From b5cc7065def46d3ae41c8c6d0a26395dfd52cb62 Mon Sep 17 00:00:00 2001 From: Claudio Maggioni Date: Sun, 27 Sep 2020 15:55:37 +0200 Subject: [PATCH] mp1: all done except 1.1 --- mp1/files_data/pagerank1.m | 4 +- mp1/files_data/pagerank2.m | 13 +- mp1/template.pdf | Bin 554623 -> 570579 bytes mp1/template.tex | 472 ++++++++++++++++++++++++++++++++++--- 4 files changed, 450 insertions(+), 39 deletions(-) diff --git a/mp1/files_data/pagerank1.m b/mp1/files_data/pagerank1.m index 63d73dd..c3b5862 100644 --- a/mp1/files_data/pagerank1.m +++ b/mp1/files_data/pagerank1.m @@ -35,7 +35,7 @@ new_x = x; old_norm = -1; no = +Inf; -while old_norm == -1 || old_norm > no +while (old_norm == -1 || old_norm > no) && no > 1e-8 x = new_x; old_norm = no; new_x = G * x + e * (z * x); @@ -44,6 +44,8 @@ while old_norm == -1 || old_norm > no no = norm(new_x - x, 2); end +display(it); + % ------------------------------------------------------------------------- % Normalize so that sum(x) == 1. diff --git a/mp1/files_data/pagerank2.m b/mp1/files_data/pagerank2.m index 3d4ced6..c974690 100644 --- a/mp1/files_data/pagerank2.m +++ b/mp1/files_data/pagerank2.m @@ -32,28 +32,25 @@ x = e/n; % Check if B will be a singular matrix. If so, change it alpha = 1; -while rcond(A - alpha * I) <= eps +while rcond(A - alpha * I) < eps alpha = alpha + 0.01; end -display(alpha); - -B = (A - alpha * I); old_x = zeros(n, 1); old_norm = -1; no = +Inf; it = 0; -while old_norm == -1 || old_norm > no +while (old_norm == -1 || old_norm > no) && no > 1e-8 old_norm = no; old_x = x; x = B \ x; - x = x/norm(x, 2); + x = x/sum(x); it = it + 1; - no = norm(x - old_x, 2); + no = norm(x - old_x, 1); end -x = old_x; +x = abs(old_x); display(it); % ------------------------------------------------------------------------- diff --git a/mp1/template.pdf b/mp1/template.pdf index 0c46877e7449ec26ecba5afb317be29106416e68..623d90fef2b4a4841d40bcd2b11708516348b1ab 100644 GIT binary patch delta 123064 zcmZs?LtrKf&?Oq%PCB-2+qP}n$rszUosMnWwr!)sx&O?()tg z2`C2>Q~H2AFeRWyTgPF$9o>JfE~Cw|-bTFp;t+$fQ3}>Hu-VF_fHH}9oWxr^QatP2 zxUTK{;Tu89O1zc%^)Eaqc2dzS7w^}s+CelDz!y1MEM=57(YIl<_x&d*Qq@ov5i#r) z`K|6fRO7DI_o3DQLE#HNepc}II$)OplR^JmZWwk}s|wJfsjI6M)?kQIjrs3T<^Ijz 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zV?z4>*!&Ch-^LFwfRo~X-@(zQ$f;;b;Cwqxe>3KfZ06#oYTpMMm4N_3tVb=*5G&Nub`+{nAoIkd%X=6?#}ToKnMX$|V#6^<}w^o+`gla-gE%dA_SU4Hv$8R}^g# z2%sx}O)(ci$5Bg7btn9L7_H^jlTGg9mV3aI3(cXoh3xg`lt5 ztI&%y8G}sqb{wHg=d&ROy8GV5`z+l5N?Uj=6a-;YEZ7tRAEMwgOrOsZ7{FO^>e*&Q zr7pTI97|{o{EVG`oCvO%Je<1%x0v(`IW67hP8Kb@`OO4%Ej<3d^a(xTMLI2~>z!21 zxDk`l5_{HnwT?e^GdnHD6@ChjugUiHcZ)fiMJ4!uOR`vcZoX8mEmWQ68nEnk73;HV zAgRX&m<9mFwt`?EiFw#9zDl5Uf} represents the number of +iterations required to compute the PageRanks within the termination criteria +described before. + +Here are the results for \texttt{pagerank1.m} for starting website +\texttt{http://atelier.inf.usi.ch/\~{}maggicl}: +\begin{verbatim} +Using power method implementation + +it = 73 + + page-rank in out url + 360 0.0869 31 1 https://creativecommons.org/licenses/by-sa/3.0 + 204 0.0406 8 1 https://forum.gitlab.com + 82 0.0189 117 18 https://www.mediawiki.org + 81 0.0188 117 4 https://wikimediafoundation.org + 87 0.0150 6 1 https://docs.gitea.io + 78 0.0145 114 9 https://www.mediawiki.org/wiki/Special:MyLanguage + /How_to_contribute + 77 0.0132 77 13 https://foundation.wikimedia.org/wiki/Privacy_policy + 217 0.0127 40 8 https://bugs.archlinux.org + 80 0.0115 107 6 https://foundation.wikimedia.org/wiki/Cookie_statement + 215 0.0114 38 5 https://bbs.archlinux.org + 216 0.0114 38 8 https://wiki.archlinux.org + 218 0.0114 38 6 https://security.archlinux.org + 428 0.0107 9 1 https://www.dnb.de/kataloghilfe + 219 0.0102 38 7 https://aur.archlinux.org + 359 0.0098 9 1 https://creativecommons.org/publicdomain/zero/1.0 + 366 0.0092 27 21 https://archive.org + 446 0.0089 24 5 https://foundation.wikimedia.org/wiki/Terms_of_Use + 83 0.0079 78 0 https:\/\/schema.org + 85 0.0074 77 0 https:\/\/www.wikimedia.org\/static\/images + \/wmf-hor-googpub.png + 181 0.0066 8 2 https://gitlab.com + 95 0.0062 2 1 https://www.enable-javascript.com + 113 0.0061 13 1 https://www.britannica.com/topic/polenta + 429 0.0058 8 1 https://www.dnb.de/EN/Home/home_node.html + 432 0.0058 8 1 https://www.dnb.de/expertensuche + 417 0.0058 8 1 https://www.dnb.de/DE/Home/home_node.html + 379 0.0057 24 2 https://blog.archive.org + 213 0.0057 32 7 https://www.archlinux.org + 99 0.0056 3 1 https://www.usi.ch/it + 19 0.0051 4 1 https://creativecommons.org/licenses/by-nc-sa/4.0 + 214 0.0050 31 5 https://www.archlinux.org/packages + 220 0.0050 31 6 https://www.archlinux.org/download +\end{verbatim} + +Here are the results for \texttt{pagerank2.m} for starting website +\texttt{http://atelier.inf.usi.ch/\~{}maggicl}: + +\begin{verbatim} +Using inverse iteration implementation + +it = 7 + + page-rank in out url + 360 0.0869 31 1 https://creativecommons.org/licenses/by-sa/3.0 + 204 0.0406 8 1 https://forum.gitlab.com + 82 0.0189 117 18 https://www.mediawiki.org + 81 0.0188 117 4 https://wikimediafoundation.org + 87 0.0150 6 1 https://docs.gitea.io + 78 0.0145 114 9 https://www.mediawiki.org/wiki/Special:MyLanguage + /How_to_contribute + 77 0.0132 77 13 https://foundation.wikimedia.org/wiki/Privacy_policy + 217 0.0127 40 8 https://bugs.archlinux.org + 80 0.0115 107 6 https://foundation.wikimedia.org/wiki/Cookie_statement + 215 0.0114 38 5 https://bbs.archlinux.org + 216 0.0114 38 8 https://wiki.archlinux.org + 218 0.0114 38 6 https://security.archlinux.org + 428 0.0107 9 1 https://www.dnb.de/kataloghilfe + 219 0.0102 38 7 https://aur.archlinux.org + 359 0.0098 9 1 https://creativecommons.org/publicdomain/zero/1.0 + 366 0.0092 27 21 https://archive.org + 446 0.0089 24 5 https://foundation.wikimedia.org/wiki/Terms_of_Use + 83 0.0079 78 0 https:\/\/schema.org + 85 0.0074 77 0 https:\/\/www.wikimedia.org\/static\/images + \/wmf-hor-googpub.png + 181 0.0066 8 2 https://gitlab.com + 95 0.0062 2 1 https://www.enable-javascript.com + 113 0.0061 13 1 https://www.britannica.com/topic/polenta + 429 0.0058 8 1 https://www.dnb.de/EN/Home/home_node.html + 432 0.0058 8 1 https://www.dnb.de/expertensuche + 417 0.0058 8 1 https://www.dnb.de/DE/Home/home_node.html + 379 0.0057 24 2 https://blog.archive.org + 213 0.0057 32 7 https://www.archlinux.org + 99 0.0056 3 1 https://www.usi.ch/it + 19 0.0051 4 1 https://creativecommons.org/licenses/by-nc-sa/4.0 + 220 0.0050 31 6 https://www.archlinux.org/download + 214 0.0050 31 5 https://www.archlinux.org/packages +\end{verbatim} + +Here are the results for \texttt{pagerank1.m} for starting website +\texttt{https://www.iisbadoni.edu.it/}: + +\begin{verbatim} +Using power method implementation + +it = 75 + + page-rank in out url + 411 0.0249 42 1 https://twitter.com/mozilla + 63 0.0248 145 1 https://twitter.com/firefox + 68 0.0203 142 1 https://www.instagram.com/firefox + 412 0.0164 37 1 https://www.instagram.com/mozilla + 62 0.0080 21 1 https://github.com/mozilla/kitsune + 81 0.0070 110 2 https://www.apple.com + 384 0.0064 5 1 https://www.xfinity.com/privacy/policy/dns + 4 0.0064 32 0 https: + 377 0.0059 19 1 https://abouthome-snippets-service.readthedocs.io + /en/latest/data_collection.html + 393 0.0059 19 1 https://www.adjust.com/terms/privacy-policy + 410 0.0057 16 1 https://wiki.mozilla.org/Firefox/Data_Collection + 400 0.0057 15 1 https://yandex.ru/legal/confidential + 396 0.0057 15 1 https://github.com/mozilla-mobile/firefox-ios + /blob/master/Docs/MMA.md + 5 0.0056 31 0 https://ssl + 3 0.0054 36 0 https://www.iisbadoni.edu.it/sites/default/files + /favicon.ico + 6 0.0054 36 0 https://www.iisbadoni.edu.it/sites/default/files + /logo.png + 208 0.0054 159 0 https://schema.org + 74 0.0052 178 5 https://foundation.mozilla.org + 72 0.0052 33 32 https://www.mozilla.org/privacy/websites/#cookies + 23 0.0051 2 1 https://www.iisbadoni.edu.it/mad + 300 0.0051 157 0 https://accounts.firefox.com +\end{verbatim} + +Here are the results for \texttt{pagerank2.m} for starting website +\texttt{https://www.iisbadoni.edu.it}: + +\begin{verbatim} +Using inverse iteration implementation + +it = 7 + + page-rank in out url + 411 0.0249 42 1 https://twitter.com/mozilla + 63 0.0248 145 1 https://twitter.com/firefox + 68 0.0203 142 1 https://www.instagram.com/firefox + 412 0.0164 37 1 https://www.instagram.com/mozilla + 62 0.0080 21 1 https://github.com/mozilla/kitsune + 81 0.0070 110 2 https://www.apple.com + 384 0.0064 5 1 https://www.xfinity.com/privacy/policy/dns + 4 0.0064 32 0 https: + 393 0.0059 19 1 https://www.adjust.com/terms/privacy-policy + 377 0.0059 19 1 https://abouthome-snippets-service.readthedocs.io + /en/latest/data_collection.html + 410 0.0057 16 1 https://wiki.mozilla.org/Firefox/Data_Collection + 400 0.0057 15 1 https://yandex.ru/legal/confidential + 396 0.0057 15 1 https://github.com/mozilla-mobile/firefox-ios + /blob/master/Docs/MMA.md + 5 0.0056 31 0 https://ssl + 3 0.0054 36 0 https://www.iisbadoni.edu.it/sites/default/files + /favicon.ico + 6 0.0054 36 0 https://www.iisbadoni.edu.it/sites/default/files + /logo.png + 208 0.0054 159 0 https://schema.org + 74 0.0052 178 5 https://foundation.mozilla.org + 72 0.0052 33 32 https://www.mozilla.org/privacy/websites/#cookies + 23 0.0051 2 1 https://www.iisbadoni.edu.it/mad + 300 0.0051 157 0 https://accounts.firefox.com +\end{verbatim} + +Here are the results for \texttt{pagerank1.m} for starting website +\texttt{https://www.usi.ch}: + +\begin{verbatim} +Using power method implementation + +it = 66 + + page-rank in out url + 55 0.0741 354 1 https://www.instagram.com/usiuniversity + 53 0.0324 366 3 https://www.facebook.com/usiuniversity + 299 0.0248 6 1 https://twitter.com/usi_en + 329 0.0243 8 1 https://www.facebook.com/USIeLab + 308 0.0156 7 3 https://www.facebook.com/USIFinancialCommunication + 60 0.0155 316 2 https://www.swissuniversities.ch + 424 0.0144 96 1 https://it.bul.sbu.usi.ch + 330 0.0123 6 4 https://www.facebook.com/USI.ITDxC + 320 0.0122 7 1 https://www.facebook.com/usiimeg + 56 0.0107 320 0 https://www.youtube.com/usiuniversity + 5 0.0096 317 71 https://usi.ch + 62 0.0090 319 18 https://search.usi.ch + 337 0.0087 7 1 https://twitter.com/usisoftware + 63 0.0080 303 19 https://desk.usi.ch + 130 0.0077 25 0 https://www.swissuniversities.ch/it + 54 0.0072 208 0 https://twitter.com/USI_university + 323 0.0066 9 5 https://www.facebook.com/usiorientamento + 150 0.0062 12 1 https://www.innosuisse.ch/inno/it/home.html + 248 0.0061 10 1 https://www.facebook.com/usimdfc + 106 0.0060 132 8 https://newsletter.usi.ch/archive/en + 135 0.0057 201 0 https://schema.org + 326 0.0057 6 1 https://www.facebook.com/usialloggimendrisio + 322 0.0055 6 1 https://www.facebook.com/USImem + 366 0.0054 6 1 https://www.instagram.com/usi_ics_lugano + 212 0.0054 12 3 https://www.facebook.com/usimt + 7 0.0051 211 32 https://search.usi.ch/it + 6 0.0051 204 0 https://www.usi.ch/sites/all/themes/usiclean + /img/bollino-usi.svg + 14 0.0051 204 62 https://www.usi.ch/originalnode/342 + 15 0.0051 204 57 https://www.usi.ch/originalnode/358 + 16 0.0051 204 62 https://www.usi.ch/originalnode/343 + 17 0.0051 204 57 https://www.usi.ch/originalnode/344 + 18 0.0051 204 58 https://www.usi.ch/en/originalnode/12174 + 20 0.0051 204 60 https://www.usi.ch/originalnode/349 + 21 0.0051 204 62 https://www.usi.ch/originalnode/8996 + 22 0.0051 204 60 https://www.usi.ch/originalnode/348 + 23 0.0051 204 59 https://www.usi.ch/originalnode/351 + 24 0.0051 204 58 https://www.usi.ch/originalnode/350 + 25 0.0051 204 61 https://www.usi.ch/originalnode/353 + 26 0.0051 204 58 https://www.usi.ch/en/originalnode/354 + 27 0.0051 204 59 https://www.usi.ch/originalnode/8014 + 61 0.0051 204 0 https://www.usi.ch/sites/all/themes/usiclean + /img/swissuniversities.svg + 57 0.0050 188 9 https://newsletter.usi.ch/archive +\end{verbatim} + +Here are the results for \texttt{pagerank2.m} for starting website +\texttt{https://www.usi.ch}: + +\begin{verbatim} +Using inverse iteration implementation + +it = 7 + + page-rank in out url + 55 0.0741 354 1 https://www.instagram.com/usiuniversity + 53 0.0324 366 3 https://www.facebook.com/usiuniversity + 299 0.0248 6 1 https://twitter.com/usi_en + 329 0.0243 8 1 https://www.facebook.com/USIeLab + 308 0.0156 7 3 https://www.facebook.com/USIFinancialCommunication + 60 0.0155 316 2 https://www.swissuniversities.ch + 424 0.0144 96 1 https://it.bul.sbu.usi.ch + 330 0.0123 6 4 https://www.facebook.com/USI.ITDxC + 320 0.0122 7 1 https://www.facebook.com/usiimeg + 56 0.0107 320 0 https://www.youtube.com/usiuniversity + 5 0.0096 317 71 https://usi.ch + 62 0.0090 319 18 https://search.usi.ch + 337 0.0087 7 1 https://twitter.com/usisoftware + 63 0.0080 303 19 https://desk.usi.ch + 130 0.0077 25 0 https://www.swissuniversities.ch/it + 54 0.0072 208 0 https://twitter.com/USI_university + 323 0.0066 9 5 https://www.facebook.com/usiorientamento + 150 0.0062 12 1 https://www.innosuisse.ch/inno/it/home.html + 248 0.0061 10 1 https://www.facebook.com/usimdfc + 106 0.0060 132 8 https://newsletter.usi.ch/archive/en + 135 0.0057 201 0 https://schema.org + 326 0.0057 6 1 https://www.facebook.com/usialloggimendrisio + 322 0.0055 6 1 https://www.facebook.com/USImem + 366 0.0054 6 1 https://www.instagram.com/usi_ics_lugano + 212 0.0054 12 3 https://www.facebook.com/usimt + 7 0.0051 211 32 https://search.usi.ch/it + 14 0.0051 204 62 https://www.usi.ch/originalnode/342 + 27 0.0051 204 59 https://www.usi.ch/originalnode/8014 + 21 0.0051 204 62 https://www.usi.ch/originalnode/8996 + 22 0.0051 204 60 https://www.usi.ch/originalnode/348 + 25 0.0051 204 61 https://www.usi.ch/originalnode/353 + 61 0.0051 204 0 https://www.usi.ch/sites/all/themes/usiclean + /img/swissuniversities.svg + 16 0.0051 204 62 https://www.usi.ch/originalnode/343 + 23 0.0051 204 59 https://www.usi.ch/originalnode/351 + 15 0.0051 204 57 https://www.usi.ch/originalnode/358 + 17 0.0051 204 57 https://www.usi.ch/originalnode/344 + 24 0.0051 204 58 https://www.usi.ch/originalnode/350 + 6 0.0051 204 0 https://www.usi.ch/sites/all/themes/usiclean + /img/bollino-usi.svg + 20 0.0051 204 60 https://www.usi.ch/originalnode/349 + 26 0.0051 204 58 https://www.usi.ch/en/originalnode/354 + 18 0.0051 204 58 https://www.usi.ch/en/originalnode/12174 + 57 0.0050 188 9 https://newsletter.usi.ch/archive +\end{verbatim} + +The potential of the algorithm in \texttt{pagerank2.m} compared to the one in +\texttt{pagerank.m} is that by using inverse iteration, thus theoretically +avoiding a full matrix system solution process, the sparsity of matrix G can be +maintained during the computation thus saving memory costs. + +However, since my \texttt{pagerank2.m} implementation is a simplified +implementation of the algorithm and indeed uses system solution +(MATLAB's \texttt{mldivide}), this +theoretical advantages are voided: my implementation is 3 times as long as the +original one and uses approximately the same amount of memory. Advantages over +\texttt{pagerank1.m} (due to the intentionally increased rate of convergence) +are clear: in +all the examples above, the inverse iteration implementation is at least 8 times +faster than the ``vanilla'' power method. \end{document}