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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
237 lines
7.6 KiB
TeX
237 lines
7.6 KiB
TeX
\section{Results}
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\subsection{Jacobi method result}
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For system of equations we got in this task we got following results:
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\\
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Without the change in demanded tolerance:
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\[ x = \left( \begin{array}{cc}
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-0.076776098668341 \\
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2.105784262642568 \\
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0.395344797635474 \\
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0.397776619764909
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\end{array} \right)
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\]
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Error:
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\[ r = \| \mathbf{A}\mathbf{x} - \mathbf{b}\| = 1.154375287358407e-10 \]
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We managed to do this in \textbf{38} iterations of our loop, and the demanded tolerance did not change. (This required small change in code where I ommited the part of code responsible for changing demandedTolerance if $ \| \mathbf{A}x-b \| > \delta_2) $ )
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With the change in demanded tolerance:
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\[ x = \left( \begin{array}{cc}
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-0.076776098668341 \\
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2.105784262642568 \\
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0.395344797635474 \\
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0.397776619764909
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\end{array} \right)
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\]
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Error:
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\[ r = \| \mathbf{A}\mathbf{x} - \mathbf{b}\| = 5.770361548895147e-11 \]
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We got this result in \textbf{37} iterations and demanded tolerance was equal to $2*10^{-10}$
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Compared to matlab function
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\[ x_{matlab} = \left( \begin{array}{cc}
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-0.076776098662498 \\
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2.105784262636790 \\
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0.395344797637659 \\
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0.397776619767240 \\
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\end{array} \right)
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\]
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Matlab error:
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\[ r = \| \mathbf{A}\mathbf{x} - \mathbf{b}\| = 4.070144838902081e-15 \]
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\newpage
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For data from task 2a we got: \\
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Without change in demanded tolerance:
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\[ x_a = \left( \begin{array}{cc}
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-0.930024655108186 \\
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-1.223407298660663 \\
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-1.273530574212508 \\
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-1.230517757317628 \\
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-1.151356031082747 \\
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-1.056883669273682 \\
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-0.952628310081466 \\
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-0.834334594312996 \\
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-0.683708806198363 \\
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-0.450125157620744 \\
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\end{array} \right)
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\]
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Error:
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\[ r = \| \mathbf{A}\mathbf{x} - \mathbf{b}\| = 6.955194519943778e-11 \]
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We managed to do this in \textbf{59} iterations of our loop, and the demanded tolerance did not change.
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With change in demanded tolerance:
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\[ x_a = \left( \begin{array}{cc}
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-0.930024655104470 \\
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-1.223407298653515 \\
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-1.273530574202540 \\
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-1.230517757305602 \\
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-1.151356031069692 \\
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-1.056883669260597 \\
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-0.952628310069469 \\
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-0.834334594303006 \\
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-0.683708806191233 \\
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-0.450125157617020 \\
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\end{array} \right)
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\]
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Error:
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\[ r = \| \mathbf{A}\mathbf{x} - \mathbf{b}\| = 1.699812218689508e-10 \]
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We managed to do this in \textbf{57} iterations of our loop, and the demanded tolerance changed to $4*10^{-10}$
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Compared to matlab function
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\[ x_{matlab} = \left( \begin{array}{cc}
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-0.930024655110760 \\
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-1.223407298665612 \\
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-1.273530574219411 \\
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-1.230517757325956 \\
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-1.151356031091789 \\
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-1.056883669282743 \\
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-0.952628310089775 \\
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-0.834334594319914 \\
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-0.683708806203301 \\
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-0.450125157623323 \\
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\end{array} \right)
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\]
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Matlab error:
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\[ r = \| \mathbf{A}\mathbf{x} - \mathbf{b}\| = 3.662053438817790e-15 \]
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For Matrix and Vector from task 2b) error of
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\[ \| x^{(i+1)} - x^{(i)} \| \]
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grew to infinity, therefore we could never achieve demanded tolerance, therefore the program executed infinite loop.
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\subsubsection{Minimizing the demanded error}
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I tried to minimize the demanded error using this steps:
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\begin{enumerate}
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\item I copied error from matlab function and pasted it into demanded tolerance.
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\item If I did not get infinite loop I copied the newly acquired error and pasted it into demanded tolerance.
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\item If I got inifinite loop I used the previous error as "minimal" demanded error.
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\end{enumerate}
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\newpage
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\paragraph{For original system of equations:}
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We managed to get results with error as low as $1.776356839400250e-15$ with demanded tolerance = $3.202372833989376e-15$ for lower values program went into infinite loop.
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Results for demanded tolerance = $3.202372833989376e-15$
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For given matrix:
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\[ x = \left( \begin{array}{cc}
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-0.076776098662498 \\
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2.105784262636790 \\
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0.395344797637659 \\
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0.397776619767240
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\end{array} \right)
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\]
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Error:
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\[ r = \| \mathbf{A}\mathbf{x} - \mathbf{b}\| = 3.108624468950438e-15 \]
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We got this result in \textbf{53} iterations and demanded tolerance did not change.
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\newpage
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\paragraph{For task 2a) system of equations:}
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We managed to get results with error as low as
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\[ 3.108624468950438e-15 \] with demanded tolerance:
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\[ 3.202372833989376e-15 \]
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for lower values program went into infinite loop.
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For demanded tolerance = $3.202372833989376e-15$:
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Results for 2a) system of equation
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\[ x_a = \left( \begin{array}{cc}
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-0.930024655110760 \\
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-1.223407298665613 \\
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-1.273530574219411 \\
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-1.230517757325955 \\
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-1.151356031091788 \\
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-1.056883669282743 \\
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-0.952628310089775 \\
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-0.834334594319914 \\
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-0.683708806203301 \\
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-0.450125157623323
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\end{array} \right)
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\]
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Error:
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\[ r = \| \mathbf{A}\mathbf{x} - \mathbf{b}\| = 3.108624468950438e-15 \]
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We managed to do this in \textbf{84} iterations of our loop, and the demanded tolerance did not change.
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We managed to achieve slightly better (as in, the error was smaller) results than Matlab custom function.
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\newpage
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\subsection{Gauss-Seidel method result}
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For system of equations we got in this task we got following results:
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\\
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\[ x = \left( \begin{array}{cc}
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-0.076776098752996 \\
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2.105784262542701 \\
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0.395344797589652 \\
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0.397776619735316
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\end{array} \right)
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\]
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Error:
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\[ r = \| \mathbf{A}\mathbf{x} - \mathbf{b}\| = 6.999102842719934e-10 \]
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We managed to do this in \textbf{19} iterations of our loop, and the demanded tolerance did not change.
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Error:
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\[ r = \| \mathbf{A}\mathbf{x} - \mathbf{b}\| = 6.999102842719934e-10 \]
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We got this result in \textbf{19} iterations and demanded tolerance was equal to $2*10^{-10}$
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For data from task 2a we got: \\
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\[ x_a = \left( \begin{array}{cc}
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-0.930024655049330 \\
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-1.223407298590161 \\
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-1.273530574151901 \\
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-1.230517757273947 \\
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-1.151356031055568 \\
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-1.056883669259564 \\
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-0.952628310076145 \\
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-0.834334594312669 \\
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-0.683708806199986 \\
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-0.450125157622217 \\
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\end{array} \right)
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\]
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Error:
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\[ r = \| \mathbf{A}\mathbf{x} - \mathbf{b}\| = 5.311669113699570e-10 \]
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We managed to do this in \textbf{28} iterations of our loop, and the demanded tolerance did not change.
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For Matrix and Vector from task 2b) error of
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\[ \| x^{(i+1)} - x^{(i)} \| \]
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grew to infinity, therefore we could never achieve demanded tolerance, therefore the program executed infinite loop.
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\subsubsection{Minimizing the demanded error}
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I tried to minimize the demanded error using procedure from before
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\paragraph{For original system of equations:}
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We managed to get results with error as low as $1.776356839400250e-15$ with demanded tolerance = $ 1.986027322597818e-15 $ for lower values program went into infinite loop.
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Results for demanded tolerance = $1.986027322597818e-15$
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For given matrix:
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\[ x = \left( \begin{array}{cc}
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-0.076776098662498 \\
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2.105784262636790 \\
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0.395344797637659 \\
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0.397776619767240
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\end{array} \right)
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\]
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Error:
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\[ r = \| \mathbf{A}\mathbf{x} - \mathbf{b}\| = 1.776356839400250e-15 \]
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We got this result in \textbf{30} iterations and demanded tolerance did not change.
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\newpage
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\paragraph{For task 2a) system of equations:}
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We managed to get results with error as low as
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\[ 1.538370149106851e-15 \] with demanded tolerance:
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\[ 1.538370149106851e-15 \]
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for lower values program went into infinite loop.
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For demanded tolerance = $1.538370149106851e-15$:
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Results for 2a) system of equation
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\[ x_a = \left( \begin{array}{cc}
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-0.930024655110760 \\
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-1.223407298665613 \\
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-1.273530574219411 \\
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-1.230517757325955 \\
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-1.151356031091788 \\
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-1.056883669282743 \\
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-0.952628310089775 \\
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-0.834334594319914 \\
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-0.683708806203301 \\
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-0.450125157623323 \\
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\end{array} \right)
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\]
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Error:
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\[ r = \| \mathbf{A}\mathbf{x} - \mathbf{b}\| = 1.538370149106851e-15 \]
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We managed to do this in \textbf{42} iterations of our loop, and the demanded tolerance did not change.
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We managed to achieve slightly better (as in, the error was smaller) results than Matlab custom function.
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\newpage
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