\documentclass[aspectratio=169,hyperref={pdfpagelabels=false}]{beamer} \usepackage{lmodern} \usepackage[utf8]{inputenc} % this is needed for german umlauts \usepackage[ngerman]{babel} % this is needed for german umlauts \usepackage[T1]{fontenc} % this is needed for correct output of umlauts in pdf \usepackage{braket} % needed for \Set \usepackage{algorithm,algpseudocode} \usepackage{verbatim} \usepackage{tikz} \usetikzlibrary{arrows,shapes} % Define some styles for graphs \tikzstyle{vertex}=[circle,fill=black!25,minimum size=20pt,inner sep=0pt] \tikzstyle{selected vertex} = [vertex, fill=red!24] \tikzstyle{blue vertex} = [vertex, fill=blue!24] \tikzstyle{edge} = [draw,thick,-] \tikzstyle{weight} = [font=\small] \tikzstyle{selected edge} = [draw,line width=5pt,-,red!50] \tikzstyle{ignored edge} = [draw,line width=5pt,-,black!20] % see http://deic.uab.es/~iblanes/beamer_gallery/index_by_theme.html %\usetheme{Frankfurt} \usefonttheme{professionalfonts} % disables bottom navigation bar \beamertemplatenavigationsymbolsempty % http://tex.stackexchange.com/questions/23727/converting-beamer-slides-to-animated-images \setbeamertemplate{navigation symbols}{}% \newcommand{\alertline}{% \usebeamercolor[fg]{normal text}% \only{\usebeamercolor[fg]{alerted text}}} \begin{document} \pgfdeclarelayer{background} \pgfsetlayers{background,main} \newcommand\hlight[1]{\tikz[overlay, remember picture,baseline=-\the\dimexpr\fontdimen22\textfont2\relax]\node[rectangle,fill=blue!50,rounded corners,fill opacity = 0.2,draw,thick,text opacity =1] {$#1$};} \newcommand\tocalculate[1]{\tikz[overlay, remember picture,baseline=-\the\dimexpr\fontdimen22\textfont2\relax]\node[rectangle,fill=green!50,rounded corners,fill opacity = 0.2,draw,thick,text opacity =1] {$#1$};} \begin{frame} \begin{minipage}[b]{0.30\linewidth} \centering \begin{align*} A &= \begin{pmatrix} 1 & 2 & 3\\ 2 & 8 & 14\\ 3 & 14 & 34 \end{pmatrix}\\ \alertline<1> L &= \alertline<1>\begin{pmatrix} 0 & 0 & 0\\ 0 & 0 & 0\\ 0 & 0 & 0 \end{pmatrix}\\ tmp &= 0 \end{align*} \end{minipage} \hspace{0.5cm} \begin{minipage}[b]{0.60\linewidth} \centering \begin{algorithm}[H] \begin{algorithmic} \Function{Cholesky}{$A \in \mathbb{R}^{n \times n}$} \alertline<1>\State $L = \Set{0} \in \mathbb{R}^{n \times n}$ \Comment{Initialisiere $L$}\\ \alertline<2>\alertline<4>\For{($k=1$; $\;k \leq n$; $\;k$++)} \alertline<3>\State $L_{k,k} = \sqrt{A_{k,k} - \sum_{i=1}^{k-1} L_{k,i}^2}$ \For{($i=k+1$; $\;i \leq n$; $\;i$++)} \State $L_{i,k} = \frac{A_{i,k} - \sum_{j=1}^{k-1} L_{i,j} \cdot L_{k,j}}{L_{k,k}}$ \EndFor \EndFor \alertline<5>\State \Return $L$ \EndFunction \end{algorithmic} \caption{Cholesky-Zerlegung} \label{alg:seq1} \end{algorithm} \end{minipage} \end{frame} \begin{frame} \begin{align*} A &= \begin{pmatrix} \hlight{1} & 2 & 3\\ 2 & 8 & 14\\ 3 & 14 & 34 \end{pmatrix}\\ L &= \begin{pmatrix} \tocalculate{0} & 0 & 0\\ 0 & 0 & 0\\ 0 & 0 & 0 \end{pmatrix}\\ tmp &= 0 \end{align*} \end{frame} \begin{frame} \begin{align*} A &= \begin{pmatrix} 1 & 2 & 3\\ 2 & 8 & 14\\ 3 & 14 & 34 \end{pmatrix}\\ L &= \begin{pmatrix} \tocalculate{1} & 0 & 0\\ 0 & 0 & 0\\ 0 & 0 & 0 \end{pmatrix}\\ tmp &= 0 \end{align*} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Calculate L_2,1 \begin{frame} \begin{align*} A &= \begin{pmatrix} 1 & 2 & 3\\ \hlight{2} & 8 & 14\\ 3 & 14 & 34 \end{pmatrix}\\ L &= \begin{pmatrix} 1 & 0 & 0\\ \tocalculate{0} & 0 & 0\\ 0 & 0 & 0 \end{pmatrix}\\ tmp &= 0 \end{align*} \end{frame} \begin{frame} \begin{align*} A &= \begin{pmatrix} 1 & 2 & 3\\ 2 & 8 & 14\\ 3 & 14 & 34 \end{pmatrix}\\ L &= \begin{pmatrix} \hlight{1} & 0 & 0\\ \tocalculate{2} & 0 & 0\\ 0 & 0 & 0 \end{pmatrix}\\ tmp &= 0 \end{align*} \end{frame} \begin{frame} \begin{align*} A &= \begin{pmatrix} 1 & 2 & 3\\ 2 & 8 & 14\\ 3 & 14 & 34 \end{pmatrix}\\ L &= \begin{pmatrix} 1 & 0 & 0\\ \tocalculate{2} & 0 & 0\\ 0 & 0 & 0 \end{pmatrix}\\ tmp &= 0 \end{align*} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Calculate L_3,1 \begin{frame} \begin{align*} A &= \begin{pmatrix} 1 & 2 & 3\\ 2 & 8 & 14\\ \hlight{3} & 14 & 34 \end{pmatrix}\\ L &= \begin{pmatrix} 1 & 0 & 0\\ 2 & 0 & 0\\ \tocalculate{0} & 0 & 0 \end{pmatrix}\\ tmp &= 0 \end{align*} \end{frame} \begin{frame} \begin{align*} A &= \begin{pmatrix} \hlight{1} & 2 & 3\\ 2 & 8 & 14\\ 3 & 14 & 34 \end{pmatrix}\\ L &= \begin{pmatrix} 1 & 0 & 0\\ 2 & 0 & 0\\ \tocalculate{3} & 0 & 0 \end{pmatrix}\\ tmp &= 0 \end{align*} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Calculate L_2,2 \begin{frame} \begin{align*} A &= \begin{pmatrix} 1 & 2 & 3\\ 2 & \hlight{8} & 14\\ 3 & 14 & 34 \end{pmatrix}\\ L &= \begin{pmatrix} 1 & 0 & 0\\ 2 & \tocalculate{0} & 0\\ 3 & 0 & 0 \end{pmatrix}\\ tmp &= 0 \end{align*} \end{frame} \begin{frame} \begin{align*} A &= \begin{pmatrix} 1 & 2 & 3\\ 2 & 8 & 14\\ 3 & 14 & 34 \end{pmatrix}\\ L &= \begin{pmatrix} 1 & 0 & 0\\ \hlight{2} & \tocalculate{8} & 0\\ 3 & 0 & 0 \end{pmatrix}\\ tmp &= 0 \end{align*} \end{frame} \begin{frame} \begin{align*} A &= \begin{pmatrix} 1 & 2 & 3\\ 2 & 8 & 14\\ 3 & 14 & 34 \end{pmatrix}\\ L &= \begin{pmatrix} 1 & 0 & 0\\ 2 & \tocalculate{8} & 0\\ 3 & 0 & 0 \end{pmatrix}\\ tmp &= \hlight{4} \end{align*} \end{frame} \begin{frame} \begin{align*} A &= \begin{pmatrix} 1 & 2 & 3\\ 2 & 8 & 14\\ 3 & 14 & 34 \end{pmatrix}\\ L &= \begin{pmatrix} 1 & 0 & 0\\ 2 & \tocalculate{4} & 0\\ 3 & 0 & 0 \end{pmatrix}\\ tmp &= 0 \end{align*} \end{frame} \begin{frame} \begin{align*} A &= \begin{pmatrix} 1 & 2 & 3\\ 2 & 8 & 14\\ 3 & 14 & 34 \end{pmatrix}\\ L &= \begin{pmatrix} 1 & 0 & 0\\ 2 & \tocalculate{2} & 0\\ 3 & 0 & 0 \end{pmatrix}\\ tmp &= 0 \end{align*} \end{frame} \end{document}