diff options
Diffstat (limited to 'buch/chapters/70-graphen/images')
| -rw-r--r-- | buch/chapters/70-graphen/images/Makefile | 14 | ||||
| -rw-r--r-- | buch/chapters/70-graphen/images/fundamental.pdf | bin | 0 -> 25976 bytes | |||
| -rw-r--r-- | buch/chapters/70-graphen/images/fundamental.tex | 54 | ||||
| -rw-r--r-- | buch/chapters/70-graphen/images/gh.pdf | bin | 0 -> 26177 bytes | |||
| -rw-r--r-- | buch/chapters/70-graphen/images/gh.tex | 55 | ||||
| -rw-r--r-- | buch/chapters/70-graphen/images/nine.pdf | bin | 0 -> 2136 bytes | |||
| -rw-r--r-- | buch/chapters/70-graphen/images/nine.tex | 67 | ||||
| -rw-r--r-- | buch/chapters/70-graphen/images/petersonchrind.pdf | bin | 0 -> 15217 bytes | |||
| -rw-r--r-- | buch/chapters/70-graphen/images/petersonchrind.tex | 142 |
9 files changed, 331 insertions, 1 deletions
diff --git a/buch/chapters/70-graphen/images/Makefile b/buch/chapters/70-graphen/images/Makefile index b42cbae..5db54c8 100644 --- a/buch/chapters/70-graphen/images/Makefile +++ b/buch/chapters/70-graphen/images/Makefile @@ -3,11 +3,14 @@ # # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -all: peterson.pdf adjazenzu.pdf adjazenzd.pdf kreis.pdf +all: peterson.pdf adjazenzu.pdf adjazenzd.pdf kreis.pdf fundamental.pdf \ + petersonchrind.pdf nine.pdf gh.pdf peterson.pdf: peterson.tex pdflatex peterson.tex +petersonchrind.pdf: petersonchrind.tex + pdflatex petersonchrind.tex adjazenzu.pdf: adjazenzu.tex pdflatex adjazenzu.tex @@ -17,3 +20,12 @@ adjazenzd.pdf: adjazenzd.tex kreis.pdf: kreis.tex pdflatex kreis.tex +fundamental.pdf: fundamental.tex + pdflatex fundamental.tex + +nine.pdf: nine.tex + pdflatex nine.tex + +gh.pdf: gh.tex + pdflatex gh.tex + diff --git a/buch/chapters/70-graphen/images/fundamental.pdf b/buch/chapters/70-graphen/images/fundamental.pdf Binary files differnew file mode 100644 index 0000000..66b82ca --- /dev/null +++ b/buch/chapters/70-graphen/images/fundamental.pdf diff --git a/buch/chapters/70-graphen/images/fundamental.tex b/buch/chapters/70-graphen/images/fundamental.tex new file mode 100644 index 0000000..b7fe9c4 --- /dev/null +++ b/buch/chapters/70-graphen/images/fundamental.tex @@ -0,0 +1,54 @@ +% +% fundamental.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] + +\begin{scope}[xshift=-4.6cm] + \draw[color=red,line width=2pt] (1.8,0) -- (1.8,2); + \draw[color=red,line width=2pt] (0,0) -- (4,0); + \node at (1.8,0) [below] {$i$}; + \draw[->] (-0.1,0) -- (4.3,0) coordinate[label={$x$}]; + \draw[->] (0,-2.1) -- (0,2.3) coordinate[label={right:$y$}]; + + \node at (2,-2.3) [below] {Standarbasis}; +\end{scope} + +\begin{scope} + \draw[color=red,line width=1.4pt] + plot[domain=0:360,samples=100] ({\x/90},{2*sin(\x)}); + \draw[color=blue,line width=1.4pt] + plot[domain=0:360,samples=100] ({\x/90},{2*cos(\x)}); + \node[color=blue] at (1,-1) {$\Re f_i$}; + \node[color=red] at (2,1) {$\Im f_i$}; + \draw[->] (-0.1,0) -- (4.3,0) coordinate[label={$x$}]; + \draw[->] (0,-2.1) -- (0,2.3) coordinate[label={right:$y$}]; + \node at (2,-2.3) [below] {Eigenbasis}; +\end{scope} + +\begin{scope}[xshift=4.6cm] + \foreach \t in {0.02,0.05,0.1,0.2,0.5}{ + \draw[color=red,line width=1.0pt] + plot[domain=-1.8:2.2,samples=100] + ({\x+1.8},{exp(-\x*\x/(4*\t))/(sqrt(4*3.1415*\t))}); + } + \fill[color=red] (1.8,0) circle[radius=0.08]; + \node at (1.8,0) [below] {$\xi$}; + \draw[->] (-0.1,0) -- (4.3,0) coordinate[label={$x$}]; + \draw[->] (0,-2.1) -- (0,2.3) coordinate[label={right:$y$}]; + \node at (2,-2.3) [below] {Fundamentallösung}; +\end{scope} + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/70-graphen/images/gh.pdf b/buch/chapters/70-graphen/images/gh.pdf Binary files differnew file mode 100644 index 0000000..c6e48d7 --- /dev/null +++ b/buch/chapters/70-graphen/images/gh.pdf diff --git a/buch/chapters/70-graphen/images/gh.tex b/buch/chapters/70-graphen/images/gh.tex new file mode 100644 index 0000000..fcceb5f --- /dev/null +++ b/buch/chapters/70-graphen/images/gh.tex @@ -0,0 +1,55 @@ +% +% gh.tex -- Lokalsierungsfunktionen für Wavelets auf einem Graphen +% +% (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] +\definecolor{darkgreen}{rgb}{0,0.6,0} + +\def\kurve#1#2{ + \draw[color=#2,line width=1.4pt] + plot[domain=0:6.3,samples=400] + ({\x},{7*\x*exp(-(\x/#1)*(\x/#1))/#1}); +} + +\begin{scope} + +\draw[->] (-0.1,0) -- (6.6,0) coordinate[label={$\lambda$}]; + +\kurve{1}{red} +\foreach \k in {0,...,4}{ + \pgfmathparse{0.30*exp(ln(2)*\k)} + \xdef\l{\pgfmathresult} + \kurve{\l}{blue} +} + +\node[color=red] at ({0.7*1},3) [above] {$g(\lambda)$}; +\node[color=blue] at ({0.7*0.3*16},3) [above] {$g_i(\lambda)$}; + +\draw[->] (0,-0.1) -- (0,3.3); +\end{scope} + +\begin{scope}[xshift=7cm] + +\draw[->] (-0.1,0) -- (6.6,0) coordinate[label={$\lambda$}]; + +\draw[color=darkgreen,line width=1.4pt] + plot[domain=0:6.3,samples=100] + ({\x},{3*exp(-(\x/0.5)*(\x/0.5)}); + +\draw[->] (0,-0.1) -- (0,3.3) coordinate[label={right:$\color{darkgreen}h(\lambda)$}]; + +\end{scope} + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/70-graphen/images/nine.pdf b/buch/chapters/70-graphen/images/nine.pdf Binary files differnew file mode 100644 index 0000000..2ae9f68 --- /dev/null +++ b/buch/chapters/70-graphen/images/nine.pdf diff --git a/buch/chapters/70-graphen/images/nine.tex b/buch/chapters/70-graphen/images/nine.tex new file mode 100644 index 0000000..f214c1e --- /dev/null +++ b/buch/chapters/70-graphen/images/nine.tex @@ -0,0 +1,67 @@ +% +% nine.tex -- Nine node graph to illustrate Wilf's theorem +% +% (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} +\def\kante#1#2{ + \draw[shorten >= 0.2cm,shorten <= 0.2cm] (#1) -- (#2); +} +\def\knoten#1#2{ + \fill[color=#2!30] (#1) circle[radius=0.2]; + \draw[color=#2] (#1) circle[radius=0.2]; + \draw (#1) circle[radius=0.2]; +} +\def\R{1.5} +\definecolor{rot}{rgb}{1,0,0} +\definecolor{gruen}{rgb}{0,0.6,0} +\definecolor{blau}{rgb}{0,0,1} + +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\coordinate (A) at (0:\R); +\coordinate (B) at (40:\R); +\coordinate (C) at (80:\R); +\coordinate (D) at (120:\R); +\coordinate (E) at (160:\R); +\coordinate (F) at (200:\R); +\coordinate (G) at (240:\R); +\coordinate (H) at (280:\R); +\coordinate (I) at (320:\R); + +\knoten{A}{rot} +\knoten{B}{blau} +\knoten{C}{gruen} +\knoten{D}{blau} +\knoten{E}{rot} +\knoten{F}{blau} +\knoten{G}{rot} +\knoten{H}{gruen} +\knoten{I}{blau} + +\kante{A}{B} +\kante{B}{C} +\kante{C}{D} +\kante{D}{E} +\kante{E}{F} +\kante{F}{G} +\kante{G}{H} +\kante{H}{I} +\kante{I}{A} + +\kante{A}{C} +\kante{A}{D} +\kante{D}{G} + + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/70-graphen/images/petersonchrind.pdf b/buch/chapters/70-graphen/images/petersonchrind.pdf Binary files differnew file mode 100644 index 0000000..23ef6e9 --- /dev/null +++ b/buch/chapters/70-graphen/images/petersonchrind.pdf diff --git a/buch/chapters/70-graphen/images/petersonchrind.tex b/buch/chapters/70-graphen/images/petersonchrind.tex new file mode 100644 index 0000000..4ae9f39 --- /dev/null +++ b/buch/chapters/70-graphen/images/petersonchrind.tex @@ -0,0 +1,142 @@ +% +% tikztemplate.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\Ra{2} +\def\Ri{1} +\def\e{1.0} +\def\r{0.2} + +\begin{scope}[xshift=-3.5cm] + +\definecolor{rot}{rgb}{0.8,0,0.8} +\definecolor{gruen}{rgb}{0.2,0.6,0.2} +\definecolor{blau}{rgb}{1,0.6,0.2} + +\coordinate (PA) at ({\Ri*sin(0*72)},{\e*\Ri*cos(0*72)}); +\coordinate (PB) at ({\Ri*sin(1*72)},{\e*\Ri*cos(1*72)}); +\coordinate (PC) at ({\Ri*sin(2*72)},{\e*\Ri*cos(2*72)}); +\coordinate (PD) at ({\Ri*sin(3*72)},{\e*\Ri*cos(3*72)}); +\coordinate (PE) at ({\Ri*sin(4*72)},{\e*\Ri*cos(4*72)}); + +\coordinate (QA) at ({\Ra*sin(0*72)},{\e*\Ra*cos(0*72)}); +\coordinate (QB) at ({\Ra*sin(1*72)},{\e*\Ra*cos(1*72)}); +\coordinate (QC) at ({\Ra*sin(2*72)},{\e*\Ra*cos(2*72)}); +\coordinate (QD) at ({\Ra*sin(3*72)},{\e*\Ra*cos(3*72)}); +\coordinate (QE) at ({\Ra*sin(4*72)},{\e*\Ra*cos(4*72)}); + +\draw (PA)--(PC)--(PE)--(PB)--(PD)--cycle; +\draw (QA)--(QB)--(QC)--(QD)--(QE)--cycle; +\draw (PA)--(QA); +\draw (PB)--(QB); +\draw (PC)--(QC); +\draw (PD)--(QD); +\draw (PE)--(QE); + +\fill[color=blau] (PA) circle[radius=\r]; +\fill[color=rot] (PB) circle[radius=\r]; +\fill[color=rot] (PC) circle[radius=\r]; +\fill[color=gruen] (PD) circle[radius=\r]; +\fill[color=gruen] (PE) circle[radius=\r]; + +\fill[color=rot] (QA) circle[radius=\r]; +\fill[color=blau] (QB) circle[radius=\r]; +\fill[color=gruen] (QC) circle[radius=\r]; +\fill[color=rot] (QD) circle[radius=\r]; +\fill[color=blau] (QE) circle[radius=\r]; + +\draw (PA) circle[radius=\r]; +\draw (PB) circle[radius=\r]; +\draw (PC) circle[radius=\r]; +\draw (PD) circle[radius=\r]; +\draw (PE) circle[radius=\r]; + +\draw (QA) circle[radius=\r]; +\draw (QB) circle[radius=\r]; +\draw (QC) circle[radius=\r]; +\draw (QD) circle[radius=\r]; +\draw (QE) circle[radius=\r]; + +\node at (0,{-\Ra}) [below] {$\operatorname{chr}P=3\mathstrut$}; + +\end{scope} + +\begin{scope}[xshift=3.5cm] +\definecolor{rot}{rgb}{0.8,0,0.8} +\definecolor{gruen}{rgb}{0.2,0.6,0.2} +\definecolor{blau}{rgb}{1,0.6,0.2} +\definecolor{gelb}{rgb}{0,0,1} + +\coordinate (PA) at ({\Ri*sin(0*72)},{\e*\Ri*cos(0*72)}); +\coordinate (PB) at ({\Ri*sin(1*72)},{\e*\Ri*cos(1*72)}); +\coordinate (PC) at ({\Ri*sin(2*72)},{\e*\Ri*cos(2*72)}); +\coordinate (PD) at ({\Ri*sin(3*72)},{\e*\Ri*cos(3*72)}); +\coordinate (PE) at ({\Ri*sin(4*72)},{\e*\Ri*cos(4*72)}); + +\coordinate (QA) at ({\Ra*sin(0*72)},{\e*\Ra*cos(0*72)}); +\coordinate (QB) at ({\Ra*sin(1*72)},{\e*\Ra*cos(1*72)}); +\coordinate (QC) at ({\Ra*sin(2*72)},{\e*\Ra*cos(2*72)}); +\coordinate (QD) at ({\Ra*sin(3*72)},{\e*\Ra*cos(3*72)}); +\coordinate (QE) at ({\Ra*sin(4*72)},{\e*\Ra*cos(4*72)}); + +\draw (PA)--(PC)--(PE)--(PB)--(PD)--cycle; +\draw (QA)--(QB)--(QC)--(QD)--(QE)--cycle; +\draw (PA)--(QA); +\draw (PB)--(QB); +\draw (PC)--(QC); +\draw (PD)--(QD); +\draw (PE)--(QE); + +\fill[color=rot] (QA) circle[radius={1.5*\r}]; +\fill[color=rot!40] (QB) circle[radius=\r]; +\fill[color=rot!40] (QE) circle[radius=\r]; +\fill[color=rot!40] (PA) circle[radius=\r]; + +\fill[color=blau] (PB) circle[radius={1.5*\r}]; +\fill[color=blau!40] (PD) circle[radius=\r]; +\fill[color=blau!40] (PE) circle[radius=\r]; +\fill[color=blau!80,opacity=0.5] (QB) circle[radius=\r]; + +\fill[color=gruen] (PC) circle[radius={1.5*\r}]; +\fill[color=gruen!40] (QC) circle[radius=\r]; +\fill[color=gruen!80,opacity=0.5] (PA) circle[radius=\r]; +\fill[color=gruen!80,opacity=0.5] (PE) circle[radius=\r]; + +\fill[color=gelb] (QD) circle[radius={1.5*\r}]; +\fill[color=gelb!80,opacity=0.5] (QC) circle[radius=\r]; +\fill[color=gelb!80,opacity=0.5] (QE) circle[radius=\r]; +\fill[color=gelb!80,opacity=0.5] (PD) circle[radius=\r]; + +\draw (PA) circle[radius=\r]; +\draw (PB) circle[radius={1.5*\r}]; +\draw (PC) circle[radius={1.5*\r}]; +\draw (PD) circle[radius=\r]; +\draw (PE) circle[radius=\r]; + +\draw (QA) circle[radius={1.5*\r}]; +\draw (QB) circle[radius=\r]; +\draw (QC) circle[radius=\r]; +\draw (QD) circle[radius={1.5*\r}]; +\draw (QE) circle[radius=\r]; + +\node at (0,{-\Ra}) [below] {$\operatorname{ind}P=4\mathstrut$}; + +\end{scope} + + + +\end{tikzpicture} +\end{document} + |