*< 0, 0, E.z >, 3*< E.x, 0, E.z >, r0 } + + cylinder { 3*< E.x, E.y, 0 >, 3*E, r0 } + cylinder { 3*< 0, E.y, E.z >, 3*E, r0 } + cylinder { 3*< E.x, 0, E.z >, 3*E, r0 } + pigment { + color rgb<1,0.6,1>*0.6 + } + finish { + specular 0.9 + metallic + } +} +#end + +#include "quadrant.inc" + +//union { +// pigment { +// color rgb<0.8,1,1>*0.6 +// } +// finish { +// specular 0.9 +// metallic +// } +//} + diff --git a/buch/chapters/80-wahrscheinlichkeit/images/positiv.tex b/buch/chapters/80-wahrscheinlichkeit/images/positiv.tex new file mode 100644 index 0000000..911b599 --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/positiv.tex @@ -0,0 +1,51 @@ +% +% positiv.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{7} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=14cm]{positiv.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\node at (-2.6,-3.8) [right] {$x_1$}; +\node at (-5.4,3.8) [right] {$x_3$}; + +\node[color=red] at (-4.5,-1.3) {$0$}; +\node[color=red] at (-4.15,-1.25) {$1$}; +\node[color=red] at (-3.75,-0.90) {$2$}; +\node[color=red] at (-3.22,-0.80) {$3$}; +\node[color=red] at (-2.6,-0.70) {$4$}; +\node[color=red] at (-1.8,-0.60) {$5$}; +\node[color=red] at (-0.9,-0.50) {$6$}; +\node[color=red] at (0.2,-0.40) {$7$}; +\node[color=red] at (1.6,-0.20) {$8$}; +\node[color=red] at (4.0,0.10) {$9$}; + +\end{tikzpicture} + +\end{document} + diff --git a/buch/chapters/80-wahrscheinlichkeit/images/spielB.pdf b/buch/chapters/80-wahrscheinlichkeit/images/spielB.pdf Binary files differnew file mode 100644 index 0000000..466974d --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/spielB.pdf diff --git a/buch/chapters/80-wahrscheinlichkeit/images/spielB.tex b/buch/chapters/80-wahrscheinlichkeit/images/spielB.tex new file mode 100644 index 0000000..92989ed --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/spielB.tex @@ -0,0 +1,59 @@ +% +% spielB.tex -- Zutandsdiagramm für Spiel B +% +% (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\R{2} +\def\r{0.5} +\coordinate (A) at (0,\R); +\coordinate (B) at ({\R*sqrt(3)/2},{-0.5*\R}); +\coordinate (C) at ({-\R*sqrt(3)/2},{-0.5*\R}); + +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (A) -- (B); +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (A) -- (C); +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (C) -- (B); + +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (B) to[out=90,in=-30] (A); +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (C) to[out=90,in=-150] (A); +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (B) to[out=-150,in=-30] (C); + +\pgfmathparse{0.93*\R} +\xdef\Rgross{\pgfmathresult} + +\node at (30:\Rgross) {$\frac34$}; +\node at (150:\Rgross) {$\frac14$}; +\node at (-90:\Rgross) {$\frac14$}; + +\pgfmathparse{0.33*\R} +\xdef\Rklein{\pgfmathresult} + +\node at (-90:\Rklein) {$\frac34$}; +\node at (30:\Rklein) {$\frac9{10}$}; +\node at (150:\Rklein) {$\frac1{10}$}; + +\fill[color=white] (A) circle[radius=\r]; +\draw (A) circle[radius=\r]; +\node at (A) {$0$}; + +\fill[color=white] (B) circle[radius=\r]; +\draw (B) circle[radius=\r]; +\node at (B) {$2$}; + +\fill[color=white] (C) circle[radius=\r]; +\draw (C) circle[radius=\r]; +\node at (C) {$1$}; + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.pdf b/buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.pdf Binary files differnew file mode 100644 index 0000000..7812c9c --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.pdf diff --git a/buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.tex b/buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.tex new file mode 100644 index 0000000..b2d4b01 --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/spielBtilde.tex @@ -0,0 +1,59 @@ +% +% spielBtilde.tex -- Zustandsdiagramm des modifzierten Spiels +% +% (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\R{2.5} +\def\r{0.5} +\coordinate (A) at (0,\R); +\coordinate (B) at ({\R*sqrt(3)/2},{-0.5*\R}); +\coordinate (C) at ({-\R*sqrt(3)/2},{-0.5*\R}); + +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (A) -- (B); +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (A) -- (C); +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (C) -- (B); + +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (B) to[out=90,in=-30] (A); +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (C) to[out=90,in=-150] (A); +\draw[->,shorten >= 0.5cm,shorten <= 0.5cm] (B) to[out=-150,in=-30] (C); + +\pgfmathparse{0.93*\R} +\xdef\Rgross{\pgfmathresult} + +\node at (30:\Rgross) {$\frac34-\varepsilon$}; +\node at (150:\Rgross) {$\frac14+\varepsilon$}; +\node at (-90:\Rgross) {$\frac14+\varepsilon$}; + +\pgfmathparse{0.32*\R} +\xdef\Rklein{\pgfmathresult} + +\node at (-90:\Rklein) {$\frac34-\varepsilon$}; +\node at (30:\Rklein) {$\frac9{10}+\varepsilon$}; +\node at (150:\Rklein) {$\frac1{10}-\varepsilon$}; + +\fill[color=white] (A) circle[radius=\r]; +\draw (A) circle[radius=\r]; +\node at (A) {$0$}; + +\fill[color=white] (B) circle[radius=\r]; +\draw (B) circle[radius=\r]; +\node at (B) {$2$}; + +\fill[color=white] (C) circle[radius=\r]; +\draw (C) circle[radius=\r]; +\node at (C) {$1$}; + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/80-wahrscheinlichkeit/images/trenn.pdf b/buch/chapters/80-wahrscheinlichkeit/images/trenn.pdf Binary files differnew file mode 100644 index 0000000..f4fa58f --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/trenn.pdf diff --git a/buch/chapters/80-wahrscheinlichkeit/images/trenn.tex b/buch/chapters/80-wahrscheinlichkeit/images/trenn.tex new file mode 100644 index 0000000..f34879c --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/trenn.tex @@ -0,0 +1,44 @@ +% +% trenn.tex -- Trenntrick graphische Darstellung +% +% (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\d{6} + +\coordinate (u) at (5,3); +\coordinate (v) at (3,1); +\coordinate (ve) at (5,1.666); + +\fill[color=gray!40] (0,0) rectangle (u); + +\begin{scope} +\clip (0,0) rectangle (6.1,4.1); +\draw[color=red] (0,0) -- (9,3); +\end{scope} + +\draw[->] (-0.1,0) -- (6.3,0) coordinate[label={$x_1$}]; +\draw[->] (0,-0.1) -- (0,4.3) coordinate[label={right:$x_2$}]; + +\fill (u) circle[radius=0.05]; +\node at (u) [above right] {$u$}; + +\fill (v) circle[radius=0.05]; +\node at (v) [above right] {$v$}; + +\fill[color=red] (ve) circle[radius=0.05]; +\node[color=red] at (ve) [above,rotate={atan(1/3)}] {$(1+\varepsilon)v$}; + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/80-wahrscheinlichkeit/images/vergleich.jpg b/buch/chapters/80-wahrscheinlichkeit/images/vergleich.jpg Binary files differnew file mode 100644 index 0000000..3274f42 --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/vergleich.jpg diff --git a/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdf b/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdf Binary files differnew file mode 100644 index 0000000..b7215b4 --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pdf diff --git a/buch/chapters/80-wahrscheinlichkeit/images/vergleich.png b/buch/chapters/80-wahrscheinlichkeit/images/vergleich.png Binary files differnew file mode 100644 index 0000000..f20bd48 --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/vergleich.png diff --git a/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pov b/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pov new file mode 100644 index 0000000..e696481 --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/vergleich.pov @@ -0,0 +1,203 @@ +// +// diffusion.pov +// +// (c) 2021 Prof Dr Andreas Müller, OST Ostscheizer Fachhochschule +// +#version 3.7; +#include "colors.inc" +#include "textures.inc" +#include "transforms.inc" + +global_settings { + assumed_gamma 1 +} + +#declare imagescale = 0.077; +#declare N = 30; +#declare vscale = 10; +#declare r = 0.04; + +camera { + location <43, 20, -20> + look_at <1, 0.83, 2.5> + right 16/9 * x * imagescale + up y * imagescale +} + +light_source { + <20, 60, -80> color White + area_light <1,0,0> <0,0,1>, 40, 40 + adaptive 1 + jitter +} + +sky_sphere { + pigment { + color rgb<1,1,1> + } +} + +// +// draw an arrow from <from> to <to> with thickness <arrowthickness> with +// color <c> +// +#macro arrow(from, to, arrowthickness, c) +#declare arrowdirection = vnormalize(to - from); +#declare arrowlength = vlength(to - from); +union { + sphere { + from, 1.1 * arrowthickness + } + cylinder { + from, + from + (arrowlength - 5 * arrowthickness) * arrowdirection, + arrowthickness + } + cone { + from + (arrowlength - 5 * arrowthickness) * arrowdirection, + 2 * arrowthickness, + to, + 0 + } + pigment { + color c + } + finish { + specular 0.9 + metallic + } +} +#end + +#declare O = <0,0,0>; +#declare Ex = <1,0,0>; +#declare Ey = <0,1,0>; +#declare Ez = <0,0,1>; +#declare s = 3; + +#declare A_transformation = Matrix_Trans(<1.0300,0.2050,0.1050>,<0.4100,1.0250,0.1100>,<0.4200,0.2200,1.0150>,<0,0,0>); +//#declare A_transformation = Matrix_Trans(<1.0300,0.2050,0.1050>,<0.4100,1.0250,0.1100>,<0.4200,0.2200,0.5150>,<0,0,0>); + +arrow(O, s * Ex, r, rgb<0.6,0.2,0.4>) +arrow(O, s * Ez, r, rgb<0.2,0.4,0.2>) +arrow(O, s * Ey, r, rgb<0.2,0.2,0.4>) + +#declare A = vtransform(Ex, A_transformation); +#declare B = vtransform(Ey, A_transformation); +#declare C = vtransform(Ez, A_transformation); + +#macro quadrant(rad) +intersection { + sphere { <0, 0, 0>, rad + //A_transformation + matrix <A.x, A.y, A.z, + B.x, B.y, B.z, + C.x, C.y, C.z, + 0, 0, 0 > + } + plane { vnormalize(-vcross(A, B)), 0 } + plane { vnormalize(-vcross(B, C)), 0 } + plane { vnormalize(-vcross(C, A)), 0 } + pigment { + color rgbf<0.8,1,1,0.5> + //color rgb<0.8,1,1> + } + finish { + specular 0.9 + metallic + } +} +union { + cylinder { O, s*A, 0.3*r } + sphere { s*A, 0.3*r } + cylinder { O, s*B, 0.3*r } + sphere { s*B, 0.3*r } + cylinder { O, s*C, 0.3*r } + sphere { s*C, 0.3*r } + pigment { + color White + } + finish { + specular 0.9 + metallic + } +} +#end + +#declare d = 3; +//union { +// plane { <0, 1, 0>, -d } +// plane { <1, 0, 0>, -d } +// pigment { +// color Gray +// } +// finish { +// specular 0.9 +// } +//} + +quadrant(s) + +#declare V = < 1, 1, 0 >; +#declare U = < 1.3, 2.5, 0 >; + +#declare VV = vtransform(V, A_transformation); +#declare Vx = vtransform(<V.x, 0, 0>, A_transformation); +#declare Vy = vtransform(<0, V.y, 0>, A_transformation); +#declare UU = vtransform(U, A_transformation); +#declare Ux = vtransform(<U.x, 0, 0>, A_transformation); +#declare Uy = vtransform(<0, U.y, 0>, A_transformation); + +union { + sphere { V, r } + sphere { U, r } + cylinder { U, V, 0.5*r } + pigment { + color Red + } + finish { + specular 0.9 + metallic + } +} + +union { + cylinder { < U.x, 0, 0 >, < U.x, U.y, 0>, 0.3 * r } + cylinder { < V.x, 0, 0 >, < V.x, V.y, 0>, 0.3 * r } + cylinder { < 0, U.y, 0 >, < U.x, U.y, 0>, 0.3 * r } + cylinder { < 0, V.y, 0 >, < V.x, V.y, 0>, 0.3 * r } + pigment { + color rgb<1, 0.6, 1> + } + finish { + specular 0.9 + metallic + } +} + +union { + sphere { VV, r } + sphere { UU, r } + cylinder { UU, VV, 0.5*r } + pigment { + color Yellow + } + finish { + specular 0.9 + metallic + } +} + +union { + cylinder { Ux, UU, 0.3 * r } + cylinder { Uy, UU, 0.3 * r } + cylinder { Vx, VV, 0.3 * r } + cylinder { Vy, VV, 0.3 * r } + pigment { + color rgb<1, 1, 0.6> + } + finish { + specular 0.9 + metallic + } +} diff --git a/buch/chapters/80-wahrscheinlichkeit/images/vergleich.tex b/buch/chapters/80-wahrscheinlichkeit/images/vergleich.tex new file mode 100644 index 0000000..23d7d66 --- /dev/null +++ b/buch/chapters/80-wahrscheinlichkeit/images/vergleich.tex @@ -0,0 +1,46 @@ +% +% vergleich.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{5} +\def\hoehe{5} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=10cm]{vergleich.jpg}}; + +\node at (-1.3,-4.8) [right] {$x_1$}; +\node[opacity=0.5] at (1.9,-0.9) [right] {$x_2$}; +\node at (-4.6,4.7) [right] {$x_3$}; + +\node at (-3.2,2.6) [above] {$u$}; +\node at (-3.5,-0.7) [below left] {$v$}; +\node at (-1,2.8) [above] {$Au$}; +\node at (-2.6,-0.5) [below] {$Av$}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\end{tikzpicture} + +\end{document} + |
