Add first slide of 2025-01-07 presentation

Makefile

@@ -3,5 +3,8 @@ all:
 
 	latexmk src/2024-12-03/presentation.tex
 	mv build/presentation.pdf build/presentation_2024-12-03.pdf
+
+	latexmk src/2025-01-07/presentation.tex
+	mv build/presentation.pdf build/presentation_2025-01-07.pdf
 clean:
 	rm -rf build

src/2025-01-07/presentation.tex

@@ -0,0 +1,248 @@
+\documentclass[10pt, aspectratio=169, usenames, dvipsnames]{beamer}
+                   
+\usepackage{tikz}
+\usepackage{tikz-3dplot}
+\usetikzlibrary{spy, external, intersections}
+%\tikzexternalize[prefix=build/]
+
+\usepackage{pgfplots}
+\pgfplotsset{compat=newest}
+\usepgfplotslibrary{fillbetween}
+
+
+\usepackage{listings}
+\usepackage{subcaption}
+\usepackage{bbm}
+
+\usepackage{xcolor}
+\usepackage[outputdir=build/]{minted}
+\usemintedstyle{gruvbox-light}
+
+\definecolor{gruvbox-bg}{HTML}{ffffff}
+% \definecolor{gruvbox-bg}{HTML}{282828}
+
+
+%
+%
+% Custom commands
+%
+%
+
+
+\input{lib/latex-common/common.tex}
+\pgfplotsset{colorscheme/rocket}
+
+\newcommand{\res}{src/2025-01-07/res}
+
+
+%
+%
+% CEL Template
+%
+%
+
+
+\newcommand{\templates}{lib/cel-template}
+
+\input{\templates/packages.tex}
+\input{\templates/modifications.tex}
+\input{\templates/makros_own.tex}
+
+% % Change the way the overview is displayed
+% \AtBeginSection[]
+% {
+%     \begin{frame}[t]
+%         \frametitle{Overview}
+%     \tableofcontents[sectionstyle=show/shaded,
+%                      subsectionstyle=show/show/shaded,
+%                      subsubsectionstyle=hide]
+%     \end{frame}
+% }
+% \AtBeginSubsubsection[]{}
+% \AtBeginSubsection[]{}
+
+
+%
+%
+% Set up document
+%
+%
+
+
+\title{HiWi Notes: Minimization Code Constraint Polynomial using Homotopy
+    Continuation Methods}
+\subtitle{\small 07.01.2025}
+\author{\vspace{1.5mm} Andreas Tsouchlos}
+\date{ }
+
+\institute{Karlsruhe Institute of Technology (KIT),
+    \\ Communications Engineering Lab (CEL) }
+
+\tikzstyle{every node}=[font=\small]
+\captionsetup[sub]{font=small}
+
+
+%
+%
+% Document body
+%
+%
+
+
+\begin{document}
+
+
+\begin{frame}[plain]
+	\maketitle
+\end{frame}
+
+\newcommand{\largecitereference}[1]{\textcolor{kit-green100}{ \large \textbf{{[#1]}} }}
+
+\begin{frame}
+
+    \frametitle{Basic Idea of Homotopy Continuation \largecitereference{CL15}}
+
+    \begin{minipage}[c]{0.65\textwidth}
+        \begin{itemize}
+            \item Goal: Solve system of equations $F(\bm{x}) = \bm{0}, \hspace{2mm} F:\mathbb{R}^n \rightarrow \mathbb{R}^n$
+            \item Problem: Depending on $F$, solving this directly may be difficult
+            \item Solution: Define \emph{homotopy function} $H(\bm{x}, t)$ with
+                \begin{gather*}
+                    H(\bm{x}, 0) = G(\bm{x}), \hspace{5mm} H(\bm{x}, 1) = F(\bm{x})
+                ,\end{gather*}
+                i.e., a deformation between two systems $G(\bm{x})$ and $F(\bm{x})$
+                (where the zeros of $G$ can be easily obtained); E.g.,
+                \begin{gather*}
+                    H(\bm{x}, t) = (t-1)G(\bm{x}) + tF(\bm{x})
+                .\end{gather*}
+                Then, compute $(\bm{x}_0, 0)$ such that $G(\bm{x}_0) = \bm{0}$ and trace path to $(\bm{x}_1, 1)$ with $F(\bm{x}_1) = \bm{0}$
+        \end{itemize}
+
+        \vspace{5mm}
+
+        \addreferences
+            {CL15}{Tianran Chen, Tien-Yien Li: \emph{Homotopy continuation method
+                for solving systems of nonlinear and polynomial equations}. 2015}
+        \stopreferences
+    \end{minipage}%
+    \hfill
+    \begin{minipage}[c]{0.3\textwidth}
+        \begin{figure}
+            \centering
+
+            \newcommand{\figlength}{0.8\textwidth}
+
+            \vspace*{-2mm}
+
+            \begin{tikzpicture}
+                \begin{axis}[
+                    xmin=-1,xmax=1,
+                    ymin=-1,ymax=1,
+                    width=\figlength,
+                    height=\figlength,
+                    ticks=none,
+                    view={0}{90},
+                    title={$t=0$},
+                    title style={yshift=-1mm},
+                    % xlabel={$x_1$},
+                    % ylabel={$x_2$},
+                    ]
+                    \addplot3[point meta=\thisrow{Hmag},
+                              point meta min=0,
+                              point meta max=2.5,
+                              quiver={u=\thisrow{H1},
+                                      v=\thisrow{H2},
+                                      scale arrows=.25,
+                                      every arrow/.append style={%
+                                        line width=.5
+                                            +\pgfplotspointmetatransformed/1000,
+                                        -{Latex[length=0pt 5,width=0pt 3]}
+                                      },
+                                  },
+                                quiver/colored = {mapped color},
+                                -stealth,
+                              ]
+                                table[col sep=comma, discard if not={t}{0.0}] {\res/H.csv};
+
+                            \addplot[mark=*] coordinates {(0,0)} node[above] {$\bm{x}_0$};
+
+                \end{axis}
+            \end{tikzpicture}
+            \begin{tikzpicture}
+                \begin{axis}[
+                    xmin=-1,xmax=1,
+                    ymin=-1,ymax=1,
+                    width=\figlength,
+                    height=\figlength,
+                    ticks=none,
+                    view={0}{90},
+                    title={$t=0.5$},
+                    title style={yshift=-1mm},
+                    % xlabel={$x_1$},
+                    % ylabel={$x_2$},
+                    ]
+                    \addplot3[point meta=\thisrow{Hmag},
+                              point meta min=0,
+                              point meta max=2.5,
+                              quiver={u=\thisrow{H1},
+                                      v=\thisrow{H2},
+                                      scale arrows=.25,
+                                      every arrow/.append style={%
+                                        line width=.5
+                                            +\pgfplotspointmetatransformed/1000,
+                                        -{Latex[length=0pt 5,width=0pt 3]}
+                                      },
+                                  },
+                                quiver/colored = {mapped color},
+                                -stealth,
+                              ]
+                                table[col sep=comma, discard if not={t}{0.5}] {\res/H.csv};
+
+                    \draw[line width=1pt] (0,0) -- (0.25,-0.25);
+                    \addplot[mark=*] coordinates {(0.25, -0.25)};
+                \end{axis}
+            \end{tikzpicture}
+
+            \vspace{2mm}
+
+            \begin{tikzpicture}
+                \begin{axis}[
+                    xmin=-1,xmax=1,
+                    ymin=-1,ymax=1,
+                    width=\figlength,
+                    height=\figlength,
+                    ticks=none,
+                    view={0}{90},
+                    title={$t=1$},
+                    title style={yshift=-1mm},
+                    % xlabel={$x_1$},
+                    % ylabel={$x_2$},
+                    ]
+                    \addplot3[point meta=\thisrow{Hmag},
+                              point meta min=0,
+                              point meta max=2.5,
+                              quiver={u=\thisrow{H1},
+                                      v=\thisrow{H2},
+                                      scale arrows=.25,
+                                      every arrow/.append style={%
+                                        line width=.5
+                                            +\pgfplotspointmetatransformed/1000,
+                                        -{Latex[length=0pt 5,width=0pt 3]}
+                                      },
+                                  },
+                                quiver/colored = {mapped color},
+                                -stealth,
+                              ]
+                                table[col sep=comma, discard if not={t}{1.0}] {\res/H.csv};
+
+                    \draw[line width=1pt] (0,0) -- (0.5,-0.5);
+                    \addplot[mark=*] coordinates {(0.5,-0.5)} node[below right] {$\bm{x}_1$};
+                \end{axis}
+            \end{tikzpicture}
+
+            \caption{Visualization of ``snapshots'' of $H$ (e.g., $F, G$) as vector fields}
+        \end{figure}
+    \end{minipage}
+\end{frame}
+
+\end{document}