mp1: preparing for submission
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20 changed files with 20 additions and 10 deletions
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@ -143,5 +143,6 @@ sympy-plots-for-*.tex/
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.DS_Store
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.DS_Store
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!*.pdf
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!*.pdf
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*.zip
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*~
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*~
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\usepackage{graphics}
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\usepackage{graphics}
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\usepackage{graphicx}
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\usepackage{graphicx}
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\usepackage{hyperref}
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\usepackage{hyperref}
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\usepackage{cleveref}
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\pagestyle{plain}
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\pagestyle{plain}
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\voffset -5mm
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\voffset -5mm
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\setassignment
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\setassignment
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\setduedate{Thursday, 8 October 2020, 12:00 AM}
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\setduedate{Thursday, 8 October 2020, 12:00 AM}
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\serieheader{Numerical Computing}{2020}{Student: Claudio Maggioni}{Discussed with: --}{Solution for Project 1}{}
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\serieheader{Numerical Computing}{2020}{Student: Claudio Maggioni}{Discussed
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ewline
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with: --}{Solution for Project 1}{}\newline
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\assignmentpolicy
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\assignmentpolicy
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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.
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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.
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@ -68,7 +68,7 @@ factor $\gamma$ that will converge to a denormalized version of $x_1$, named
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$\beta x_1$. We can then simplify the $a_1\lambda_1^{i}x_1$ terms in the
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$\beta x_1$. We can then simplify the $a_1\lambda_1^{i}x_1$ terms in the
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sequences with $\beta_{i} x_1$ since $\beta_i$ can be set freely.
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sequences with $\beta_{i} x_1$ since $\beta_i$ can be set freely.
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Now we consider that if $|\lambda_2| > |\lambda_i| \forall i \in 3..n$ (since we
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Now we consider that if $|\lambda_2| > |\lambda_i| \; \forall i \in 3 \dots n$ (since we
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sorted the eigenvalues), then
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sorted the eigenvalues), then
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$\left(\frac{\lambda_i}{\lambda_1}\right)^n$ for $i > 2$ will always converge faster to
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$\left(\frac{\lambda_i}{\lambda_1}\right)^n$ for $i > 2$ will always converge faster to
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0 than $\left(\frac{\lambda_2}{\lambda_1}\right)^n$ thus all terms other than
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0 than $\left(\frac{\lambda_2}{\lambda_1}\right)^n$ thus all terms other than
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@ -116,7 +116,7 @@ is the corresponding eigenvalue, while if $x$ is an eigenvector approximation, f
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\subsection{Other webgraphs [10 points]}
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\subsection{Other webgraphs [10 points]}
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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}.
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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}.
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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.
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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.
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@ -153,8 +153,8 @@ Finally, we can always observe a line starting from the top-left of G and ending
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\end{verbatim}
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\end{verbatim}
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\caption{Top 10 webpages with highest PageRank}
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\caption{Top 10 webpages with highest PageRank}
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\end{subfigure}
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\end{subfigure}
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\label{fig:run1}
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\caption{Results of first PageRank calculation (for starting website \texttt{http://atelier.inf.usi.ch/~maggicl/})}
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\caption{Results of first PageRank calculation (for starting website \texttt{http://atelier.inf.usi.ch/~maggicl/})}
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\label{fig:run1}
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\end{figure}
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\end{figure}
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\begin{figure}[h]
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\begin{figure}[h]
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@ -187,8 +187,8 @@ Finally, we can always observe a line starting from the top-left of G and ending
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\end{verbatim}
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\end{verbatim}
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\caption{Top 10 webpages with highest PageRank}
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\caption{Top 10 webpages with highest PageRank}
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\end{subfigure}
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\end{subfigure}
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\label{fig:run2}
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\caption{Results of second PageRank calculation (for starting website \texttt{https://www.iisbadoni.edu.it/})}
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\caption{Results of second PageRank calculation (for starting website \texttt{https://www.iisbadoni.edu.it/})}
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\label{fig:run2}
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\end{figure}
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\end{figure}
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\begin{figure}[h]
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\begin{figure}[h]
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@ -219,8 +219,8 @@ Finally, we can always observe a line starting from the top-left of G and ending
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\end{verbatim}
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\end{verbatim}
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\caption{Top 10 webpages with highest PageRank}
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\caption{Top 10 webpages with highest PageRank}
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\end{subfigure}
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\end{subfigure}
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\label{fig:run3}
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\caption{Results of third PageRank calculation (for starting website \texttt{https://www.usi.ch/})}
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\caption{Results of third PageRank calculation (for starting website \texttt{https://www.usi.ch/})}
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\label{fig:run3}
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\end{figure}
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\end{figure}
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\subsection{Connectivity matrix and subcliques [10 points]}
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\subsection{Connectivity matrix and subcliques [10 points]}
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mp1/submit.sh
Executable file
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mp1/submit.sh
Executable file
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#!/bin/sh
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PID="1"
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dname="Project.$PID.Maggioni.Claudio"
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zname="project.$PID.Maggioni.Claudio"
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rm -v $zname.zip
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zip $zname.zip $zname.{pdf,tex} $dname/run{1..3}.mat $dname/pagerank{1..2}.m
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