diff options
| -rw-r--r-- | vorlesungen/slides/8/Makefile.inc | 1 | ||||
| -rw-r--r-- | vorlesungen/slides/8/chapter.tex | 1 | ||||
| -rw-r--r-- | vorlesungen/slides/8/produkt.tex | 100 | ||||
| -rw-r--r-- | vorlesungen/slides/test.tex | 5 |
4 files changed, 105 insertions, 2 deletions
diff --git a/vorlesungen/slides/8/Makefile.inc b/vorlesungen/slides/8/Makefile.inc index cc2c497..233835a 100644 --- a/vorlesungen/slides/8/Makefile.inc +++ b/vorlesungen/slides/8/Makefile.inc @@ -12,6 +12,7 @@ chapter8 = \ ../slides/8/inzidenzd.tex \ ../slides/8/diffusion.tex \ ../slides/8/laplace.tex \ + ../slides/8/produkt.tex \ ../slides/8/fourier.tex \ ../slides/8/spanningtree.tex \ ../slides/8/pfade/adjazenz.tex \ diff --git a/vorlesungen/slides/8/chapter.tex b/vorlesungen/slides/8/chapter.tex index b29145f..ac06775 100644 --- a/vorlesungen/slides/8/chapter.tex +++ b/vorlesungen/slides/8/chapter.tex @@ -10,6 +10,7 @@ \folie{8/inzidenzd.tex} \folie{8/diffusion.tex} \folie{8/laplace.tex} +\folie{8/produkt.tex} \folie{8/fourier.tex} \folie{8/spanningtree.tex} diff --git a/vorlesungen/slides/8/produkt.tex b/vorlesungen/slides/8/produkt.tex new file mode 100644 index 0000000..1d8b725 --- /dev/null +++ b/vorlesungen/slides/8/produkt.tex @@ -0,0 +1,100 @@ +% +% produkt.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\definecolor{darkgreen}{rgb}{0,0.6,0} +\begin{frame}[t] +\frametitle{Inzidenz- und Laplace-Matrix} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.40\textwidth} +\begin{center} +\begin{tikzpicture}[>=latex,thick] + +\def\r{2.2} + +\coordinate (A) at ({\r*cos(0*72)},{\r*sin(0*72)}); +\coordinate (B) at ({\r*cos(1*72)},{\r*sin(1*72)}); +\coordinate (C) at ({\r*cos(2*72)},{\r*sin(2*72)}); +\coordinate (D) at ({\r*cos(3*72)},{\r*sin(3*72)}); +\coordinate (E) at ({\r*cos(4*72)},{\r*sin(4*72)}); + +\draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (A) -- (C); +\draw[color=white,line width=5pt] (B) -- (D); +\draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (B) -- (D); + +\draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (A) -- (B); +\draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (B) -- (C); +\draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (C) -- (D); +\draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (D) -- (E); +\draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (E) -- (A); + +\draw (A) circle[radius=0.2]; +\draw (B) circle[radius=0.2]; +\draw (C) circle[radius=0.2]; +\draw (D) circle[radius=0.2]; +\draw (E) circle[radius=0.2]; + +\node at (A) {$1$}; +\node at (B) {$2$}; +\node at (C) {$3$}; +\node at (D) {$4$}; +\node at (E) {$5$}; +\node at (0,0) {$G$}; + +\node at ($0.5*(A)+0.5*(B)-(0.1,0.1)$) [above right] {$\scriptstyle 1$}; +\node at ($0.5*(B)+0.5*(C)+(0.05,-0.07)$) [above left] {$\scriptstyle 2$}; +\node at ($0.5*(C)+0.5*(D)+(0.05,0)$) [left] {$\scriptstyle 3$}; +\node at ($0.5*(D)+0.5*(E)$) [below] {$\scriptstyle 4$}; +\node at ($0.5*(E)+0.5*(A)+(-0.1,0.1)$) [below right] {$\scriptstyle 5$}; +\node at ($0.6*(A)+0.4*(C)$) [above] {$\scriptstyle 6$}; +\node at ($0.4*(B)+0.6*(D)$) [left] {$\scriptstyle 7$}; + +\end{tikzpicture} +\end{center} +\vspace{-15pt} +\begin{block}{Berechne} +\vspace{-20pt} +\begin{align*} +\uncover<4->{L(G)}&\uncover<4->{=}B(G)B(G)^t +\end{align*} +\end{block} +\end{column} +\begin{column}{0.58\textwidth} +\begin{center} +\begin{tikzpicture}[>=latex,thick] + +\def\dx{0.84} +\def\dy{0.48} + +\node at (0,0) {$\displaystyle +\begin{aligned} +B(G) +&= +\begin{pmatrix*}[r] +-1& 0& 0& 0&+1&-1& 0\\ ++1&-1& 0& 0& 0& 0&-1\\ + 0&+1&-1& 0& 0&+1& 0\\ + 0& 0&+1&-1& 0& 0&+1\\ + 0& 0& 0&+1&-1& 0& 0 +\end{pmatrix*} +\\[20pt] +\uncover<2->{ +L(G) +&= +\begin{pmatrix*}[r] + 3&\uncover<3->{-1}&\uncover<3->{-1}&\uncover<3->{ 0}&\uncover<3->{-1}\\ +\uncover<3->{-1}& 3&\uncover<3->{-1}&\uncover<3->{-1}&\uncover<3->{ 0}\\ +\uncover<3->{-1}&\uncover<3->{-1}& 3&\uncover<3->{-1}&\uncover<3->{ 0}\\ +\uncover<3->{ 0}&\uncover<3->{-1}&\uncover<3->{-1}& 3&\uncover<3->{-1}\\ +\uncover<3->{-1}&\uncover<3->{ 0}&\uncover<3->{ 0}&\uncover<3->{-1}& 2 +\end{pmatrix*}} +\end{aligned}$}; +\end{tikzpicture} +\end{center} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/test.tex b/vorlesungen/slides/test.tex index 6c5d5ff..411414e 100644 --- a/vorlesungen/slides/test.tex +++ b/vorlesungen/slides/test.tex @@ -6,10 +6,11 @@ %\folie{8/dgraph.tex} %\folie{8/graph.tex} %\folie{8/grad.tex} -\folie{8/inzidenz.tex} +%\folie{8/inzidenz.tex} \folie{8/inzidenzd.tex} %\folie{8/diffusion.tex} -%\folie{8/laplace.tex} +\folie{8/laplace.tex} +\folie{8/produkt.tex} %\folie{8/fourier.tex} %\folie{8/spanningtree.tex} |