{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "library(talweg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ts_data = read.csv(system.file(\"extdata\",\"pm10_mesures_H_loc.csv\",package=\"talweg\"))\n",
    "exo_data = read.csv(system.file(\"extdata\",\"meteo_extra_noNAs.csv\",package=\"talweg\"))\n",
    "data = getData(ts_data, exo_data, input_tz = \"Europe/Paris\", working_tz=\"Europe/Paris\", predict_at=7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "J'ai fait quelques essais dans différentes configurations pour la méthode \"Neighbors\" (la seule dont on a parlé).<br>Il semble que le mieux soit\n",
    "\n",
    " * simtype=\"mix\" : on utilise les similarités endogènes et exogènes (fenêtre optimisée par VC)\n",
    " * same_season=FALSE : les indices pour la validation croisée ne tiennent pas compte des saisons\n",
    " * mix_strategy=\"mult\" : on multiplie les poids (au lieu d'en éteindre)\n",
    "\n",
    "(valeurs par défaut).\n",
    "\n",
    "J'ai systématiquement comparé à deux autres approches : la persistence et la moyennes des lendemains des jours \"similaires\" dans tout le passé ; à chaque fois sans prédiction du saut (sauf pour Neighbors : prédiction basée sur les poids calculés).\n",
    "\n",
    "Ensuite j'affiche les erreurs, quelques courbes prévues/mesurées, quelques filaments puis les histogrammes de quelques poids. 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.\n",
    "\n",
    "<h2 style=\"color:blue;font-size:2em\">Pollution par chauffage</h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "indices_ch = seq(as.Date(\"2015-01-18\"),as.Date(\"2015-01-24\"),\"days\")\n",
    "p_ch_nn = computeForecast(data,indices_ch, \"Neighbors\", \"Neighbors\", simtype=\"mix\")\n",
    "p_ch_pz = computeForecast(data, indices_ch, \"Persistence\", \"Zero\", same_day=TRUE)\n",
    "p_ch_az = computeForecast(data, indices_ch, \"Average\", \"Zero\") #, memory=183)\n",
    "#p_ch_zz = computeForecast(data, indices_ch, \"Zero\", \"Zero\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "e_ch_nn = computeError(data, p_ch_nn)\n",
    "e_ch_pz = computeError(data, p_ch_pz)\n",
    "e_ch_az = computeError(data, p_ch_az)\n",
    "#e_ch_zz = computeError(data, p_ch_zz)\n",
    "options(repr.plot.width=9, repr.plot.height=7)\n",
    "plotError(list(e_ch_nn, e_ch_pz, e_ch_az), cols=c(1,2,colors()[258]))\n",
    "\n",
    "#Noir: neighbors, rouge: persistence, vert: moyenne"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "options(repr.plot.width=9, repr.plot.height=4)\n",
    "plotPredReal(data, p_ch_nn, 3)\n",
    "plotPredReal(data, p_ch_nn, 4)\n",
    "\n",
    "#Bleu: prévue, noir: réalisée"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prédictions d'autant plus lisses que le jour à prévoir est atypique (pollué)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "plotPredReal(data, p_ch_az, 3)\n",
    "plotPredReal(data, p_ch_az, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "f3_ch = computeFilaments(data, p_ch_nn$getIndexInData(3), plot=TRUE)\n",
    "f4_ch = computeFilaments(data, p_ch_nn$getIndexInData(4), plot=TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(2,2))\n",
    "options(repr.plot.width=9, repr.plot.height=7)\n",
    "plotFilamentsBox(data, f3_ch$indices)\n",
    "plotFilamentsBox(data, f3_ch$indices+1)\n",
    "plotFilamentsBox(data, f4_ch$indices)\n",
    "plotFilamentsBox(data, f4_ch$indices+1)\n",
    "\n",
    "#En haut : jour 3 + lendemain (4) ; en bas : jour 4 + lendemain (5)\n",
    "#À gauche : premières 24h ; à droite : 24h suivantes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dans les deux cas, un voisinage \"raisonnable\" est trouvé ; mais grande variabilité le lendemain \"pollué\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "options(repr.plot.width=9, repr.plot.height=4)\n",
    "plotRelativeVariability(data, f3_ch$indices)\n",
    "plotRelativeVariability(data, f4_ch$indices)\n",
    "\n",
    "#Variabilité sur 60 courbes au hasard en rouge ; sur nos 60 voisins (+ lendemains) en noir"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il faudrait que la courbe noire soit nettement plus basse que la courbe rouge."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,3))\n",
    "plotSimils(p_ch_nn, 3)\n",
    "plotSimils(p_ch_nn, 4)\n",
    "plotSimils(p_ch_nn, 5)\n",
    "\n",
    "#Non pollué à gauche, pollué au milieu, autre pollué à droite"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La plupart des poids très proches de zéro ; pas pour le jour 5 : autre type de jour, cf. ci-dessous."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "plotPredReal(data, p_ch_nn, 5)\n",
    "ignored <- computeFilaments(data, p_ch_nn$getIndexInData(5), plot=TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Fenêtres sélectionnées dans ]0,10] / endo à gauche, exo à droite\n",
    "p_ch_nn$getParams(3)$window\n",
    "p_ch_nn$getParams(4)$window"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 style=\"color:blue;font-size:2em\">Pollution par épandage</h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "indices_ep = seq(as.Date(\"2015-03-15\"),as.Date(\"2015-03-21\"),\"days\")\n",
    "p_ep_nn = computeForecast(data,indices_ep, \"Neighbors\", \"Neighbors\", simtype=\"mix\")\n",
    "p_ep_pz = computeForecast(data, indices_ep, \"Persistence\", \"Zero\", same_day=TRUE)\n",
    "p_ep_az = computeForecast(data, indices_ep, \"Average\", \"Zero\") #, memory=183)\n",
    "#p_ep_zz = computeForecast(data, indices_ep, \"Zero\", \"Zero\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "e_ep_nn = computeError(data, p_ep_nn)\n",
    "e_ep_pz = computeError(data, p_ep_pz)\n",
    "e_ep_az = computeError(data, p_ep_az)\n",
    "#e_ep_zz = computeError(data, p_ep_zz)\n",
    "options(repr.plot.width=9, repr.plot.height=7)\n",
    "plotError(list(e_ep_nn, e_ep_pz, e_ep_az), cols=c(1,2,colors()[258]))\n",
    "\n",
    "#Noir: neighbors, rouge: persistence, vert: moyenne"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "options(repr.plot.width=9, repr.plot.height=4)\n",
    "plotPredReal(data, p_ep_nn, 4)\n",
    "plotPredReal(data, p_ep_nn, 6)\n",
    "\n",
    "#Bleu: prévue, noir: réalisée"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "À gauche un jour \"bien\" prévu, à droite le pic d'erreur (jour 6)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "plotPredReal(data, p_ep_az, 4)\n",
    "plotPredReal(data, p_ep_az, 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "f4_ep = computeFilaments(data, p_ep_nn$getIndexInData(4), plot=TRUE)\n",
    "f6_ep = computeFilaments(data, p_ep_nn$getIndexInData(6), plot=TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(2,2))\n",
    "options(repr.plot.width=9, repr.plot.height=7)\n",
    "plotFilamentsBox(data, f4_ep$indices)\n",
    "plotFilamentsBox(data, f4_ep$indices+1)\n",
    "plotFilamentsBox(data, f6_ep$indices)\n",
    "plotFilamentsBox(data, f6_ep$indices+1)\n",
    "\n",
    "#En haut : jour 4 + lendemain (5) ; en bas : jour 6 + lendemain (7)\n",
    "#À gauche : premières 24h ; à droite : 24h suivantes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"Voisinages\" catastrophiques : les jours 4 et 6 sont trop atypiques."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "options(repr.plot.width=9, repr.plot.height=4)\n",
    "plotRelativeVariability(data, f4_ep$indices)\n",
    "plotRelativeVariability(data, f6_ep$indices)\n",
    "\n",
    "#Variabilité sur 60 courbes au hasard en rouge ; sur nos 60 voisins (+ lendemains) en noir"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il faudrait que la courbe noire soit nettement plus basse que la courbe rouge."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "plotSimils(p_ep_nn, 4)\n",
    "plotSimils(p_ep_nn, 6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Poids très concentrés près de zéro pour les prédictions avec peu de voisins."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Fenêtres sélectionnées dans ]0,10] / endo à gauche, exo à droite\n",
    "p_ep_nn$getParams(4)$window\n",
    "p_ep_nn$getParams(6)$window"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 style=\"color:blue;font-size:2em\">Semaine non polluée</h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "indices_np = seq(as.Date(\"2015-04-26\"),as.Date(\"2015-05-02\"),\"days\")\n",
    "p_np_nn = computeForecast(data,indices_np, \"Neighbors\", \"Neighbors\", simtype=\"mix\")\n",
    "p_np_pz = computeForecast(data, indices_np, \"Persistence\", \"Zero\", same_day=FALSE)\n",
    "p_np_az = computeForecast(data, indices_np, \"Average\", \"Zero\") #, memory=183)\n",
    "#p_np_zz = computeForecast(data, indices_np, \"Zero\", \"Zero\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "e_np_nn = computeError(data, p_np_nn)\n",
    "e_np_pz = computeError(data, p_np_pz)\n",
    "e_np_az = computeError(data, p_np_az)\n",
    "#e_np_zz = computeError(data, p_np_zz)\n",
    "options(repr.plot.width=9, repr.plot.height=7)\n",
    "plotError(list(e_np_nn, e_np_pz, e_np_az), cols=c(1,2,colors()[258]))\n",
    "\n",
    "#Noir: neighbors, rouge: persistence, vert: moyenne"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Performances des méthodes \"Average\" et \"Neighbors\" comparables ; mauvais résultats pour la persistence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "options(repr.plot.width=9, repr.plot.height=4)\n",
    "plotPredReal(data, p_np_nn, 5)\n",
    "plotPredReal(data, p_np_nn, 6)\n",
    "\n",
    "#Bleu: prévue, noir: réalisée"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "plotPredReal(data, p_np_az, 5)\n",
    "plotPredReal(data, p_np_az, 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "f5_np = computeFilaments(data, p_np_nn$getIndexInData(5), plot=TRUE)\n",
    "f6_np = computeFilaments(data, p_np_nn$getIndexInData(6), plot=TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(2,2))\n",
    "options(repr.plot.width=9, repr.plot.height=7)\n",
    "plotFilamentsBox(data, f5_np$indices)\n",
    "plotFilamentsBox(data, f5_np$indices+1)\n",
    "plotFilamentsBox(data, f6_np$indices)\n",
    "plotFilamentsBox(data, f6_np$indices+1)\n",
    "\n",
    "#En haut : jour 3 + lendemain (4) ; en bas : jour 6 + lendemain (7)\n",
    "#À gauche : premières 24h ; à droite : 24h suivantes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Jours \"typiques\", donc beaucoup de voisins. En revanche les lendemains des jours similaires sont très variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "options(repr.plot.width=9, repr.plot.height=4)\n",
    "plotRelativeVariability(data, f5_np$indices)\n",
    "plotRelativeVariability(data, f6_np$indices)\n",
    "\n",
    "#Variabilité sur 60 courbes au hasard en rouge ; sur nos 60 voisins (+ lendemains) en noir"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bonne situation : la courbe noire est toujours assez nettement en dessous."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "plotSimils(p_np_nn, 5)\n",
    "plotSimils(p_np_nn, 6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Répartition idéale des poids : quelques uns au-delà de 0.3-0.4, le reste très proche de zéro."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Fenêtres sélectionnées dans ]0,10] / endo à gauche, exo à droite\n",
    "p_np_nn$getParams(5)$window\n",
    "p_np_nn$getParams(6)$window"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bilan\n",
    "\n",
    "Problème difficile : on ne fait guère mieux qu'une naïve moyenne des lendemains des jours similaires dans le passé, ce qui n'est pas loin de prédire une série constante égale à la dernière valeur observée (méthode \"zéro\"). La persistence donne parfois de bons résultats mais est trop instable (sensibilité à l'argument <code>same_day</code>).\n",
    "\n",
    "Comment améliorer la méthode ?"
   ]
  }
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