mp1: preparing for submission

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Claudio Maggioni 2020-09-29 13:25:31 +02:00
parent 18e275d120
commit a91194c78a
20 changed files with 20 additions and 10 deletions

1
.gitignore vendored
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@ -143,5 +143,6 @@ sympy-plots-for-*.tex/
.DS_Store .DS_Store
!*.pdf !*.pdf
*.zip
*~ *~

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@ -3,6 +3,7 @@
\usepackage{graphics} \usepackage{graphics}
\usepackage{graphicx} \usepackage{graphicx}
\usepackage{hyperref} \usepackage{hyperref}
\usepackage{cleveref}
\pagestyle{plain} \pagestyle{plain}
\voffset -5mm \voffset -5mm

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@ -10,8 +10,8 @@
\setassignment \setassignment
\setduedate{Thursday, 8 October 2020, 12:00 AM} \setduedate{Thursday, 8 October 2020, 12:00 AM}
\serieheader{Numerical Computing}{2020}{Student: Claudio Maggioni}{Discussed with: --}{Solution for Project 1}{} \serieheader{Numerical Computing}{2020}{Student: Claudio Maggioni}{Discussed
ewline with: --}{Solution for Project 1}{}\newline
\assignmentpolicy \assignmentpolicy
The purpose of this assignment\footnote{This document is originally based on a SIAM book chapter from \textsl{Numerical Computing with Matlab} from Clever B. Moler.} is to learn the importance of numerical linear algebra algorithms to solve fundamental linear algebra problems that occur in search engines. The purpose of this assignment\footnote{This document is originally based on a SIAM book chapter from \textsl{Numerical Computing with Matlab} from Clever B. Moler.} is to learn the importance of numerical linear algebra algorithms to solve fundamental linear algebra problems that occur in search engines.
@ -68,7 +68,7 @@ factor $\gamma$ that will converge to a denormalized version of $x_1$, named
$\beta x_1$. We can then simplify the $a_1\lambda_1^{i}x_1$ terms in the $\beta x_1$. We can then simplify the $a_1\lambda_1^{i}x_1$ terms in the
sequences with $\beta_{i} x_1$ since $\beta_i$ can be set freely. sequences with $\beta_{i} x_1$ since $\beta_i$ can be set freely.
Now we consider that if $|\lambda_2| > |\lambda_i| \forall i \in 3..n$ (since we Now we consider that if $|\lambda_2| > |\lambda_i| \; \forall i \in 3 \dots n$ (since we
sorted the eigenvalues), then sorted the eigenvalues), then
$\left(\frac{\lambda_i}{\lambda_1}\right)^n$ for $i > 2$ will always converge faster to $\left(\frac{\lambda_i}{\lambda_1}\right)^n$ for $i > 2$ will always converge faster to
0 than $\left(\frac{\lambda_2}{\lambda_1}\right)^n$ thus all terms other than 0 than $\left(\frac{\lambda_2}{\lambda_1}\right)^n$ thus all terms other than
@ -116,7 +116,7 @@ is the corresponding eigenvalue, while if $x$ is an eigenvector approximation, f
\subsection{Other webgraphs [10 points]} \subsection{Other webgraphs [10 points]}
The provided PageRank MATLAB implementation was run 3 times on the starting websites \texttt{http://atelier.inf.usi.ch/~maggicl}, \texttt{https://www.iisbadoni.edu.it}, and \texttt{https://www.usi.ch}, with results listed respectively in Figure \ref{fig:run1}, Figure \ref{fig:run2} and Figure \ref{fig:run3}. The provided PageRank MATLAB implementation was run 3 times on the starting websites \texttt{http://atelier.inf.usi.ch/~maggicl}, \texttt{https://www.iisbadoni.edu.it}, and \texttt{https://www.usi.ch}, with results listed respectively in \Cref{fig:run1}, \Cref{fig:run2} and \Cref{fig:run3}.
One patten that emerges on the first and third execution is the presence of 1s in the main diagonal. This indicates that several pages found have a link to themselves. One patten that emerges on the first and third execution is the presence of 1s in the main diagonal. This indicates that several pages found have a link to themselves.
@ -153,8 +153,8 @@ Finally, we can always observe a line starting from the top-left of G and ending
\end{verbatim} \end{verbatim}
\caption{Top 10 webpages with highest PageRank} \caption{Top 10 webpages with highest PageRank}
\end{subfigure} \end{subfigure}
\label{fig:run1}
\caption{Results of first PageRank calculation (for starting website \texttt{http://atelier.inf.usi.ch/~maggicl/})} \caption{Results of first PageRank calculation (for starting website \texttt{http://atelier.inf.usi.ch/~maggicl/})}
\label{fig:run1}
\end{figure} \end{figure}
\begin{figure}[h] \begin{figure}[h]
@ -187,8 +187,8 @@ Finally, we can always observe a line starting from the top-left of G and ending
\end{verbatim} \end{verbatim}
\caption{Top 10 webpages with highest PageRank} \caption{Top 10 webpages with highest PageRank}
\end{subfigure} \end{subfigure}
\label{fig:run2}
\caption{Results of second PageRank calculation (for starting website \texttt{https://www.iisbadoni.edu.it/})} \caption{Results of second PageRank calculation (for starting website \texttt{https://www.iisbadoni.edu.it/})}
\label{fig:run2}
\end{figure} \end{figure}
\begin{figure}[h] \begin{figure}[h]
@ -219,8 +219,8 @@ Finally, we can always observe a line starting from the top-left of G and ending
\end{verbatim} \end{verbatim}
\caption{Top 10 webpages with highest PageRank} \caption{Top 10 webpages with highest PageRank}
\end{subfigure} \end{subfigure}
\label{fig:run3}
\caption{Results of third PageRank calculation (for starting website \texttt{https://www.usi.ch/})} \caption{Results of third PageRank calculation (for starting website \texttt{https://www.usi.ch/})}
\label{fig:run3}
\end{figure} \end{figure}
\subsection{Connectivity matrix and subcliques [10 points]} \subsection{Connectivity matrix and subcliques [10 points]}

8
mp1/submit.sh Executable file
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@ -0,0 +1,8 @@
#!/bin/sh
PID="1"
dname="Project.$PID.Maggioni.Claudio"
zname="project.$PID.Maggioni.Claudio"
rm -v $zname.zip
zip $zname.zip $zname.{pdf,tex} $dname/run{1..3}.mat $dname/pagerank{1..2}.m