X-Git-Url: https://git.auder.net/?p=talweg.git;a=blobdiff_plain;f=reports%2Frapport_final%2Freport_P7_H17.tex;fp=reports%2Frapport_final%2Freport_P7_H17.tex;h=0000000000000000000000000000000000000000;hp=5d0886b7445f92b2041c0a3de4b54f1c8f8690d3;hb=af718fd5a9a330b13b331e78824a47407a3479ae;hpb=c8a81efd2e8302cde424165539f49e4bb7466fc3 diff --git a/reports/rapport_final/report_P7_H17.tex b/reports/rapport_final/report_P7_H17.tex deleted file mode 100644 index 5d0886b..0000000 --- a/reports/rapport_final/report_P7_H17.tex +++ /dev/null @@ -1,986 +0,0 @@ - -% Default to the notebook output style - - - - -% Inherit from the specified cell style. - - - - - -\documentclass[11pt]{article} - - - - \usepackage[T1]{fontenc} - % Nicer default font (+ math font) than Computer Modern for most use cases - \usepackage{mathpazo} - - % Basic figure setup, for now with no caption control since it's done - % automatically by Pandoc (which extracts ![](path) syntax from Markdown). - \usepackage{graphicx} - % We will generate all images so they have a width \maxwidth. This means - % that they will get their normal width if they fit onto the page, but - % are scaled down if they would overflow the margins. - \makeatletter - \def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth - \else\Gin@nat@width\fi} - \makeatother - \let\Oldincludegraphics\includegraphics - % Set max figure width to be 80% of text width, for now hardcoded. - \renewcommand{\includegraphics}[1]{\Oldincludegraphics[width=.8\maxwidth]{#1}} - % Ensure that by default, figures have no caption (until we provide a - % proper Figure object with a Caption API and a way to capture that - % in the conversion process - todo). - \usepackage{caption} - \DeclareCaptionLabelFormat{nolabel}{} - \captionsetup{labelformat=nolabel} - - \usepackage{adjustbox} % Used to constrain images to a maximum size - \usepackage{xcolor} % Allow colors to be defined - \usepackage{enumerate} % Needed for markdown enumerations to work - \usepackage{geometry} % Used to adjust the document margins - \usepackage{amsmath} % Equations - \usepackage{amssymb} % Equations - \usepackage{textcomp} % defines textquotesingle - % Hack from http://tex.stackexchange.com/a/47451/13684: - \AtBeginDocument{% - \def\PYZsq{\textquotesingle}% Upright quotes in Pygmentized code - } - \usepackage{upquote} % Upright quotes for verbatim code - \usepackage{eurosym} % defines \euro - \usepackage[mathletters]{ucs} % Extended unicode (utf-8) support - \usepackage[utf8x]{inputenc} % Allow utf-8 characters in the tex document - \usepackage{fancyvrb} % verbatim replacement that allows latex - \usepackage{grffile} % extends the file name processing of package graphics - % to support a larger range - % The hyperref package gives us a pdf with properly built - % internal navigation ('pdf bookmarks' for the table of contents, - % internal cross-reference links, web links for URLs, etc.) - \usepackage{hyperref} - \usepackage{longtable} % longtable support required by pandoc >1.10 - \usepackage{booktabs} % table 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-\makeatother - - - % Exact colors from NB - \definecolor{incolor}{rgb}{0.0, 0.0, 0.5} - \definecolor{outcolor}{rgb}{0.545, 0.0, 0.0} - - - - - % Prevent overflowing lines due to hard-to-break entities - \sloppy - % Setup hyperref package - \hypersetup{ - breaklinks=true, % so long urls are correctly broken across lines - colorlinks=true, - urlcolor=urlcolor, - linkcolor=linkcolor, - citecolor=citecolor, - } - % Slightly bigger margins than the latex defaults - - \geometry{verbose,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in} - - -\graphicspath{{./figs/}} - - \begin{document} - - - \maketitle - - - - - \subsection*{Introduction} - -Cette partie montre les résultats obtenus via des variantes de -l'algorithme décrit à la section 2, en utilisant le package présenté à -la section 3. Cet algorithme est systématiquement comparé à deux -approches naïves : * la moyenne des lendemains des jours "similaires" -dans tout le passé, c'est-à-dire prédiction = moyenne de tous les mardis -passé si le jour courant est un lndi par exemple. * la persistence, -reproduisant le jour courant ou allant chercher le lendemain de la -dernière journée "similaire" (même principe que ci-dessus ; argument -"same\_day"). - -Concernant l'algorithme principal à voisins, trois variantes sont -étudiées dans cette partie : * avec simtype="mix" et raccordement -"Neighbors" dans le cas "non local", i.e. on va chercher des voisins -n'importe où du moment qu'ils correspondent au premier élément d'un -couple de deux jours consécutifs sans valeurs manquantes. * avec -simtype="endo" + raccordement "Neighbors" puis simtype="none" + -raccordement "Zero" (sans ajustement) dans le cas "local" : voisins de -même niveau de pollution et même saison. - -Pour chaque période retenue -\/- chauffage, épandage, semaine non -polluée -\/- les erreurs de prédiction sont d'abord affichées, puis -quelques graphes de courbes réalisées/prévues (sur le jour "en moyenne -le plus facile" à gauche, et "en moyenne le plus difficile" à droite). -Ensuite plusieurs types de graphes apportant des précisions sur la -nature et la difficulté du problème viennent compléter ces premières -courbes. Concernant les graphes de filaments, la moitié gauche du graphe -correspond aux jours similaires au jour courant, tandis que la moitié -droite affiche les lendemains : ce sont donc les voisinages tels -qu'utilisés dans l'algorithme. - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}1}]:} \PY{n}{library}\PY{p}{(}\PY{n}{talweg}\PY{p}{)} - - \PY{n}{P} \PY{o}{=} \PY{l+m+mi}{7} \PY{c+c1}{\PYZsh{}instant de prévision} - \PY{n}{H} \PY{o}{=} \PY{l+m+mi}{17} \PY{c+c1}{\PYZsh{}horizon (en heures)} - - \PY{n}{ts\PYZus{}data} \PY{o}{=} \PY{n}{read}\PY{o}{.}\PY{n}{csv}\PY{p}{(}\PY{n}{system}\PY{o}{.}\PY{n}{file}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{extdata}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{pm10\PYZus{}mesures\PYZus{}H\PYZus{}loc\PYZus{}report.csv}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} - \PY{n}{package}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{talweg}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}\PY{p}{)} - \PY{n}{exo\PYZus{}data} \PY{o}{=} \PY{n}{read}\PY{o}{.}\PY{n}{csv}\PY{p}{(}\PY{n}{system}\PY{o}{.}\PY{n}{file}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{extdata}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{meteo\PYZus{}extra\PYZus{}noNAs.csv}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{package}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{talweg}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}\PY{p}{)} - \PY{c+c1}{\PYZsh{} NOTE: \PYZsq{}GMT\PYZsq{} because DST gaps are filled and multiple values merged in above dataset.} - \PY{c+c1}{\PYZsh{} Prediction from P+1 to P+H included.} - \PY{n}{data} \PY{o}{=} \PY{n}{getData}\PY{p}{(}\PY{n}{ts\PYZus{}data}\PY{p}{,} \PY{n}{exo\PYZus{}data}\PY{p}{,} \PY{n}{input\PYZus{}tz} \PY{o}{=} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{GMT}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{working\PYZus{}tz}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{GMT}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{predict\PYZus{}at}\PY{o}{=}\PY{n}{P}\PY{p}{)} - - \PY{n}{indices\PYZus{}ch} \PY{o}{=} \PY{n}{seq}\PY{p}{(}\PY{k}{as}\PY{o}{.}\PY{n}{Date}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{2015\PYZhy{}01\PYZhy{}18}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}\PY{p}{,}\PY{k}{as}\PY{o}{.}\PY{n}{Date}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{2015\PYZhy{}01\PYZhy{}24}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}\PY{p}{,}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{days}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)} - \PY{n}{indices\PYZus{}ep} \PY{o}{=} \PY{n}{seq}\PY{p}{(}\PY{k}{as}\PY{o}{.}\PY{n}{Date}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{2015\PYZhy{}03\PYZhy{}15}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}\PY{p}{,}\PY{k}{as}\PY{o}{.}\PY{n}{Date}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{2015\PYZhy{}03\PYZhy{}21}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}\PY{p}{,}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{days}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)} - \PY{n}{indices\PYZus{}np} \PY{o}{=} \PY{n}{seq}\PY{p}{(}\PY{k}{as}\PY{o}{.}\PY{n}{Date}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{2015\PYZhy{}04\PYZhy{}26}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}\PY{p}{,}\PY{k}{as}\PY{o}{.}\PY{n}{Date}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{2015\PYZhy{}05\PYZhy{}02}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}\PY{p}{,}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{days}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)} -\end{Verbatim} - - \subsection*{Pollution par chauffage} - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}2}]:} \PY{n}{p1} \PY{o}{=} \PY{n}{computeForecast}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{indices\PYZus{}ch}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Neighbors}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Neighbors}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{horizon}\PY{o}{=}\PY{n}{H}\PY{p}{,} - \PY{n}{simtype}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{mix}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{local}\PY{o}{=}\PY{n}{FALSE}\PY{p}{)} - \PY{n}{p2} \PY{o}{=} \PY{n}{computeForecast}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{indices\PYZus{}ch}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Neighbors}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Neighbors}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{horizon}\PY{o}{=}\PY{n}{H}\PY{p}{,} - \PY{n}{simtype}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{endo}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{local}\PY{o}{=}\PY{n}{TRUE}\PY{p}{)} - \PY{n}{p3} \PY{o}{=} \PY{n}{computeForecast}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{indices\PYZus{}ch}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Neighbors}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Zero}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{horizon}\PY{o}{=}\PY{n}{H}\PY{p}{,} - \PY{n}{simtype}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{none}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{local}\PY{o}{=}\PY{n}{TRUE}\PY{p}{)} - \PY{n}{p4} \PY{o}{=} \PY{n}{computeForecast}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{indices\PYZus{}ch}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Average}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Zero}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{horizon}\PY{o}{=}\PY{n}{H}\PY{p}{)} - \PY{n}{p5} \PY{o}{=} \PY{n}{computeForecast}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{indices\PYZus{}ch}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Persistence}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Zero}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{horizon}\PY{o}{=}\PY{n}{H}\PY{p}{,} - \PY{n}{same\PYZus{}day}\PY{o}{=}\PY{n}{TRUE}\PY{p}{)} -\end{Verbatim} - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}3}]:} \PY{n}{e1} \PY{o}{=} \PY{n}{computeError}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p1}\PY{p}{,} \PY{n}{H}\PY{p}{)} - \PY{n}{e2} \PY{o}{=} \PY{n}{computeError}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p2}\PY{p}{,} \PY{n}{H}\PY{p}{)} - \PY{n}{e3} \PY{o}{=} \PY{n}{computeError}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p3}\PY{p}{,} \PY{n}{H}\PY{p}{)} - \PY{n}{e4} \PY{o}{=} \PY{n}{computeError}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p4}\PY{p}{,} \PY{n}{H}\PY{p}{)} - \PY{n}{e5} \PY{o}{=} \PY{n}{computeError}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p5}\PY{p}{,} \PY{n}{H}\PY{p}{)} - \PY{n}{options}\PY{p}{(}\PY{n+nb}{repr}\PY{o}{.}\PY{n}{plot}\PY{o}{.}\PY{n}{width}\PY{o}{=}\PY{l+m+mi}{9}\PY{p}{,} \PY{n+nb}{repr}\PY{o}{.}\PY{n}{plot}\PY{o}{.}\PY{n}{height}\PY{o}{=}\PY{l+m+mi}{7}\PY{p}{)} - \PY{n}{plotError}\PY{p}{(}\PY{n+nb}{list}\PY{p}{(}\PY{n}{e1}\PY{p}{,} \PY{n}{e5}\PY{p}{,} \PY{n}{e4}\PY{p}{,} \PY{n}{e2}\PY{p}{,} \PY{n}{e3}\PY{p}{)}\PY{p}{,} \PY{n}{cols}\PY{o}{=}\PY{n}{c}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{n}{colors}\PY{p}{(}\PY{p}{)}\PY{p}{[}\PY{l+m+mi}{258}\PY{p}{]}\PY{p}{,}\PY{l+m+mi}{4}\PY{p}{,}\PY{l+m+mi}{6}\PY{p}{)}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} noir: Neighbors non\PYZhy{}local (p1), bleu: Neighbors local endo (p2),} - \PY{c+c1}{\PYZsh{} mauve: Neighbors local none (p3), vert: moyenne (p4),} - \PY{c+c1}{\PYZsh{} rouge: persistence (p5)} - - \PY{n}{sum\PYZus{}p123} \PY{o}{=} \PY{n}{e1}\PY{err}{\PYZdl{}}\PY{n+nb}{abs}\PY{err}{\PYZdl{}}\PY{n}{indices} \PY{o}{+} \PY{n}{e2}\PY{err}{\PYZdl{}}\PY{n+nb}{abs}\PY{err}{\PYZdl{}}\PY{n}{indices} \PY{o}{+} \PY{n}{e3}\PY{err}{\PYZdl{}}\PY{n+nb}{abs}\PY{err}{\PYZdl{}}\PY{n}{indices} - \PY{n}{i\PYZus{}np} \PY{o}{=} \PY{n}{which}\PY{o}{.}\PY{n}{min}\PY{p}{(}\PY{n}{sum\PYZus{}p123}\PY{p}{)} \PY{c+c1}{\PYZsh{}indice de (veille de) jour \PYZdq{}facile\PYZdq{}} - \PY{n}{i\PYZus{}p} \PY{o}{=} \PY{n}{which}\PY{o}{.}\PY{n}{max}\PY{p}{(}\PY{n}{sum\PYZus{}p123}\PY{p}{)} \PY{c+c1}{\PYZsh{}indice de (veille de) jour \PYZdq{}difficile\PYZdq{}} -\end{Verbatim} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_4_0.png} - \end{center} - { \hspace*{\fill} \\} - - L'erreur absolue dépasse 20 sur 1 à 2 jours suivant les modèles (graphe -en haut à droite). C'est au-delà de ce que l'on aimerait voir (disons -+/- 5 environ). Sur cet exemple le modèle à voisins "contraint" -(local=TRUE) utilisant des pondérations basées sur les similarités de -forme (simtype="endo") obtient en moyenne les meilleurs résultats, avec -un MAPE restant en général inférieur à 30\% de 8h à 19h (7+1 à 7+12 : -graphe en bas à gauche). - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}4}]:} \PY{n}{options}\PY{p}{(}\PY{n+nb}{repr}\PY{o}{.}\PY{n}{plot}\PY{o}{.}\PY{n}{width}\PY{o}{=}\PY{l+m+mi}{9}\PY{p}{,} \PY{n+nb}{repr}\PY{o}{.}\PY{n}{plot}\PY{o}{.}\PY{n}{height}\PY{o}{=}\PY{l+m+mi}{4}\PY{p}{)} - \PY{n}{par}\PY{p}{(}\PY{n}{mfrow}\PY{o}{=}\PY{n}{c}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)} - - \PY{n}{plotPredReal}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p1}\PY{p}{,} \PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PredReal p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotPredReal}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p1}\PY{p}{,} \PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PredReal p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{n}{plotPredReal}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p2}\PY{p}{,} \PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PredReal p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotPredReal}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p2}\PY{p}{,} \PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PredReal p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{n}{plotPredReal}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p3}\PY{p}{,} \PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PredReal p3 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotPredReal}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p3}\PY{p}{,} \PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PredReal p3 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} Bleu: prévue, noir: réalisée} -\end{Verbatim} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_6_0.png} - \end{center} - { \hspace*{\fill} \\} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_6_1.png} - \end{center} - { \hspace*{\fill} \\} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_6_2.png} - \end{center} - { \hspace*{\fill} \\} - - Le jour "facile à prévoir", à gauche, se décompose en deux modes : un -léger vers 10h (7+3), puis un beaucoup plus marqué vers 19h (7+12). Ces -deux modes sont retrouvés par les trois variantes de l'algorithme à -voisins, bien que l'amplitude soit mal prédite. Concernant le jour -"difficile à prévoir" il y a deux pics en tout début et toute fin de -journée (à 9h et 23h), qui ne sont pas du tout anticipés par le -programme ; la grande amplitude de ces pics explique alors l'intensité -de l'erreur observée. - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}5}]:} \PY{n}{par}\PY{p}{(}\PY{n}{mfrow}\PY{o}{=}\PY{n}{c}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)} - \PY{n}{f\PYZus{}np1} \PY{o}{=} \PY{n}{computeFilaments}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p1}\PY{p}{,} \PY{n}{i\PYZus{}np}\PY{p}{,} \PY{n}{plot}\PY{o}{=}\PY{n}{TRUE}\PY{p}{)} - \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Filaments p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{f\PYZus{}p1} \PY{o}{=} \PY{n}{computeFilaments}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p1}\PY{p}{,} \PY{n}{i\PYZus{}p}\PY{p}{,} \PY{n}{plot}\PY{o}{=}\PY{n}{TRUE}\PY{p}{)} - \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Filaments p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{n}{f\PYZus{}np2} \PY{o}{=} \PY{n}{computeFilaments}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p2}\PY{p}{,} \PY{n}{i\PYZus{}np}\PY{p}{,} \PY{n}{plot}\PY{o}{=}\PY{n}{TRUE}\PY{p}{)} - \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Filaments p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{f\PYZus{}p2} \PY{o}{=} \PY{n}{computeFilaments}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p2}\PY{p}{,} \PY{n}{i\PYZus{}p}\PY{p}{,} \PY{n}{plot}\PY{o}{=}\PY{n}{TRUE}\PY{p}{)} - \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Filaments p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} -\end{Verbatim} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_8_0.png} - \end{center} - { \hspace*{\fill} \\} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_8_1.png} - \end{center} - { \hspace*{\fill} \\} - - Les voisins du jour courant (période de 24h allant de 8h à 7h le -lendemain) sont affichés avec un trait d'autant plus sombre qu'ils sont -proches. On constate dans le cas non contraint (en haut) une grande -variabilité des lendemains, très nette sur le graphe en haut à droite. -Ceci indique une faible corrélation entre la forme d'une courbe sur une -période de 24h et la forme sur les 24h suivantes ; \textbf{cette -observation est la source des difficultés rencontrées par l'algorithme -sur ce jeu de données.} - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}6}]:} \PY{n}{par}\PY{p}{(}\PY{n}{mfrow}\PY{o}{=}\PY{n}{c}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)} - \PY{n}{plotFilamentsBox}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{f\PYZus{}np1}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{FilBox p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotFilamentsBox}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{f\PYZus{}p1}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{FilBox p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} En pointillés la courbe du jour courant + lendemain (à prédire)} -\end{Verbatim} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_10_0.png} - \end{center} - { \hspace*{\fill} \\} - - Sur cette boxplot fonctionnelle (voir la fonction fboxplot() du package -R "rainbow") l'on constate essentiellement deux choses : le lendemain -d'un voisin "normal" peut se révéler être une courbe atypique, fort -éloignée de ce que l'on souhaite prédire (courbes bleue et rouge à -gauche) ; et, dans le cas d'une courbe à prédire atypique (à droite) la -plupart des voisins sont trop éloignés de la forme à prédire et forcent -ainsi un aplatissement de la prédiction. - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}7}]:} \PY{n}{par}\PY{p}{(}\PY{n}{mfrow}\PY{o}{=}\PY{n}{c}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)} - \PY{n}{plotRelVar}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{f\PYZus{}np1}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{StdDev p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotRelVar}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{f\PYZus{}p1}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{StdDev p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{n}{plotRelVar}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{f\PYZus{}np2}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{StdDev p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotRelVar}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{f\PYZus{}p2}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{StdDev p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} Variabilité globale en rouge ; sur les 60 voisins (+ lendemains) en noir} -\end{Verbatim} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_12_0.png} - \end{center} - { \hspace*{\fill} \\} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_12_1.png} - \end{center} - { \hspace*{\fill} \\} - - Ces graphes viennent confirmer l'impression visuelle après observation -des filaments. En effet, la variabilité globale en rouge (écart-type -heure par heure sur l'ensemble des couples "aujourd'hui/lendemain" du -passé) devrait rester nettement au-dessus de la variabilité locale, -calculée respectivement sur un voisinage d'une soixantaine de jours -(pour p1) et d'une dizaine de jours (pour p2). Or on constate que ce -n'est pas du tout le cas sur la période "lendemain", sauf en partie pour -p2 le jour 4 \(-\) mais ce n'est pas suffisant. - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}8}]:} \PY{n}{par}\PY{p}{(}\PY{n}{mfrow}\PY{o}{=}\PY{n}{c}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)} - \PY{n}{plotSimils}\PY{p}{(}\PY{n}{p1}\PY{p}{,} \PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Weights p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotSimils}\PY{p}{(}\PY{n}{p1}\PY{p}{,} \PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Weights p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{n}{plotSimils}\PY{p}{(}\PY{n}{p2}\PY{p}{,} \PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Weights p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotSimils}\PY{p}{(}\PY{n}{p2}\PY{p}{,} \PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Weights p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} \PYZhy{} pollué à gauche, + pollué à droite} -\end{Verbatim} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_14_0.png} - \end{center} - { \hspace*{\fill} \\} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_14_1.png} - \end{center} - { \hspace*{\fill} \\} - - Les poids se concentrent près de 0 dans le cas "non local" (p1), et se -répartissent assez uniformément dans \([0,0.2]\) dans le cas "local" -(p2). C'est ce que l'on souhaite observer pour éviter d'effectuer une -simple moyenne. - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}9}]:} \PY{c+c1}{\PYZsh{} Fenêtres sélectionnées dans ]0,7] / non\PYZhy{}loc 2 premières lignes, loc ensuite} - \PY{n}{p1}\PY{err}{\PYZdl{}}\PY{n}{getParams}\PY{p}{(}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{err}{\PYZdl{}}\PY{n}{window} - \PY{n}{p1}\PY{err}{\PYZdl{}}\PY{n}{getParams}\PY{p}{(}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{err}{\PYZdl{}}\PY{n}{window} - - \PY{n}{p2}\PY{err}{\PYZdl{}}\PY{n}{getParams}\PY{p}{(}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{err}{\PYZdl{}}\PY{n}{window} - \PY{n}{p2}\PY{err}{\PYZdl{}}\PY{n}{getParams}\PY{p}{(}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{err}{\PYZdl{}}\PY{n}{window} -\end{Verbatim} - - \begin{enumerate*} -\item 0.168824188864717 -\item 0.336969608767438 -\end{enumerate*} - - - \begin{enumerate*} -\item 0.18004595760919 -\item 0.353963007643311 -\end{enumerate*} - - - 1.16620655388085 - - - 1.18148881881259 - - - \subsection*{Pollution par épandage} - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}10}]:} \PY{n}{p1} \PY{o}{=} \PY{n}{computeForecast}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{indices\PYZus{}ep}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Neighbors}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Neighbors}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{horizon}\PY{o}{=}\PY{n}{H}\PY{p}{,} - \PY{n}{simtype}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{mix}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{local}\PY{o}{=}\PY{n}{FALSE}\PY{p}{)} - \PY{n}{p2} \PY{o}{=} \PY{n}{computeForecast}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{indices\PYZus{}ep}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Neighbors}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Neighbors}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{horizon}\PY{o}{=}\PY{n}{H}\PY{p}{,} - \PY{n}{simtype}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{endo}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{local}\PY{o}{=}\PY{n}{TRUE}\PY{p}{)} - \PY{n}{p3} \PY{o}{=} \PY{n}{computeForecast}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{indices\PYZus{}ep}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Neighbors}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Zero}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{horizon}\PY{o}{=}\PY{n}{H}\PY{p}{,} - 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\PY{n}{e2} \PY{o}{=} \PY{n}{computeError}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p2}\PY{p}{,} \PY{n}{H}\PY{p}{)} - \PY{n}{e3} \PY{o}{=} \PY{n}{computeError}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p3}\PY{p}{,} \PY{n}{H}\PY{p}{)} - \PY{n}{e4} \PY{o}{=} \PY{n}{computeError}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p4}\PY{p}{,} \PY{n}{H}\PY{p}{)} - \PY{n}{e5} \PY{o}{=} \PY{n}{computeError}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p5}\PY{p}{,} \PY{n}{H}\PY{p}{)} - \PY{n}{options}\PY{p}{(}\PY{n+nb}{repr}\PY{o}{.}\PY{n}{plot}\PY{o}{.}\PY{n}{width}\PY{o}{=}\PY{l+m+mi}{9}\PY{p}{,} \PY{n+nb}{repr}\PY{o}{.}\PY{n}{plot}\PY{o}{.}\PY{n}{height}\PY{o}{=}\PY{l+m+mi}{7}\PY{p}{)} - \PY{n}{plotError}\PY{p}{(}\PY{n+nb}{list}\PY{p}{(}\PY{n}{e1}\PY{p}{,} \PY{n}{e5}\PY{p}{,} \PY{n}{e4}\PY{p}{,} \PY{n}{e2}\PY{p}{,} \PY{n}{e3}\PY{p}{)}\PY{p}{,} \PY{n}{cols}\PY{o}{=}\PY{n}{c}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{n}{colors}\PY{p}{(}\PY{p}{)}\PY{p}{[}\PY{l+m+mi}{258}\PY{p}{]}\PY{p}{,}\PY{l+m+mi}{4}\PY{p}{,}\PY{l+m+mi}{6}\PY{p}{)}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} noir: Neighbors non\PYZhy{}local (p1), bleu: Neighbors local endo (p2),} - \PY{c+c1}{\PYZsh{} mauve: Neighbors local none (p3), vert: moyenne (p4),} - \PY{c+c1}{\PYZsh{} rouge: persistence (p5)} - - \PY{n}{sum\PYZus{}p123} \PY{o}{=} \PY{n}{e1}\PY{err}{\PYZdl{}}\PY{n+nb}{abs}\PY{err}{\PYZdl{}}\PY{n}{indices} \PY{o}{+} \PY{n}{e2}\PY{err}{\PYZdl{}}\PY{n+nb}{abs}\PY{err}{\PYZdl{}}\PY{n}{indices} \PY{o}{+} \PY{n}{e3}\PY{err}{\PYZdl{}}\PY{n+nb}{abs}\PY{err}{\PYZdl{}}\PY{n}{indices} - \PY{n}{i\PYZus{}np} \PY{o}{=} \PY{n}{which}\PY{o}{.}\PY{n}{min}\PY{p}{(}\PY{n}{sum\PYZus{}p123}\PY{p}{)} \PY{c+c1}{\PYZsh{}indice de (veille de) jour \PYZdq{}facile\PYZdq{}} - \PY{n}{i\PYZus{}p} \PY{o}{=} \PY{n}{which}\PY{o}{.}\PY{n}{max}\PY{p}{(}\PY{n}{sum\PYZus{}p123}\PY{p}{)} \PY{c+c1}{\PYZsh{}indice de (veille de) jour \PYZdq{}difficile\PYZdq{}} -\end{Verbatim} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_19_0.png} - \end{center} - { \hspace*{\fill} \\} - - Il est difficile dans ce cas de déterminer une méthode meilleure que les -autres : elles donnent toutes de plutôt mauvais résultats, avec une -erreur absolue moyennée sur la journée dépassant presque toujours 15 -(graphe en haut à droite). - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}12}]:} \PY{n}{options}\PY{p}{(}\PY{n+nb}{repr}\PY{o}{.}\PY{n}{plot}\PY{o}{.}\PY{n}{width}\PY{o}{=}\PY{l+m+mi}{9}\PY{p}{,} \PY{n+nb}{repr}\PY{o}{.}\PY{n}{plot}\PY{o}{.}\PY{n}{height}\PY{o}{=}\PY{l+m+mi}{4}\PY{p}{)} - \PY{n}{par}\PY{p}{(}\PY{n}{mfrow}\PY{o}{=}\PY{n}{c}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)} - - \PY{n}{plotPredReal}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p1}\PY{p}{,} \PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PredReal p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotPredReal}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p1}\PY{p}{,} \PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PredReal p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{n}{plotPredReal}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p2}\PY{p}{,} \PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PredReal p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotPredReal}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p2}\PY{p}{,} \PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PredReal p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{n}{plotPredReal}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p3}\PY{p}{,} \PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PredReal p3 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotPredReal}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p3}\PY{p}{,} \PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PredReal p3 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} Bleu: prévue, noir: réalisée} -\end{Verbatim} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_21_0.png} - \end{center} - { \hspace*{\fill} \\} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_21_1.png} - \end{center} - { \hspace*{\fill} \\} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_21_2.png} - \end{center} - { \hspace*{\fill} \\} - - Dans le cas d'un jour "facile" à prédire \(-\) à gauche \(-\) la forme -est plus ou moins retrouvée, mais le niveau moyen est trop bas (courbe -en bleu). Concernant le jour "difficile" à droite, non seulement la -forme n'est pas anticipée mais surtout le niveau prédit est très -inférieur au niveau de pollution observé. Comme on le voit ci-dessous -cela découle d'un manque de voisins au comportement similaire. - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}13}]:} \PY{n}{par}\PY{p}{(}\PY{n}{mfrow}\PY{o}{=}\PY{n}{c}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)} - \PY{n}{f\PYZus{}np1} \PY{o}{=} \PY{n}{computeFilaments}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p1}\PY{p}{,} \PY{n}{i\PYZus{}np}\PY{p}{,} \PY{n}{plot}\PY{o}{=}\PY{n}{TRUE}\PY{p}{)} - \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Filaments p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{f\PYZus{}p1} \PY{o}{=} \PY{n}{computeFilaments}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p1}\PY{p}{,} \PY{n}{i\PYZus{}p}\PY{p}{,} \PY{n}{plot}\PY{o}{=}\PY{n}{TRUE}\PY{p}{)} - \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Filaments p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{n}{f\PYZus{}np2} \PY{o}{=} \PY{n}{computeFilaments}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p2}\PY{p}{,} \PY{n}{i\PYZus{}np}\PY{p}{,} \PY{n}{plot}\PY{o}{=}\PY{n}{TRUE}\PY{p}{)} - \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Filaments p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{f\PYZus{}p2} \PY{o}{=} \PY{n}{computeFilaments}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p2}\PY{p}{,} \PY{n}{i\PYZus{}p}\PY{p}{,} \PY{n}{plot}\PY{o}{=}\PY{n}{TRUE}\PY{p}{)} - \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Filaments p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} -\end{Verbatim} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_23_0.png} - \end{center} - { \hspace*{\fill} \\} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_23_1.png} - \end{center} - { \hspace*{\fill} \\} - - Les observations sont les mêmes qu'au paragraphe précédent : trop de -variabilité des lendemains (et même des voisins du jour courant). - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}14}]:} \PY{n}{par}\PY{p}{(}\PY{n}{mfrow}\PY{o}{=}\PY{n}{c}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)} - \PY{n}{plotFilamentsBox}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{f\PYZus{}np1}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{FilBox p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotFilamentsBox}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{f\PYZus{}p1}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{FilBox p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} En pointillés la courbe du jour courant + lendemain (à prédire)} -\end{Verbatim} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_25_0.png} - \end{center} - { \hspace*{\fill} \\} - - On constate la présence d'un voisin au lendemain complètement atypique -avec un pic en début de journée (courbe en vert à gauche), et d'un autre -phénomène semblable avec la courbe rouge sur le graphe de droite. Ajouté -au fait que le lendemain à prévoir est lui-même un jour "hors norme", -cela montre l'impossibilité de bien prévoir une courbe en utilisant -l'algorithme à voisins. - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}15}]:} \PY{n}{par}\PY{p}{(}\PY{n}{mfrow}\PY{o}{=}\PY{n}{c}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)} - \PY{n}{plotRelVar}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{f\PYZus{}np1}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{StdDev p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotRelVar}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{f\PYZus{}p1}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{StdDev p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{n}{plotRelVar}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{f\PYZus{}np2}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{StdDev p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotRelVar}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{f\PYZus{}p2}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{StdDev p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} Variabilité globale en rouge ; sur les 60 voisins (+ lendemains) en noir} -\end{Verbatim} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_27_0.png} - \end{center} - { \hspace*{\fill} \\} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_27_1.png} - \end{center} - { \hspace*{\fill} \\} - - Comme précédemment les variabilités locales et globales sont confondues -dans les parties droites des graphes \(-\) sauf pour la version "locale" -sur le jour "facile" ; mais cette bonne propriété n'est pas suffisante -si l'on ne trouve pas les bons poids à appliquer. - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}16}]:} \PY{n}{par}\PY{p}{(}\PY{n}{mfrow}\PY{o}{=}\PY{n}{c}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)} - \PY{n}{plotSimils}\PY{p}{(}\PY{n}{p1}\PY{p}{,} \PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Weights p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotSimils}\PY{p}{(}\PY{n}{p1}\PY{p}{,} \PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Weights p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{n}{plotSimils}\PY{p}{(}\PY{n}{p2}\PY{p}{,} \PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Weights p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotSimils}\PY{p}{(}\PY{n}{p2}\PY{p}{,} \PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Weights p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} \PYZhy{} pollué à gauche, + pollué à droite} -\end{Verbatim} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_29_0.png} - \end{center} - { \hspace*{\fill} \\} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_29_1.png} - \end{center} - { \hspace*{\fill} \\} - - En comparaison avec le pragraphe précédent on retrouve le même (bon) -comportement des poids pour la version "non locale". En revanche la -fenêtre optimisée est trop grande sur le jour "facile" pour la méthode -"locale" (voir affichage ci-dessous) : il en résulte des poids tous -semblables autour de 0.084, l'algorithme effectue donc une moyenne -simple \(-\) expliquant pourquoi les courbes mauve et bleue sont très -proches sur le graphe d'erreurs. - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}17}]:} \PY{c+c1}{\PYZsh{} Fenêtres sélectionnées dans ]0,7] / non\PYZhy{}loc 2 premières lignes, loc ensuite} - \PY{n}{p1}\PY{err}{\PYZdl{}}\PY{n}{getParams}\PY{p}{(}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{err}{\PYZdl{}}\PY{n}{window} - \PY{n}{p1}\PY{err}{\PYZdl{}}\PY{n}{getParams}\PY{p}{(}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{err}{\PYZdl{}}\PY{n}{window} - - \PY{n}{p2}\PY{err}{\PYZdl{}}\PY{n}{getParams}\PY{p}{(}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{err}{\PYZdl{}}\PY{n}{window} - \PY{n}{p2}\PY{err}{\PYZdl{}}\PY{n}{getParams}\PY{p}{(}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{err}{\PYZdl{}}\PY{n}{window} -\end{Verbatim} - - \begin{enumerate*} -\item 0.206604806619633 -\item 0.661854053860987 -\end{enumerate*} - - - \begin{enumerate*} -\item 0.367945958636072 -\item 0.244429852740092 -\end{enumerate*} - - - 6.99993248587025 - - - 1.24825506305085 - - - \subsection*{Semaine non polluée} - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}18}]:} \PY{n}{p1} \PY{o}{=} \PY{n}{computeForecast}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{indices\PYZus{}np}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Neighbors}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Neighbors}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{horizon}\PY{o}{=}\PY{n}{H}\PY{p}{,} - \PY{n}{simtype}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{mix}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{local}\PY{o}{=}\PY{n}{FALSE}\PY{p}{)} - \PY{n}{p2} \PY{o}{=} \PY{n}{computeForecast}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{indices\PYZus{}np}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Neighbors}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Neighbors}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{horizon}\PY{o}{=}\PY{n}{H}\PY{p}{,} - \PY{n}{simtype}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{endo}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{local}\PY{o}{=}\PY{n}{TRUE}\PY{p}{)} - \PY{n}{p3} \PY{o}{=} \PY{n}{computeForecast}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{indices\PYZus{}np}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Neighbors}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Zero}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{horizon}\PY{o}{=}\PY{n}{H}\PY{p}{,} - \PY{n}{simtype}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{none}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{local}\PY{o}{=}\PY{n}{TRUE}\PY{p}{)} - \PY{n}{p4} \PY{o}{=} \PY{n}{computeForecast}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{indices\PYZus{}np}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Average}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Zero}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{horizon}\PY{o}{=}\PY{n}{H}\PY{p}{)} - \PY{n}{p5} \PY{o}{=} \PY{n}{computeForecast}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{indices\PYZus{}np}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Persistence}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Zero}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,} \PY{n}{horizon}\PY{o}{=}\PY{n}{H}\PY{p}{,} - \PY{n}{same\PYZus{}day}\PY{o}{=}\PY{n}{FALSE}\PY{p}{)} -\end{Verbatim} - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}19}]:} \PY{n}{e1} \PY{o}{=} \PY{n}{computeError}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p1}\PY{p}{,} \PY{n}{H}\PY{p}{)} - \PY{n}{e2} \PY{o}{=} \PY{n}{computeError}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p2}\PY{p}{,} \PY{n}{H}\PY{p}{)} - \PY{n}{e3} \PY{o}{=} \PY{n}{computeError}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p3}\PY{p}{,} \PY{n}{H}\PY{p}{)} - \PY{n}{e4} \PY{o}{=} \PY{n}{computeError}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p4}\PY{p}{,} \PY{n}{H}\PY{p}{)} - \PY{n}{e5} \PY{o}{=} \PY{n}{computeError}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p5}\PY{p}{,} \PY{n}{H}\PY{p}{)} - \PY{n}{options}\PY{p}{(}\PY{n+nb}{repr}\PY{o}{.}\PY{n}{plot}\PY{o}{.}\PY{n}{width}\PY{o}{=}\PY{l+m+mi}{9}\PY{p}{,} \PY{n+nb}{repr}\PY{o}{.}\PY{n}{plot}\PY{o}{.}\PY{n}{height}\PY{o}{=}\PY{l+m+mi}{7}\PY{p}{)} - \PY{n}{plotError}\PY{p}{(}\PY{n+nb}{list}\PY{p}{(}\PY{n}{e1}\PY{p}{,} \PY{n}{e5}\PY{p}{,} \PY{n}{e4}\PY{p}{,} \PY{n}{e2}\PY{p}{,} \PY{n}{e3}\PY{p}{)}\PY{p}{,} \PY{n}{cols}\PY{o}{=}\PY{n}{c}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{n}{colors}\PY{p}{(}\PY{p}{)}\PY{p}{[}\PY{l+m+mi}{258}\PY{p}{]}\PY{p}{,}\PY{l+m+mi}{4}\PY{p}{,}\PY{l+m+mi}{6}\PY{p}{)}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} noir: Neighbors non\PYZhy{}local (p1), bleu: Neighbors local endo (p2),} - \PY{c+c1}{\PYZsh{} mauve: Neighbors local none (p3), vert: moyenne (p4),} - \PY{c+c1}{\PYZsh{} rouge: persistence (p5)} - - \PY{n}{sum\PYZus{}p123} \PY{o}{=} \PY{n}{e1}\PY{err}{\PYZdl{}}\PY{n+nb}{abs}\PY{err}{\PYZdl{}}\PY{n}{indices} \PY{o}{+} \PY{n}{e2}\PY{err}{\PYZdl{}}\PY{n+nb}{abs}\PY{err}{\PYZdl{}}\PY{n}{indices} \PY{o}{+} \PY{n}{e3}\PY{err}{\PYZdl{}}\PY{n+nb}{abs}\PY{err}{\PYZdl{}}\PY{n}{indices} - \PY{n}{i\PYZus{}np} \PY{o}{=} \PY{n}{which}\PY{o}{.}\PY{n}{min}\PY{p}{(}\PY{n}{sum\PYZus{}p123}\PY{p}{)} \PY{c+c1}{\PYZsh{}indice de (veille de) jour \PYZdq{}facile\PYZdq{}} - \PY{n}{i\PYZus{}p} \PY{o}{=} \PY{n}{which}\PY{o}{.}\PY{n}{max}\PY{p}{(}\PY{n}{sum\PYZus{}p123}\PY{p}{)} \PY{c+c1}{\PYZsh{}indice de (veille de) jour \PYZdq{}difficile\PYZdq{}} -\end{Verbatim} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_34_0.png} - \end{center} - { \hspace*{\fill} \\} - - Dans ce cas plus favorable les intensité des erreurs absolues ont -clairement diminué : elles restent souvent en dessous de 5. En revanche -le MAPE moyen reste au-delà de 20\%, et même souvent plus de 30\%. Comme -dans le cas de l'épandage on constate une croissance globale de la -courbe journalière d'erreur absolue moyenne (en haut à gauche) ; ceci -peut être dû au fait que l'on ajuste le niveau du jour à prédire en le -recollant sur la dernière valeur observée. - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}20}]:} \PY{n}{options}\PY{p}{(}\PY{n+nb}{repr}\PY{o}{.}\PY{n}{plot}\PY{o}{.}\PY{n}{width}\PY{o}{=}\PY{l+m+mi}{9}\PY{p}{,} \PY{n+nb}{repr}\PY{o}{.}\PY{n}{plot}\PY{o}{.}\PY{n}{height}\PY{o}{=}\PY{l+m+mi}{4}\PY{p}{)} - \PY{n}{par}\PY{p}{(}\PY{n}{mfrow}\PY{o}{=}\PY{n}{c}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)} - - \PY{n}{plotPredReal}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p1}\PY{p}{,} \PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PredReal p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotPredReal}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p1}\PY{p}{,} \PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PredReal p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{n}{plotPredReal}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p2}\PY{p}{,} \PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PredReal p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotPredReal}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p2}\PY{p}{,} \PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PredReal p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{n}{plotPredReal}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p3}\PY{p}{,} \PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PredReal p3 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotPredReal}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p3}\PY{p}{,} \PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{PredReal p3 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} Bleu: prévue, noir: réalisée} -\end{Verbatim} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_36_0.png} - \end{center} - { \hspace*{\fill} \\} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_36_1.png} - \end{center} - { \hspace*{\fill} \\} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_36_2.png} - \end{center} - { \hspace*{\fill} \\} - - La forme est raisonnablement retrouvée pour les méthodes "locales", -l'autre version lissant trop les prédictions. Le biais reste cependant -important, surtout en fin de journée sur le jour "difficile". - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}21}]:} \PY{n}{par}\PY{p}{(}\PY{n}{mfrow}\PY{o}{=}\PY{n}{c}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)} - \PY{n}{f\PYZus{}np1} \PY{o}{=} \PY{n}{computeFilaments}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p1}\PY{p}{,} \PY{n}{i\PYZus{}np}\PY{p}{,} \PY{n}{plot}\PY{o}{=}\PY{n}{TRUE}\PY{p}{)} - \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Filaments p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{f\PYZus{}p1} \PY{o}{=} \PY{n}{computeFilaments}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p1}\PY{p}{,} \PY{n}{i\PYZus{}p}\PY{p}{,} \PY{n}{plot}\PY{o}{=}\PY{n}{TRUE}\PY{p}{)} - \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Filaments p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{n}{f\PYZus{}np2} \PY{o}{=} \PY{n}{computeFilaments}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p2}\PY{p}{,} \PY{n}{i\PYZus{}np}\PY{p}{,} \PY{n}{plot}\PY{o}{=}\PY{n}{TRUE}\PY{p}{)} - \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Filaments p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{f\PYZus{}p2} \PY{o}{=} \PY{n}{computeFilaments}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{p2}\PY{p}{,} \PY{n}{i\PYZus{}p}\PY{p}{,} \PY{n}{plot}\PY{o}{=}\PY{n}{TRUE}\PY{p}{)} - \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Filaments p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} -\end{Verbatim} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_38_0.png} - \end{center} - { \hspace*{\fill} \\} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_38_1.png} - \end{center} - { \hspace*{\fill} \\} - - Les graphes de filaments ont encore la même allure, avec une assez -grande variabilité observée. Cette observation est cependant trompeuse, -comme l'indique plus bas le graphe de variabilité relative. - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}22}]:} \PY{n}{par}\PY{p}{(}\PY{n}{mfrow}\PY{o}{=}\PY{n}{c}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)} - \PY{n}{plotFilamentsBox}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{f\PYZus{}np1}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{FilBox p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotFilamentsBox}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{f\PYZus{}p1}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{FilBox p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} En pointillés la courbe du jour courant + lendemain (à prédire)} -\end{Verbatim} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_40_0.png} - \end{center} - { \hspace*{\fill} \\} - - On peut réappliquer les mêmes remarques qu'auparavant sur les boxplots -fonctionnels : lendemains de voisins atypiques, courbe à prévoir -elle-même légèrement "hors norme". - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}23}]:} \PY{n}{par}\PY{p}{(}\PY{n}{mfrow}\PY{o}{=}\PY{n}{c}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)} - \PY{n}{plotRelVar}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{f\PYZus{}np1}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{StdDev p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotRelVar}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{f\PYZus{}p1}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{StdDev p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{n}{plotRelVar}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{f\PYZus{}np2}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{StdDev p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotRelVar}\PY{p}{(}\PY{n}{data}\PY{p}{,} \PY{n}{f\PYZus{}p2}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{StdDev p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} Variabilité globale en rouge ; sur les 60 voisins (+ lendemains) en noir} -\end{Verbatim} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_42_0.png} - \end{center} - { \hspace*{\fill} \\} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_42_1.png} - \end{center} - { \hspace*{\fill} \\} - - Cette fois la situation idéale est observée : la variabilité globale est -nettement au-dessus de la variabilité locale. Bien que cela ne suffise -pas à obtenir de bonnes prédictions de forme, on constate au moins -l'amélioration dans la prédiction du niveau. - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}24}]:} \PY{n}{par}\PY{p}{(}\PY{n}{mfrow}\PY{o}{=}\PY{n}{c}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)} - \PY{n}{plotSimils}\PY{p}{(}\PY{n}{p1}\PY{p}{,} \PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Weights p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotSimils}\PY{p}{(}\PY{n}{p1}\PY{p}{,} \PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Weights p1 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{n}{plotSimils}\PY{p}{(}\PY{n}{p2}\PY{p}{,} \PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Weights p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{p}{)} - \PY{n}{plotSimils}\PY{p}{(}\PY{n}{p2}\PY{p}{,} \PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{;} \PY{n}{title}\PY{p}{(}\PY{n}{paste}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Weights p2 day}\PY{l+s+s2}{\PYZdq{}}\PY{p}{,}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} \PYZhy{} pollué à gauche, + pollué à droite} -\end{Verbatim} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_44_0.png} - \end{center} - { \hspace*{\fill} \\} - - \begin{center} - \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_44_1.png} - \end{center} - { \hspace*{\fill} \\} - - Concernant les poids en revanche, deux cas a priori mauvais se cumulent -: * les poids dans le cas "non local" ne sont pas assez concentrés -autour de 0, menant à un lissage trop fort \(-\) comme observé sur les -graphes des courbes réalisées/prévues ; * les poids dans le cas "local" -sont trop semblables (à cause de la trop grande fenêtre optimisée par -validation croisée, cf. ci-dessous), résultant encore en une moyenne -simple \(-\) mais sur moins de jours, plus proches du jour courant. - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}25}]:} \PY{c+c1}{\PYZsh{} Fenêtres sélectionnées dans ]0,7] / non\PYZhy{}loc 2 premières lignes, loc ensuite} - \PY{n}{p1}\PY{err}{\PYZdl{}}\PY{n}{getParams}\PY{p}{(}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{err}{\PYZdl{}}\PY{n}{window} - \PY{n}{p1}\PY{err}{\PYZdl{}}\PY{n}{getParams}\PY{p}{(}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{err}{\PYZdl{}}\PY{n}{window} - - \PY{n}{p2}\PY{err}{\PYZdl{}}\PY{n}{getParams}\PY{p}{(}\PY{n}{i\PYZus{}np}\PY{p}{)}\PY{err}{\PYZdl{}}\PY{n}{window} - \PY{n}{p2}\PY{err}{\PYZdl{}}\PY{n}{getParams}\PY{p}{(}\PY{n}{i\PYZus{}p}\PY{p}{)}\PY{err}{\PYZdl{}}\PY{n}{window} -\end{Verbatim} - - \begin{enumerate*} -\item 0.205055690975915 -\item 0.703482647754766 -\end{enumerate*} - - - \begin{enumerate*} -\item 1.1038650998802 -\item 0.885155748316133 -\end{enumerate*} - - - 3.64336124381868 - - - 6.99994501761361 - - - \subsection*{Bilan} - -Nos algorithmes à voisins ne sont pas adaptés à ce jeu de données où la -forme varie considérablement d'un jour à l'autre. Plus généralement -cette décorrélation de forme rend ardue la tâche de prévision pour toute -autre méthode \(-\) du moins, nous ne savons pas comment procéder pour -parvenir à une bonne précision. - -Toutefois, un espoir reste permis par exemple en aggréger les courbes -spatialement (sur plusieurs stations situées dans la même agglomération -ou dans une même zone). - - - % Add a bibliography block to the postdoc - - - - \end{document}