mp1: added template

.gitignore

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+*.ijvm
+*.mic1
+
+# ---> TeX
+## Core latex/pdflatex auxiliary files:
+*.aux
+*.lof
+*.log
+*.lot
+*.fls
+*.out
+*.toc
+
+## Intermediate documents:
+*.dvi
+*-converted-to.*
+# these rules might exclude image files for figures etc.
+# *.ps
+# *.eps
+# *.pdf
+
+## Bibliography auxiliary files (bibtex/biblatex/biber):
+*.bbl
+*.bcf
+*.blg
+*-blx.aux
+*-blx.bib
+*.brf
+*.run.xml
+
+## Build tool auxiliary files:
+*.fdb_latexmk
+*.synctex
+*.synctex.gz
+*.synctex.gz(busy)
+*.pdfsync
+
+## Auxiliary and intermediate files from other packages:
+
+
+# algorithms
+*.alg
+*.loa
+
+# achemso
+acs-*.bib
+
+# amsthm
+*.thm
+
+# beamer
+*.nav
+*.snm
+*.vrb
+
+#(e)ledmac/(e)ledpar
+*.end
+*.[1-9]
+*.[1-9][0-9]
+*.[1-9][0-9][0-9]
+*.[1-9]R
+*.[1-9][0-9]R
+*.[1-9][0-9][0-9]R
+*.eledsec[1-9]
+*.eledsec[1-9]R
+*.eledsec[1-9][0-9]
+*.eledsec[1-9][0-9]R
+*.eledsec[1-9][0-9][0-9]
+*.eledsec[1-9][0-9][0-9]R
+
+# glossaries
+*.acn
+*.acr
+*.glg
+*.glo
+*.gls
+
+# gnuplottex
+*-gnuplottex-*
+
+# hyperref
+*.brf
+
+# knitr
+*-concordance.tex
+*.tikz
+*-tikzDictionary
+
+# listings
+*.lol
+
+# makeidx
+*.idx
+*.ilg
+*.ind
+*.ist
+
+# minitoc
+*.maf
+*.mtc
+*.mtc[0-9]
+*.mtc[1-9][0-9]
+
+# minted
+_minted*
+*.pyg
+
+# morewrites
+*.mw
+
+# mylatexformat
+*.fmt
+
+# nomencl
+*.nlo
+
+# sagetex
+*.sagetex.sage
+*.sagetex.py
+*.sagetex.scmd
+
+# sympy
+*.sout
+*.sympy
+sympy-plots-for-*.tex/
+
+# TikZ & PGF
+*.dpth
+*.md5
+*.auxlock
+
+# todonotes
+*.tdo
+
+# xindy
+*.xdy
+
+# WinEdt
+*.bak
+*.sav
+
+# Mac stupid tmp files
+.DS_Store
+
+!*.pdf
+
+*~

mp1/Makefile

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+filename=template
+
+pdf:
+	pdflatex ${filename}
+	pdflatex ${filename}
+	make clean
+
+read:
+	evince ${filename}.pdf &
+
+
+clean:
+	rm -f ${filename}.out ${filename}.log ${filename}.bbl ${filename}.blg ${filename}.au ${filename}.log  ${filename}.ps ${filename}.aux ${filename}.out ${filename}.dvi ${filename}.bbl ${filename}.blg ${filename}.toc  ${filename}.nav ${filename}.vrb ${filename}.snm

mp1/assignment.sty

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+\usepackage{ifthen}
+\usepackage[utf8]{inputenc}
+\usepackage{graphics}
+\usepackage{graphicx}
+\usepackage{hyperref}
+
+\pagestyle{plain}
+\voffset -5mm
+\oddsidemargin  0mm
+\evensidemargin -11mm
+\marginparwidth 2cm
+\marginparsep 0pt
+\topmargin 0mm
+\headheight 0pt
+\headsep 0pt
+\topskip 0pt        
+\textheight 255mm
+\textwidth 165mm
+
+\newcommand{\duedate} {}
+\newcommand{\setduedate}[1]{%
+\renewcommand\duedate {Due date:~ #1}}
+\newcommand\isassignment {false}
+\newcommand{\setassignment}{\renewcommand\isassignment {true}}
+\newcommand{\ifassignment}[1]{\ifthenelse{\boolean{\isassignment}}{#1}{}}
+\newcommand{\ifnotassignment}[1]{\ifthenelse{\boolean{\isassignment}}{}{#1}}
+
+\newcommand{\assignmentpolicy}{
+\begin{table}[h]
+\begin{center}
+\scalebox{0.8} {%
+\begin{tabular}{|p{0.02cm}p{16cm}|}
+\hline
+&\\
+\multicolumn{2}{|c|}{\Large\textbf{Numerical Computing 2020 ---  Submission Instructions}}\\
+\multicolumn{2}{|c|}{\large\textbf{(Please, notice that following instructions are mandatory: }}\\
+\multicolumn{2}{|c|}{\large\textbf{submissions that don't comply with, won't be considered)}}\\
+&\\
+\textbullet & Assignments must be submitted to \href{https://www.icorsi.ch/course/view.php?id=10018}{iCorsi} (i.e. in electronic format).\\
+\textbullet & Provide both executable package and sources (e.g. C/C++ files, Matlab). 
+If you are using libraries, please add them in the file. Sources must be organized in directories called:\\
+\multicolumn{2}{|c|}{\textit{Project\_number\_lastname\_firstname}}\\
+& and  the  file must be called:\\
+\multicolumn{2}{|c|}{\textit{project\_number\_lastname\_firstname.zip}}\\
+\multicolumn{2}{|c|}{\textit{project\_number\_lastname\_firstname.pdf}}\\
+\textbullet &  The TAs will grade your project by reviewing your project write-up, and looking at the implementation 
+                 you attempted, and benchmarking your code's performance.\\
+
+\textbullet & You are allowed to discuss all questions with anyone you like; however: (i) your submission must list anyone you discussed problems with and (ii) you must write up your submission independently.\\
+\hline
+\end{tabular}
+}
+\end{center}
+\end{table}
+}
+\newcommand{\punkte}[1]{\hspace{1ex}\emph{\mdseries\hfill(#1~\ifcase#1{Points}\or{Points}\else{Points}\fi)}}
+
+
+\newcommand\serieheader[6]{
+\thispagestyle{empty}%
+\begin{flushleft}
+\includegraphics[width=0.4\textwidth]{usi_inf}
+\end{flushleft}
+  \noindent%
+  {\large\ignorespaces{\textbf{#1}}\hspace{\fill}\ignorespaces{ \textbf{#2}}}\\ \\%
+  {\large\ignorespaces #3 \hspace{\fill}\ignorespaces #4}\\
+  \noindent%
+  \bigskip
+  \hrule\par\bigskip\noindent%
+  \bigskip {\ignorespaces {\Large{\textbf{#5}}}
+  \hspace{\fill}\ignorespaces \large \ifthenelse{\boolean{\isassignment}}{\duedate}{#6}}
+  \hrule\par\bigskip\noindent%  \linebreak
+ }
+
+\makeatletter
+\def\enumerateMod{\ifnum \@enumdepth >3 \@toodeep\else
+      \advance\@enumdepth \@ne
+      \edef\@enumctr{enum\romannumeral\the\@enumdepth}\list
+      {\csname label\@enumctr\endcsname}{\usecounter
+        {\@enumctr}%%%? the following differs from "enumerate"
+	\topsep0pt%
+	\partopsep0pt%
+	\itemsep0pt%
+	\def\makelabel##1{\hss\llap{##1}}}\fi}
+\let\endenumerateMod =\endlist
+\makeatother
+
+
+
+
+\usepackage{textcomp}
+
+
+
+

mp1/files_data/pagerank.m

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+function x = pagerank(U,G,p)
+% PAGERANK  Google's PageRank
+% pagerank(U,G,p) uses the URLs and adjacency matrix produced by SURFER,
+% together with a damping factory p, (default is .85), to compute and plot
+% a bar graph of page rank, and print the dominant URLs in page rank order.
+% x = pagerank(U,G,p) returns the page ranks instead of printing.
+% See also SURFER, SPY.
+
+if nargin < 3, p = .85; end
+
+% Eliminate any self-referential links
+%G = G - diag(diag(G));
+
+% c = out-degree, r = in-degree
+[~,n] = size(G);
+c = sum(G,1);
+r = sum(G,2);
+
+% Scale column sums to be 1 (or 0 where there are no out links).
+k = find(c~=0);
+D = sparse(k,k,1./c(k),n,n);
+
+e = ones(n,1);
+I = speye(n,n);
+
+% ---------------------------------- DEFAULT ------------------------------
+% Solve (I - p*G*D)*x = e
+disp('Using default implementation\n');
+x = (I - p*G*D)\e;
+
+% -------------------------------------------------------------------------
+
+% Normalize so that sum(x) == 1.
+x = x/sum(x);
+
+% Bar graph of page rank.
+shg
+bar(x)
+title('Page Rank')
+
+% Print URLs in page rank order.
+
+if nargout < 1
+   [~,q] = sort(-x);
+   disp('     page-rank  in  out  url')
+   k = 1;
+   maxN = length(U);
+   while  (k <= maxN) && (x(q(k)) >= .005)
+       disp(k)
+      j = q(k);
+      temp1  = r(j);
+      temp2  = c(j);
+      disp(fprintf(' %3.0f %8.4f %4.0f %4.0f  %s', j,x(j),full(temp1),full(temp2),U{j}))
+      k = k+1;
+   end
+end

mp1/files_data/surfer.m

@@ -0,0 +1,149 @@
+function [U,G] = surfer(root,n)
+% UPDATED VERSION
+
+% SURFER  Create the adjacency graph of a portion of the Web.
+%    [U,G] = surfer(root,n) starts at the URL root and follows
+%    Web links until it forms an adjacency graph with n nodes.
+%    U = a cell array of n strings, the URLs of the nodes.
+%    G = an n-by-n sparse matrix with G(i,j)=1 if node j is linked to node i.
+%
+%    Example:  [U,G] = surfer('https://inf.ethz.ch/',500);
+%    See also PAGERANK.
+%
+%    This function currently has two defects.  (1) The algorithm for
+%    finding links is naive.  We just look for the string 'http:'.
+%    (2) An attempt to read from a URL that is accessible, but very slow,
+%    might take an unacceptably long time to complete.  In some cases,
+%    it may be necessary to have the operating system terminate MATLAB.
+%    Key words from such URLs can be added to the skip list in surfer.m.
+
+% Initialize
+
+clf
+shg
+set(gcf,'doublebuffer','on')
+axis([0 n 0 n])
+axis square
+axis ij
+box on
+set(gca,'position',[.12 .20 .78 .78])
+uicontrol('style','frame','units','normal','position',[.01 .09 .98 .07]);
+uicontrol('style','frame','units','normal','position',[.01 .01 .98 .07]);
+t1 = uicontrol('style','text','units','normal','position',[.02 .10 .94 .04], ...
+   'horiz','left');
+t2 = uicontrol('style','text','units','normal','position',[.02 .02 .94 .04], ...
+   'horiz','left');
+slow = uicontrol('style','toggle','units','normal', ...
+   'position',[.01 .24 .07 .05],'string','slow','value',0);
+quit = uicontrol('style','toggle','units','normal', ...
+   'position',[.01 .17 .07 .05],'string','quit','value',0);
+
+U = cell(n,1);
+hash = zeros(n,1);
+G = logical(sparse(n,n));
+m = 1;
+U{m} = root;
+hash(m) = hashfun(root);
+
+j = 1;
+while j < n && get(quit,'value') == 0
+   
+   % Try to open a page.
+
+   try
+      set(t1,'string',sprintf('%5d %s',j,U{j}))
+      set(t2,'string','');
+      drawnow
+      page = urlread(U{j});
+   catch
+      set(t1,'string',sprintf('fail: %5d %s',j,U{j}))
+      drawnow
+      j = j+1;
+      continue
+   end
+   if get(slow,'value')
+      pause(.25)
+   end
+
+   % Follow the links from the open page.
+
+   for f = strfind(page, 'https:')
+
+      % A link starts with 'http:' and ends with the next quote.
+
+      e = min([strfind(page(f:end),'"') strfind(page(f:end),'''')]);
+      if isempty(e), continue, end
+      url = deblank(page(f:f+e-2));
+      url(url<' ') = '!';   % Nonprintable characters
+      if url(end) == '/', url(end) = []; end
+
+      % Look for links that should be skipped.
+
+      skips = {'.gif','.jpg','.jpeg','.pdf','.css','.asp','.mwc','.ram', ...
+               '.cgi','lmscadsi','cybernet','w3.org','google','yahoo', ...
+               'scripts','netscape','shockwave','webex','fansonly', ...
+               'idref.fr', 'purl.org', 'freedomdefined','wernfbox' };
+
+      skip = any(url=='!') | any(url=='?');
+      k = 0;
+      while ~skip && (k < length(skips))
+         k = k+1;
+         skip = ~isempty(strfind(url,skips{k}));
+      end
+      if skip
+         if ~contains(url,'.gif') && ~contains(url,'.jpg')
+            set(t2,'string',sprintf('skip: %s',url))
+            drawnow
+            if get(slow,'value')
+               pause(.25)
+            end
+         end
+         continue
+      end
+
+      % Check if page is already in url list.
+
+      i = 0;
+      for k = find(hash(1:m) == hashfun(url))'
+         if isequal(U{k},url)
+            i = k;
+            break
+         end
+      end
+
+      % Add a new url to the graph there if are fewer than n.
+
+      if (i == 0) && (m < n)
+         m = m+1;
+         U{m} = url;
+         hash(m) = hashfun(url);
+         i = m;
+      end
+
+      % Add a new link.
+
+      if i > 0
+         G(i,j) = 1;
+         set(t2,'string',sprintf('%5d %s',i,url))
+         line(j,i,'marker','.','markersize',6)
+         drawnow
+         if get(slow,'value')
+            pause(.5)
+         end
+      end
+   end
+
+   j = j+1;
+end
+delete(t1)
+delete(t2)
+delete(slow)
+set(quit,'string','close','callback','close(gcf)','value',0)
+
+
+
+%------------------------
+
+function h = hashfun(url)
+% Almost unique numeric hash code for pages already visited.
+h = length(url) + 1024*sum(url);

mp1/template.tex

@@ -0,0 +1,31 @@
+\documentclass[unicode,11pt,a4paper,oneside,numbers=endperiod,openany]{scrartcl}
+
+\input{assignment.sty}
+\begin{document}
+
+
+\setassignment
+\setduedate{Thursday, 8 October 2020, 12:00 AM}
+
+\serieheader{Numerical Computing}{2020}{Student: Claudio Maggioni}{Discussed with: --}{Solution for Project 1}{}
+\newline
+
+\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.
+
+
+
+\section{Page-Rank Algorithm }
+
+\subsection{Theory [20 points]}
+
+\subsection{Other webgraphs [10 points]}
+
+\subsection{Connectivity matrix and subcliques [10 points]}
+
+\subsection{Connectivity matrix and disjoint subgraphs [10 points]}
+
+\subsection{PageRanks by solving a sparse linear system [50 points]}
+
+
+\end{document}