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Krzysztof kuhy Rudnicki
ffa5dad02a
The 250-line cap applies to prose too, and the reports were the worst
offenders -- ENUME's projectA.tex alone was 1,876 lines. Each is now a
preamble plus one \input{} per section, which is how a long LaTeX document is
normally organised; not one byte of prose was rewritten.
"The PDF is unchanged" is checked by a script rather than by eye, because
hashing the PDF cannot work: pdflatex stamps a /CreationDate and an /ID into
every build, so two runs of the SAME source already differ. tex_fingerprint.sh
compares what a reader sees instead -- page count plus a hash of the extracted
text -- and it is stable across rebuilds of untouched sources, which is the
property that makes it usable as a gate.
It earned its keep immediately. Both ECOTE reports quote an example LaTeX
document inside an lstlisting block, so \end{document} appears in the middle
of the file; splitting on the FIRST one stranded everything after it. Same
page count, different text, caught automatically. EOPSY lab3 exposed a second
bug: a \section{} title that runs onto the next line.
Result: 19 .tex over the cap -> 1. The survivor,
ELAC/.../03-building-nfa-...tex, is 418 lines of consecutive tikz figures
with no subsection to split on and needs a hand-placed boundary.
Verified: 29 splits across two passes (section, then subsection for the
pieces still over), every one reporting `unchanged` from
scripts/tex_fingerprint.sh --check.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_0172dj34FDpao6wsix8ZuCzE
175 lines
3.6 KiB
TeX
175 lines
3.6 KiB
TeX
\section{Results}
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\begin{center}
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\includegraphics[scale=0.25]{task3overall.eps}
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\end{center}
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\begin{center}
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\includegraphics[scale=0.25]{task3left.eps}
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\end{center}
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\begin{center}
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\includegraphics[scale=0.25]{task3right.eps}
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\end{center}
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\begin{center}
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\includegraphics[scale=0.25]{task3complexoverall.eps}
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\end{center}
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\begin{center}
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\includegraphics[scale=0.25]{task3complexleft.eps}
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\end{center}
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\begin{center}
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\includegraphics[scale=0.25]{task3complexright.eps}
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\end{center}
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\begin{center}
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\includegraphics[scale=0.25]{task3complexup.eps}
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\end{center}
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\begin{center}
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\begin{tabular}{| c c c |}
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\hline
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Iteration & root & f(root) \\
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\hline
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1 & -1.25 & -20.32 \\
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\hline
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2 & -0.67905 & -0.017268 \\
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\hline
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3 & -0.67787 & -3.1489e-07 \\
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\hline
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4 & -0.67787 & 0 \\
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\hline
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\hline
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\hline
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\end{tabular}
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\end{center}
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\begin{center}
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\begin{tabular}{| c c c |}
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\hline
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Iteration & root & f(root) \\
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\hline
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1 & 6.25 & 43.43 \\
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\hline
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2 & 6.3376 & -1.8647 \\
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\hline
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3 & 6.3341 & 0.0029631 \\
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\hline
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4 & 6.3341 & 7.9942e-09\\
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\hline
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5 & 6.3341 & -7.1942e-14\\
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\hline
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\end{tabular}
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\end{center}
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\begin{center}
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\begin{tabular}{| c c c |}
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\hline
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Iteration & root & f(root) \\
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\hline
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1 & 0+0i & 3 \\
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\hline
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2 & -0.042857+0.71586i & 4.1826 \\
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\hline
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3 & 0.172+0.56266i & 0.040584 \\
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\hline
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4 & 0.17188+0.56551i & 2.8484e-06 \\
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\hline
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5 & 0.17188+0.56551i & 2.2952e-14 \\
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\hline
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6 & 0.17188+0.56551i & 0 \\
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\hline
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\end{tabular}
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\end{center}
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\subsection{Comparison of results between Laguerre's method and MM2 method}
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\subsubsection{Tables for MM2}
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\begin{center}
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\begin{tabular}{| c c c |}
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\hline
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Iteration & root & f(root) \\
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\hline
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1 & -1.25+0i & -20.32+0i \\
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\hline
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2 & -0.72604-0.25326i & 1.0515-4.0744i \\
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\hline
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3 & -0.68613-0.01483i & -0.11667-0.22303i \\
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\hline
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4 & -0.67788+2.5407e-06i & -0.00010163+3.7123e-05i \\
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\hline
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5 & -0.67787-8.0819e-13i & 1.4105e-11-1.1809e-11i \\
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\hline
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\hline
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\end{tabular}
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\end{center}
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\begin{center}
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\begin{tabular}{| c c c |}
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\hline
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Iteration & root & f(root) \\
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\hline
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1 & 6.25 & 43.43 \\
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\hline
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2 & 6.3376 & -1.8647 \\
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\hline
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3 & 6.3341 & 0.0029695 \\
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\hline
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4 & 6.3341 & 1.6294e-08 \\
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\hline
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5 & 6.3341 & -4.6896e-13 \\
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\hline
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\hline
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\end{tabular}
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\end{center}
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\begin{center}
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\begin{tabular}{| c c c |}
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\hline
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Iteration & root & f(root) \\
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\hline
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1 & 0+0i & 3 \\
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\hline
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2 & -0.125+0.85696i & 8.0341 \\
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\hline
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3 & 0.16892+0.62593i & 0.94053 \\
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\hline
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4 & 0.17203+0.56536i & 0.0031354 \\
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\hline
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5 & 0.17188+0.56551i & 3.8615e-09 \\
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\hline
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6 & 0.17188+0.56551i & 0 \\
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\hline
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\hline
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\end{tabular}
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\end{center}
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As expected Laguerre's method reigns supreme, it is:
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\begin{enumerate}
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\item Faster
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With 5 iterations on average compared to around 5.3 for MM2
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\item More accurate
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For real root -0.67787 matlab calculated the value of this function for Laguerre's method as equal to exactly 0 as opposed to around $10^{-11}$ error for MM2.
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\item With no errors
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Laguerre's method did not mistakenly added imaginary part to real root -0.67787 as MM2 did.
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\end{enumerate}
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Laguerre's method is faster and more accurate than MM2 which means that we can compare it to faster version of MM1, this means that it is the best method we tested in this exercise.
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\chapter{Code appendix}
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