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Martin Thoma
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6 changed files with 339 additions and 5 deletions
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\documentclass[aspectratio=169,hyperref={pdfpagelabels=false}]{beamer}
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\usepackage{lmodern}
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\usepackage[utf8]{inputenc} % this is needed for german umlauts
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\usepackage[ngerman]{babel} % this is needed for german umlauts
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\usepackage[T1]{fontenc} % this is needed for correct output of umlauts in pdf
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\usepackage{braket} % needed for \Set
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\usepackage{algorithm,algpseudocode}
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\usepackage{verbatim}
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\usepackage{tikz}
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\usetikzlibrary{arrows,shapes}
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% Define some styles for graphs
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\tikzstyle{vertex}=[circle,fill=black!25,minimum size=20pt,inner sep=0pt]
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\tikzstyle{selected vertex} = [vertex, fill=red!24]
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\tikzstyle{blue vertex} = [vertex, fill=blue!24]
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\tikzstyle{edge} = [draw,thick,-]
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\tikzstyle{weight} = [font=\small]
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\tikzstyle{selected edge} = [draw,line width=5pt,-,red!50]
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\tikzstyle{ignored edge} = [draw,line width=5pt,-,black!20]
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% see http://deic.uab.es/~iblanes/beamer_gallery/index_by_theme.html
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%\usetheme{Frankfurt}
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\usefonttheme{professionalfonts}
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% disables bottom navigation bar
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\beamertemplatenavigationsymbolsempty
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% http://tex.stackexchange.com/questions/23727/converting-beamer-slides-to-animated-images
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\setbeamertemplate{navigation symbols}{}%
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\newcommand{\alertline}{%
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\usebeamercolor[fg]{normal text}%
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\only{\usebeamercolor[fg]{alerted text}}}
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\begin{document}
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\pgfdeclarelayer{background}
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\pgfsetlayers{background,main}
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\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] {$#1$};}
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\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] {$#1$};}
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\begin{frame}
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\begin{minipage}[b]{0.30\linewidth}
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\centering
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\begin{align*}
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A &= \begin{pmatrix}
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1 & 2 & 3\\
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2 & 8 & 14\\
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3 & 14 & 34
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\end{pmatrix}\\
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\alertline<1> L &= \alertline<1>\begin{pmatrix}
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0 & 0 & 0\\
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0 & 0 & 0\\
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0 & 0 & 0
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\end{pmatrix}\\
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tmp &= 0
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\end{align*}
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\end{minipage}
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\hspace{0.5cm}
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\begin{minipage}[b]{0.60\linewidth}
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\centering
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\begin{algorithm}[H]
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\begin{algorithmic}
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\Function{Cholesky}{$A \in \mathbb{R}^{n \times n}$}
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\alertline<1>\State $L = \Set{0} \in \mathbb{R}^{n \times n}$ \Comment{Initialisiere $L$}\\
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\alertline<2>\alertline<4>\For{($k=1$; $\;k \leq n$; $\;k$++)}
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\alertline<3>\State $L_{k,k} = \sqrt{A_{k,k} - \sum_{i=1}^{k-1} L_{k,i}^2}$
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\For{($i=k+1$; $\;i \leq n$; $\;i$++)}
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\State $L_{i,k} = \frac{A_{i,k} - \sum_{j=1}^{k-1} L_{i,j} \cdot L_{k,j}}{L_{k,k}}$
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\EndFor
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\EndFor
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\alertline<5>\State \Return $L$
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\EndFunction
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\end{algorithmic}
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\caption{Cholesky-Zerlegung}
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\label{alg:seq1}
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\end{algorithm}
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\end{minipage}
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\end{frame}
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\begin{frame}
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\begin{align*}
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A &= \begin{pmatrix}
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\hlight{1} & 2 & 3\\
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2 & 8 & 14\\
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3 & 14 & 34
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\end{pmatrix}\\
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L &= \begin{pmatrix}
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\tocalculate{0} & 0 & 0\\
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0 & 0 & 0\\
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0 & 0 & 0
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\end{pmatrix}\\
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tmp &= 0
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\end{align*}
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\end{frame}
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\begin{frame}
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\begin{align*}
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A &= \begin{pmatrix}
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1 & 2 & 3\\
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2 & 8 & 14\\
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3 & 14 & 34
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\end{pmatrix}\\
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L &= \begin{pmatrix}
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\tocalculate{1} & 0 & 0\\
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0 & 0 & 0\\
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0 & 0 & 0
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\end{pmatrix}\\
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tmp &= 0
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\end{align*}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Calculate L_2,1
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\begin{frame}
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\begin{align*}
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A &= \begin{pmatrix}
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1 & 2 & 3\\
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\hlight{2} & 8 & 14\\
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3 & 14 & 34
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\end{pmatrix}\\
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L &= \begin{pmatrix}
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1 & 0 & 0\\
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\tocalculate{0} & 0 & 0\\
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0 & 0 & 0
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\end{pmatrix}\\
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tmp &= 0
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\end{align*}
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\end{frame}
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\begin{frame}
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\begin{align*}
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A &= \begin{pmatrix}
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1 & 2 & 3\\
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2 & 8 & 14\\
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3 & 14 & 34
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\end{pmatrix}\\
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L &= \begin{pmatrix}
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\hlight{1} & 0 & 0\\
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\tocalculate{2} & 0 & 0\\
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0 & 0 & 0
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\end{pmatrix}\\
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tmp &= 0
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\end{align*}
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\end{frame}
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\begin{frame}
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\begin{align*}
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A &= \begin{pmatrix}
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1 & 2 & 3\\
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2 & 8 & 14\\
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3 & 14 & 34
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\end{pmatrix}\\
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L &= \begin{pmatrix}
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1 & 0 & 0\\
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\tocalculate{2} & 0 & 0\\
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0 & 0 & 0
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\end{pmatrix}\\
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tmp &= 0
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\end{align*}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Calculate L_3,1
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\begin{frame}
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\begin{align*}
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A &= \begin{pmatrix}
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1 & 2 & 3\\
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2 & 8 & 14\\
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\hlight{3} & 14 & 34
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\end{pmatrix}\\
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L &= \begin{pmatrix}
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1 & 0 & 0\\
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2 & 0 & 0\\
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\tocalculate{0} & 0 & 0
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\end{pmatrix}\\
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tmp &= 0
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\end{align*}
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\end{frame}
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\begin{frame}
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\begin{align*}
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A &= \begin{pmatrix}
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\hlight{1} & 2 & 3\\
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2 & 8 & 14\\
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3 & 14 & 34
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\end{pmatrix}\\
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L &= \begin{pmatrix}
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1 & 0 & 0\\
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2 & 0 & 0\\
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\tocalculate{3} & 0 & 0
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\end{pmatrix}\\
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tmp &= 0
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\end{align*}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Calculate L_2,2
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\begin{frame}
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\begin{align*}
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A &= \begin{pmatrix}
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1 & 2 & 3\\
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2 & \hlight{8} & 14\\
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3 & 14 & 34
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\end{pmatrix}\\
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L &= \begin{pmatrix}
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1 & 0 & 0\\
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2 & \tocalculate{0} & 0\\
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3 & 0 & 0
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\end{pmatrix}\\
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tmp &= 0
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\end{align*}
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\end{frame}
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\begin{frame}
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\begin{align*}
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A &= \begin{pmatrix}
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1 & 2 & 3\\
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2 & 8 & 14\\
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3 & 14 & 34
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\end{pmatrix}\\
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L &= \begin{pmatrix}
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1 & 0 & 0\\
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\hlight{2} & \tocalculate{8} & 0\\
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3 & 0 & 0
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\end{pmatrix}\\
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tmp &= 0
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\end{align*}
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\end{frame}
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\begin{frame}
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\begin{align*}
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A &= \begin{pmatrix}
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1 & 2 & 3\\
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2 & 8 & 14\\
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3 & 14 & 34
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\end{pmatrix}\\
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L &= \begin{pmatrix}
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1 & 0 & 0\\
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2 & \tocalculate{8} & 0\\
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3 & 0 & 0
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\end{pmatrix}\\
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tmp &= \hlight{4}
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\end{align*}
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\end{frame}
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\begin{frame}
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\begin{align*}
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A &= \begin{pmatrix}
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1 & 2 & 3\\
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2 & 8 & 14\\
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3 & 14 & 34
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\end{pmatrix}\\
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L &= \begin{pmatrix}
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1 & 0 & 0\\
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2 & \tocalculate{4} & 0\\
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3 & 0 & 0
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\end{pmatrix}\\
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tmp &= 0
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\end{align*}
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\end{frame}
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\begin{frame}
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\begin{align*}
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A &= \begin{pmatrix}
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1 & 2 & 3\\
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2 & 8 & 14\\
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3 & 14 & 34
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\end{pmatrix}\\
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L &= \begin{pmatrix}
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1 & 0 & 0\\
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2 & \tocalculate{2} & 0\\
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3 & 0 & 0
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\end{pmatrix}\\
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tmp &= 0
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\end{align*}
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\end{frame}
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\end{document}
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35
source-code/Pseudocode/Cholesky-Zerlegung/Animation/Makefile
Normal file
35
source-code/Pseudocode/Cholesky-Zerlegung/Animation/Makefile
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SOURCE = Animation
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DELAY = 80
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DENSITY = 300
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WIDTH = 500
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make:
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pdflatex $(SOURCE).tex -output-format=pdf
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make clean
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clean:
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rm -rf $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
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gif:
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pdfcrop $(SOURCE).pdf
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convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
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make clean
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png:
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make
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make svg
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inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
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transparentGif:
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convert $(SOURCE).pdf -transparent white result.gif
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make clean
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svg:
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make
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#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
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pdf2svg $(SOURCE).pdf $(SOURCE).svg
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# Necessary, as pdf2svg does not always create valid svgs:
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inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg
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rsvg-convert -a -w $(WIDTH) -f svg $(SOURCE).svg -o $(SOURCE)2.svg
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inkscape $(SOURCE)2.svg --export-plain-svg=$(SOURCE).svg
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rm $(SOURCE)2.svg
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def getL(A):
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n = len(A)
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L = [[0 for i in range(n)] for j in range(n)]
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print(L)
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print("")
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for k in range(n):
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L[k][k] = (A[k][k] - sum([L[k][i]**2 for i in range(k)]))**0.5
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for i in range(k+1, n):
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L[i][k] = (A[i][k]
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- sum([L[i][j]*L[k][j] for j in range(k)])) \
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/ L[k][k]
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print("L_%i%i = A%i%i - sum(L_...)/L_%i%i) = %i" % (i, k, i, k, k, k, L[i][k]))
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return L
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A = [[1,2,3],[2,8,14],[3,14,34]]
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print getL(A)
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