\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}
