--- /dev/null
+
+% 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  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 support for pandoc > 1.12.2
+ \usepackage[inline]{enumitem} % IRkernel/repr support (it uses the enumerate* environment)
+ \usepackage[normalem]{ulem} % ulem is needed to support strikethroughs (\sout)
+ % normalem makes italics be italics, not underlines
+
+
+
+
+ % Colors for the hyperref package
+ \definecolor{urlcolor}{rgb}{0,.145,.698}
+ \definecolor{linkcolor}{rgb}{.71,0.21,0.01}
+ \definecolor{citecolor}{rgb}{.12,.54,.11}
+
+ % ANSI colors
+ \definecolor{ansi-black}{HTML}{3E424D}
+ \definecolor{ansi-black-intense}{HTML}{282C36}
+ \definecolor{ansi-red}{HTML}{E75C58}
+ \definecolor{ansi-red-intense}{HTML}{B22B31}
+ \definecolor{ansi-green}{HTML}{00A250}
+ \definecolor{ansi-green-intense}{HTML}{007427}
+ \definecolor{ansi-yellow}{HTML}{DDB62B}
+ \definecolor{ansi-yellow-intense}{HTML}{B27D12}
+ \definecolor{ansi-blue}{HTML}{208FFB}
+ \definecolor{ansi-blue-intense}{HTML}{0065CA}
+ \definecolor{ansi-magenta}{HTML}{D160C4}
+ \definecolor{ansi-magenta-intense}{HTML}{A03196}
+ \definecolor{ansi-cyan}{HTML}{60C6C8}
+ \definecolor{ansi-cyan-intense}{HTML}{258F8F}
+ \definecolor{ansi-white}{HTML}{C5C1B4}
+ \definecolor{ansi-white-intense}{HTML}{A1A6B2}
+
+ % commands and environments needed by pandoc snippets
+ % extracted from the output of `pandoc -s`
+ \providecommand{\tightlist}{%
+ \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}
+ \DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}}
+ % Add ',fontsize=\small' for more characters per line
+ \newenvironment{Shaded}{}{}
+ \newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}}
+ \newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.56,0.13,0.00}{{#1}}}
+ \newcommand{\DecValTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
+ \newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
+ \newcommand{\FloatTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
+ \newcommand{\CharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
+ \newcommand{\StringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
+ \newcommand{\CommentTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textit{{#1}}}}
+ \newcommand{\OtherTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{{#1}}}
+ \newcommand{\AlertTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}}
+ \newcommand{\FunctionTok}[1]{\textcolor[rgb]{0.02,0.16,0.49}{{#1}}}
+ \newcommand{\RegionMarkerTok}[1]{{#1}}
+ \newcommand{\ErrorTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}}
+ \newcommand{\NormalTok}[1]{{#1}}
+
+ % Additional commands for more recent versions of Pandoc
+ \newcommand{\ConstantTok}[1]{\textcolor[rgb]{0.53,0.00,0.00}{{#1}}}
+ \newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
+ \newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
+ \newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.73,0.40,0.53}{{#1}}}
+ \newcommand{\ImportTok}[1]{{#1}}
+ \newcommand{\DocumentationTok}[1]{\textcolor[rgb]{0.73,0.13,0.13}{\textit{{#1}}}}
+ \newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
+ \newcommand{\CommentVarTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
+ \newcommand{\VariableTok}[1]{\textcolor[rgb]{0.10,0.09,0.49}{{#1}}}
+ \newcommand{\ControlFlowTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}}
+ \newcommand{\OperatorTok}[1]{\textcolor[rgb]{0.40,0.40,0.40}{{#1}}}
+ \newcommand{\BuiltInTok}[1]{{#1}}
+ \newcommand{\ExtensionTok}[1]{{#1}}
+ \newcommand{\PreprocessorTok}[1]{\textcolor[rgb]{0.74,0.48,0.00}{{#1}}}
+ \newcommand{\AttributeTok}[1]{\textcolor[rgb]{0.49,0.56,0.16}{{#1}}}
+ \newcommand{\InformationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
+ \newcommand{\WarningTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
+
+
+ % Define a nice break command that doesn't care if a line doesn't already
+ % exist.
+ \def\br{\hspace*{\fill} \\* }
+ % Math Jax compatability definitions
+ \def\gt{>}
+ \def\lt{<}
+ % Document parameters
+ \title{report\_P7\_H17}
+
+
+
+
+ % Pygments definitions
+
+\makeatletter
+\def\PY@reset{\let\PY@it=\relax \let\PY@bf=\relax%
+ \let\PY@ul=\relax \let\PY@tc=\relax%
+ \let\PY@bc=\relax \let\PY@ff=\relax}
+\def\PY@tok#1{\csname PY@tok@#1\endcsname}
+\def\PY@toks#1+{\ifx\relax#1\empty\else%
+ \PY@tok{#1}\expandafter\PY@toks\fi}
+\def\PY@do#1{\PY@bc{\PY@tc{\PY@ul{%
+ \PY@it{\PY@bf{\PY@ff{#1}}}}}}}
+\def\PY#1#2{\PY@reset\PY@toks#1+\relax+\PY@do{#2}}
+
+\expandafter\def\csname PY@tok@w\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.73,0.73}{##1}}}
+\expandafter\def\csname PY@tok@c\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
+\expandafter\def\csname PY@tok@cp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.74,0.48,0.00}{##1}}}
+\expandafter\def\csname PY@tok@k\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
+\expandafter\def\csname PY@tok@kp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
+\expandafter\def\csname PY@tok@kt\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.69,0.00,0.25}{##1}}}
+\expandafter\def\csname PY@tok@o\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
+\expandafter\def\csname PY@tok@ow\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.67,0.13,1.00}{##1}}}
+\expandafter\def\csname PY@tok@nb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
+\expandafter\def\csname PY@tok@nf\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}}
+\expandafter\def\csname PY@tok@nc\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}}
+\expandafter\def\csname PY@tok@nn\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}}
+\expandafter\def\csname PY@tok@ne\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.82,0.25,0.23}{##1}}}
+\expandafter\def\csname PY@tok@nv\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
+\expandafter\def\csname PY@tok@no\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.53,0.00,0.00}{##1}}}
+\expandafter\def\csname PY@tok@nl\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.63,0.63,0.00}{##1}}}
+\expandafter\def\csname PY@tok@ni\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.60,0.60,0.60}{##1}}}
+\expandafter\def\csname PY@tok@na\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.49,0.56,0.16}{##1}}}
+\expandafter\def\csname PY@tok@nt\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
+\expandafter\def\csname PY@tok@nd\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.67,0.13,1.00}{##1}}}
+\expandafter\def\csname PY@tok@s\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
+\expandafter\def\csname PY@tok@sd\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
+\expandafter\def\csname PY@tok@si\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.53}{##1}}}
+\expandafter\def\csname PY@tok@se\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.13}{##1}}}
+\expandafter\def\csname PY@tok@sr\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.53}{##1}}}
+\expandafter\def\csname PY@tok@ss\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
+\expandafter\def\csname PY@tok@sx\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
+\expandafter\def\csname PY@tok@m\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
+\expandafter\def\csname PY@tok@gh\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,0.50}{##1}}}
+\expandafter\def\csname PY@tok@gu\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.50,0.00,0.50}{##1}}}
+\expandafter\def\csname PY@tok@gd\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.63,0.00,0.00}{##1}}}
+\expandafter\def\csname PY@tok@gi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.63,0.00}{##1}}}
+\expandafter\def\csname PY@tok@gr\endcsname{\def\PY@tc##1{\textcolor[rgb]{1.00,0.00,0.00}{##1}}}
+\expandafter\def\csname PY@tok@ge\endcsname{\let\PY@it=\textit}
+\expandafter\def\csname PY@tok@gs\endcsname{\let\PY@bf=\textbf}
+\expandafter\def\csname PY@tok@gp\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,0.50}{##1}}}
+\expandafter\def\csname PY@tok@go\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.53,0.53,0.53}{##1}}}
+\expandafter\def\csname PY@tok@gt\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.27,0.87}{##1}}}
+\expandafter\def\csname PY@tok@err\endcsname{\def\PY@bc##1{\setlength{\fboxsep}{0pt}\fcolorbox[rgb]{1.00,0.00,0.00}{1,1,1}{\strut ##1}}}
+\expandafter\def\csname PY@tok@kc\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
+\expandafter\def\csname PY@tok@kd\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
+\expandafter\def\csname PY@tok@kn\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
+\expandafter\def\csname PY@tok@kr\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
+\expandafter\def\csname PY@tok@bp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
+\expandafter\def\csname PY@tok@fm\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}}
+\expandafter\def\csname PY@tok@vc\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
+\expandafter\def\csname PY@tok@vg\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
+\expandafter\def\csname PY@tok@vi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
+\expandafter\def\csname PY@tok@vm\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
+\expandafter\def\csname PY@tok@sa\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
+\expandafter\def\csname PY@tok@sb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
+\expandafter\def\csname PY@tok@sc\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
+\expandafter\def\csname PY@tok@dl\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
+\expandafter\def\csname PY@tok@s2\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
+\expandafter\def\csname PY@tok@sh\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
+\expandafter\def\csname PY@tok@s1\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
+\expandafter\def\csname PY@tok@mb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
+\expandafter\def\csname PY@tok@mf\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
+\expandafter\def\csname PY@tok@mh\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
+\expandafter\def\csname PY@tok@mi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
+\expandafter\def\csname PY@tok@il\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
+\expandafter\def\csname PY@tok@mo\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
+\expandafter\def\csname PY@tok@ch\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
+\expandafter\def\csname PY@tok@cm\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
+\expandafter\def\csname PY@tok@cpf\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
+\expandafter\def\csname PY@tok@c1\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
+\expandafter\def\csname PY@tok@cs\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
+
+\def\PYZbs{\char`\\}
+\def\PYZus{\char`\_}
+\def\PYZob{\char`\{}
+\def\PYZcb{\char`\}}
+\def\PYZca{\char`\^}
+\def\PYZam{\char`\&}
+\def\PYZlt{\char`\<}
+\def\PYZgt{\char`\>}
+\def\PYZsh{\char`\#}
+\def\PYZpc{\char`\%}
+\def\PYZdl{\char`\$}
+\def\PYZhy{\char`\-}
+\def\PYZsq{\char`\'}
+\def\PYZdq{\char`\"}
+\def\PYZti{\char`\~}
+% for compatibility with earlier versions
+\def\PYZat{@}
+\def\PYZlb{[}
+\def\PYZrb{]}
+\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}
+
+
+
+ \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}{,}
+ \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{}ep}\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{}ep}\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}11}]:} \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_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}
projects / talweg.git / commitdiff