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Andreas Tsouchlos 2025-01-05 20:46:04 +01:00
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src/2025-01-07/presentation.tex
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@ -66,8 +66,8 @@
% %
\title{HiWi Notes: Minimization of Code Constraint Polynomial using Homotopy \title{HiWi Notes: Minimization of the Code Constraint Polynomial using
Continuation Methods} Homotopy Continuation Methods}
\subtitle{\small 07.01.2025} \subtitle{\small 07.01.2025}
\author{\vspace{1.5mm} Andreas Tsouchlos} \author{\vspace{1.5mm} Andreas Tsouchlos}
\date{ } \date{ }
@ -93,10 +93,10 @@
\maketitle \maketitle
\end{frame} \end{frame}
\newcommand{\largecitereference}[1]{\textcolor{kit-green100}{ \large \textbf{{[#1]}} }} \newcommand{\largecitereference}[1]
{\textcolor{kit-green100}{ \large \textbf{{[#1]}} }}
\begin{frame} \begin{frame}
\frametitle{Basic Idea of Homotopy Continuation \largecitereference{CL15}} \frametitle{Basic Idea of Homotopy Continuation \largecitereference{CL15}}
\begin{minipage}[c]{0.65\textwidth} \begin{minipage}[c]{0.65\textwidth}
@ -118,8 +118,10 @@
\vspace{5mm} \vspace{5mm}
\addreferences \addreferences
{CL15}{Chen, Tianran, and Tien-Yien Li.: \emph{Homotopy continuation method {CL15}{Chen, Tianran, and Tien-Yien Li.: \emph{Homotopy
for solving systems of nonlinear and polynomial equations}. Communications in Information and Systems 15.2 (2015): 119-307.} continuation method for solving systems of nonlinear and
polynomial equations}. Communications in Information and
Systems 15.2 (2015): 119-307.}
\stopreferences \stopreferences
\end{minipage}% \end{minipage}%
\hfill \hfill
@ -159,9 +161,11 @@
quiver/colored = {mapped color}, quiver/colored = {mapped color},
-stealth, -stealth,
] ]
table[col sep=comma, discard if not={t}{0.0}] {\res/H.csv}; table[col sep=comma, discard if not={t}{0.0}]
{\res/H.csv};
\addplot[mark=*] coordinates {(0,0)} node[above] {$\bm{x}_0$}; \addplot[mark=*] coordinates {(0,0)} node[above]
{$\bm{x}_0$};
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
@ -193,7 +197,8 @@
quiver/colored = {mapped color}, quiver/colored = {mapped color},
-stealth, -stealth,
] ]
table[col sep=comma, discard if not={t}{0.5}] {\res/H.csv}; table[col sep=comma, discard if not={t}{0.5}]
{\res/H.csv};
\draw[line width=1pt] (0,0) -- (0.25,-0.25); \draw[line width=1pt] (0,0) -- (0.25,-0.25);
\addplot[mark=*] coordinates {(0.25, -0.25)}; \addplot[mark=*] coordinates {(0.25, -0.25)};
@ -230,14 +235,17 @@
quiver/colored = {mapped color}, quiver/colored = {mapped color},
-stealth, -stealth,
] ]
table[col sep=comma, discard if not={t}{1.0}] {\res/H.csv}; table[col sep=comma, discard if not={t}{1.0}]
{\res/H.csv};
\draw[line width=1pt] (0,0) -- (0.5,-0.5); \draw[line width=1pt] (0,0) -- (0.5,-0.5);
\addplot[mark=*] coordinates {(0.5,-0.5)} node[below right] {$\bm{x}_1$}; \addplot[mark=*] coordinates {(0.5,-0.5)} node[below right]
{$\bm{x}_1$};
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\caption{Visualization of ``snapshots'' of $H$ (e.g., $F, G$) as vector fields} \caption{Visualization of ``snapshots'' of $H$ (e.g., $F, G$) as
vector fields}
\end{figure} \end{figure}
\end{minipage} \end{minipage}
\end{frame} \end{frame}