Package: talweg
Title: Time-Series Samples Forecasted With Exogenous Variables
Version: 0.1-0
-Description: Forecast a curve sampled within the day (seconds, minutes, hours...),
- using past measured curves + paste exogenous informations,
- which could be some aggregated measure on the past curves, the weather...
- Main starting point: computeForecast().
+Description: Forecast a curve sampled within the day (seconds, minutes,
+ hours...), using past measured curves + paste exogenous informations, which
+ could be some aggregated measure on the past curves, the weather... Main
+ starting point: computeForecast().
Author: Benjamin Auder <Benjamin.Auder@math.u-psud.fr> [aut,cre],
Jean-Michel Poggi <Jean-Michel.Poggi@parisdescartes.fr> [ctb],
Bruno Portier <Bruno.Portier@insa-rouen.fr>, [ctb]
LazyData: yes
URL: http://git.auder.net/?p=talweg.git
License: MIT + file LICENSE
-RoxygenNote: 6.0.1
-Collate:
+RoxygenNote: 5.0.1
+Collate:
'A_NAMESPACE.R'
'Data.R'
'Forecaster.R'
'F_Average.R'
'F_Neighbors.R'
+ 'F_Neighbors2.R'
'F_Persistence.R'
'F_Zero.R'
'Forecast.R'
# Indices of similar days for cross-validation; TODO: 45 = magic number
sdays = getSimilarDaysIndices(today, limit=45, same_season=FALSE)
+ cv_days = intersect(fdays,sdays)
+ # Limit to 20 most recent matching days (TODO: 20 == magic number)
+ cv_days = sort(cv_days,decreasing=TRUE)[1:min(20,length(cv_days))]
+
# Function to optimize h : h |--> sum of prediction errors on last 45 "similar" days
errorOnLastNdays = function(h, kernel, simtype)
{
error = 0
nb_jours = 0
- for (i in intersect(fdays,sdays))
+ for (i in seq_along(cv_days))
{
# mix_strategy is never used here (simtype != "mix"), therefore left blank
prediction = private$.predictShapeAux(data,
- fdays, i, horizon, h, kernel, simtype, FALSE)
+ fdays, cv_days[i], horizon, h, kernel, simtype, FALSE)
if (!is.na(prediction[1]))
{
nb_jours = nb_jours + 1
error = error +
- mean((data$getCenteredSerie(i+1)[1:horizon] - prediction)^2)
+ mean((data$getCenteredSerie(cv_days[i]+1)[1:horizon] - prediction)^2)
}
}
return (error / nb_jours)
h_endo = ifelse(simtype=="mix", h[1], h)
# Distances from last observed day to days in the past
- distances2 = rep(NA, length(fdays))
- for (i in seq_along(fdays))
- {
- delta = data$getCenteredSerie(today) - data$getCenteredSerie(fdays[i])
- # Require at least half of non-NA common values to compute the distance
- if ( !any( is.na(delta) ) )
- distances2[i] = mean(delta^2)
- Centered}
+ serieToday = data$getSerie(today)
+ distances2 = sapply(fdays, function(i) {
+ delta = serieToday - data$getSerie(i)
+ mean(delta^2)
+ })
sd_dist = sd(distances2)
if (sd_dist < .Machine$double.eps)
sigma_inv = solve(sigma) #TODO: use pseudo-inverse if needed?
# Distances from last observed day to days in the past
- distances2 = rep(NA, nrow(M)-1)
- for (i in 2:nrow(M))
- {
- delta = M[1,] - M[i,]
- distances2[i-1] = delta %*% sigma_inv %*% delta
- }
+ distances2 = sapply(seq_along(fdays), function(i) {
+ delta = M[1,] - M[i+1,]
+ delta %*% sigma_inv %*% delta
+ })
sd_dist = sd(distances2)
if (sd_dist < .Machine$double.eps)
inherit = Forecaster,
public = list(
+ predictSerie = function(data, today, memory, horizon, ...)
+ {
+ # Parameters (potentially) computed during shape prediction stage
+ predicted_shape = self$predictShape(data, today, memory, horizon, ...)
+# predicted_delta = private$.pjump(data,today,memory,horizon,private$.params,...)
+ # Predicted shape is aligned it on the end of current day + jump
+# predicted_shape+tail(data$getSerie(today),1)-predicted_shape[1]+predicted_delta
+ predicted_shape
+ },
predictShape = function(data, today, memory, horizon, ...)
{
# (re)initialize computed parameters
fdays = getNoNA2(data, max(today-memory,1), today-1)
# Get optional args
+ simtype = ifelse(hasArg("simtype"), list(...)$simtype, "mix") #or "endo", or "exo"
kernel = ifelse(hasArg("kernel"), list(...)$kernel, "Gauss") #or "Epan"
if (hasArg(h_window))
{
return ( private$.predictShapeAux(data,
- fdays, today, horizon, list(...)$h_window, kernel, TRUE) )
+ fdays, today, horizon, list(...)$h_window, kernel, simtype, TRUE) )
}
# Indices of similar days for cross-validation; TODO: 45 = magic number
sdays = getSimilarDaysIndices(today, limit=45, same_season=FALSE)
+ cv_days = intersect(fdays,sdays)
+ # Limit to 20 most recent matching days (TODO: 20 == magic number)
+ cv_days = sort(cv_days,decreasing=TRUE)[1:min(20,length(cv_days))]
+
# Function to optimize h : h |--> sum of prediction errors on last 45 "similar" days
- errorOnLastNdays = function(h, kernel)
+ errorOnLastNdays = function(h, kernel, simtype)
{
error = 0
nb_jours = 0
- for (day in intersect(fdays,sdays))
+ for (i in seq_along(cv_days))
{
# mix_strategy is never used here (simtype != "mix"), therefore left blank
- prediction = private$.predictShapeAux(data,fdays,day,horizon,h,kernel,FALSE)
+ prediction = private$.predictShapeAux(data,
+ fdays, cv_days[i], horizon, h, kernel, simtype, FALSE)
if (!is.na(prediction[1]))
{
nb_jours = nb_jours + 1
error = error +
- mean((data$getSerie(i+1)[1:horizon] - prediction)^2)
+ mean((data$getSerie(cv_days[i]+1)[1:horizon] - prediction)^2)
}
}
return (error / nb_jours)
}
- # h :: only for endo in this variation
- h_best = optimize(errorOnLastNdays, c(0,7), kernel=kernel)$minimum
- return (private$.predictShapeAux(data,fdays,today,horizon,h_best,kernel,TRUE))
+ if (simtype != "endo")
+ {
+ h_best_exo = optimize(
+ errorOnLastNdays, c(0,10), kernel=kernel, simtype="exo")$minimum
+ }
+ if (simtype != "exo")
+ {
+ h_best_endo = optimize(
+ errorOnLastNdays, c(0,10), kernel=kernel, simtype="endo")$minimum
+ }
+
+ if (simtype == "endo")
+ {
+ return (private$.predictShapeAux(data,
+ fdays, today, horizon, h_best_endo, kernel, "endo", TRUE))
+ }
+ if (simtype == "exo")
+ {
+ return (private$.predictShapeAux(data,
+ fdays, today, horizon, h_best_exo, kernel, "exo", TRUE))
+ }
+ if (simtype == "mix")
+ {
+ h_best_mix = c(h_best_endo,h_best_exo)
+ return(private$.predictShapeAux(data,
+ fdays, today, horizon, h_best_mix, kernel, "mix", TRUE))
+ }
}
),
private = list(
# Precondition: "today" is full (no NAs)
- .predictShapeAux = function(data, fdays, today, horizon, h, kernel, final_call)
+ .predictShapeAux = function(data, fdays, today, horizon, h, kernel, simtype, final_call)
{
fdays = fdays[ fdays < today ]
# TODO: 3 = magic number
sdays = getSimilarDaysIndices(today, limit=45, same_season=TRUE, data)
indices = intersect(fdays,sdays)
levelToday = data$getLevel(today)
- distances = sapply(seq_along(indices), function(i) abs(data$getLevel(i)-levelToday))
+ distances = sapply(indices, function(i) abs(data$getLevel(i)-levelToday))
same_pollution = (distances <= 2)
if (sum(same_pollution) < 3) #TODO: 3 == magic number
{
}
indices = indices[same_pollution]
- # Now OK: indices same season, same pollution level
- # ...........
-
+ if (simtype != "exo")
+ {
+ h_endo = ifelse(simtype=="mix", h[1], h)
- # ENDO:: Distances from last observed day to days in the past
- serieToday = data$getSerie(today)
- distances2 = sapply(indices, function(i) {
- delta = serieToday - data$getSerie(i)
- distances2[i] = mean(delta^2)
- })
+ # Distances from last observed day to days in the past
+ serieToday = data$getSerie(today)
+ distances2 = sapply(indices, function(i) {
+ delta = serieToday - data$getSerie(i)
+ mean(delta^2)
+ })
- sd_dist = sd(distances2)
- if (sd_dist < .Machine$double.eps)
- {
+ sd_dist = sd(distances2)
+ if (sd_dist < .Machine$double.eps)
+ {
# warning("All computed distances are very close: stdev too small")
- sd_dist = 1 #mostly for tests... FIXME:
+ sd_dist = 1 #mostly for tests... FIXME:
+ }
+ simils_endo =
+ if (kernel=="Gauss")
+ exp(-distances2/(sd_dist*h_endo^2))
+ else
+ {
+ # Epanechnikov
+ u = 1 - distances2/(sd_dist*h_endo^2)
+ u[abs(u)>1] = 0.
+ u
+ }
}
- simils_endo =
- if (kernel=="Gauss")
- exp(-distances2/(sd_dist*h_endo^2))
- else
+
+ if (simtype != "endo")
+ {
+ h_exo = ifelse(simtype=="mix", h[2], h)
+
+ M = matrix( nrow=1+length(indices), ncol=1+length(data$getExo(today)) )
+ M[1,] = c( data$getLevel(today), as.double(data$getExo(today)) )
+ for (i in seq_along(indices))
+ M[i+1,] = c( data$getLevel(indices[i]), as.double(data$getExo(indices[i])) )
+
+ sigma = cov(M) #NOTE: robust covariance is way too slow
+# sigma_inv = solve(sigma) #TODO: use pseudo-inverse if needed?
+ sigma_inv = MASS::ginv(sigma)
+#if (final_call) browser()
+ # Distances from last observed day to days in the past
+ distances2 = sapply(seq_along(indices), function(i) {
+ delta = M[1,] - M[i+1,]
+ delta %*% sigma_inv %*% delta
+ })
+
+ sd_dist = sd(distances2)
+ if (sd_dist < .25 * sqrt(.Machine$double.eps))
{
- # Epanechnikov
- u = 1 - distances2/(sd_dist*h_endo^2)
- u[abs(u)>1] = 0.
- u
+# warning("All computed distances are very close: stdev too small")
+ sd_dist = 1 #mostly for tests... FIXME:
}
+ simils_exo =
+ if (kernel=="Gauss")
+ exp(-distances2/(sd_dist*h_exo^2))
+ else
+ {
+ # Epanechnikov
+ u = 1 - distances2/(sd_dist*h_exo^2)
+ u[abs(u)>1] = 0.
+ u
+ }
+ }
-# # EXOGENS: distances computations are enough
-# # TODO: search among similar concentrations....... at this stage ?!
-# M = matrix( nrow=1+length(fdays), ncol=1+length(data$getExo(today)) )
-# M[1,] = c( data$getLevel(today), as.double(data$getExo(today)) )
-# for (i in seq_along(fdays))
-# M[i+1,] = c( data$getLevel(fdays[i]), as.double(data$getExo(fdays[i])) )
-#
-# sigma = cov(M) #NOTE: robust covariance is way too slow
-# sigma_inv = solve(sigma) #TODO: use pseudo-inverse if needed?
-#
-# # Distances from last observed day to days in the past
-# distances2 = rep(NA, nrow(M)-1)
-# for (i in 2:nrow(M))
-# {
-# delta = M[1,] - M[i,]
-# distances2[i-1] = delta %*% sigma_inv %*% delta
-# }
-
- similarities = simils_endo
+ similarities =
+ if (simtype == "exo")
+ simils_exo
+ else if (simtype == "endo")
+ simils_endo
+ else #mix
+ simils_endo * simils_exo
prediction = rep(0, horizon)
for (i in seq_along(indices))
if (final_call)
{
private$.params$weights <- similarities
- private$.params$indices <- indices
- private$.params$window <- h
+ private$.params$indices <- fdays
+ private$.params$window <-
+ if (simtype=="endo")
+ h_endo
+ else if (simtype=="exo")
+ h_exo
+ else #mix
+ c(h_endo,h_exo)
}
return (prediction)
forecaster_class_name = getFromNamespace(paste(forecaster,"Forecaster",sep=""), "talweg")
forecaster = forecaster_class_name$new( #.pjump =
getFromNamespace(paste("get",pjump,"JumpPredict",sep=""), "talweg"))
- for (today in integer_indices)
- {
- pred$append(
- new_serie = forecaster$predictSerie(data, today, memory, horizon, ...),
- new_params = forecaster$getParameters(),
- new_index_in_data = today
- )
- }
+
+#oo = forecaster$predictSerie(data, integer_indices[1], memory, horizon, ...)
+#browser()
+
+ library(parallel)
+ ppp <- parallel::mclapply(seq_along(integer_indices), function(i) {
+ list(
+ "forecast" = forecaster$predictSerie(data, integer_indices[i], memory, horizon, ...),
+ "params"= forecaster$getParameters(),
+ "index" = integer_indices[i] )
+ }, mc.cores=3)
+
+#browser()
+
+for (i in seq_along(integer_indices))
+{
+ pred$append(
+ new_serie = ppp[[i]]$forecast,
+ new_params = ppp[[i]]$params,
+ new_index_in_data = ppp[[i]]$index
+ )
+}
+
pred
}
<h2>Introduction</h2>
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
+(la seule dont on a parlé) et sa variante récente appelée pour l'instant "Neighbors2".<br>
- * simtype="exo" ou "mix" : similarités exogènes avec/sans endogènes (fenêtre optimisée par VC)
+ * simtype="exo", "endo" ou "mix" : type de similarités (fenêtre optimisée par VC)
* same_season=FALSE : les indices pour la validation croisée ne tiennent pas compte des saisons
* mix_strategy="mult" : on multiplie les poids (au lieu d'en éteindre)
"cells": [
{
"cell_type": "markdown",
- "metadata": {},
+ "metadata": {
+ "deletable": true,
+ "editable": true
+ },
"source": [
"\n",
"\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"library(talweg)\n",
"\n",
"ts_data = read.csv(system.file(\"extdata\",\"pm10_mesures_H_loc_report.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\",\n",
- "\tpredict_at=7) #predict from P+1 to P+H included\n",
+ "# Predict from P+1 to P+H included\n",
+ "H = 17\n",
+ "data = getData(ts_data, exo_data, input_tz = \"GMT\", working_tz=\"GMT\", predict_at=7)\n",
"\n",
"indices_ch = seq(as.Date(\"2015-01-18\"),as.Date(\"2015-01-24\"),\"days\")\n",
"indices_ep = seq(as.Date(\"2015-03-15\"),as.Date(\"2015-03-21\"),\"days\")\n",
- "indices_np = seq(as.Date(\"2015-04-26\"),as.Date(\"2015-05-02\"),\"days\")\n"
+ "indices_np = seq(as.Date(\"2015-04-26\"),as.Date(\"2015-05-02\"),\"days\")"
]
},
{
"cell_type": "markdown",
- "metadata": {},
+ "metadata": {
+ "deletable": true,
+ "editable": true
+ },
"source": [
"\n",
"\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
- "p_nn_exo = computeForecast(data, indices_ch, \"Neighbors\", \"Neighbors\",\n",
- "\thorizon=3, simtype=\"exo\")\n",
- "p_nn_mix = computeForecast(data, indices_ch, \"Neighbors\", \"Neighbors\",\n",
- "\thorizon=3, simtype=\"mix\")\n",
- "p_az = computeForecast(data, indices_ch, \"Average\", \"Zero\",\n",
- "\thorizon=3)\n",
- "p_pz = computeForecast(data, indices_ch, \"Persistence\", \"Zero\",\n",
- "\thorizon=3, same_day=TRUE)"
+ "reload(\"../pkg\")\n",
+ "p1 = computeForecast(data, indices_ch, \"Neighbors\", \"Zero\", horizon=H, simtype=\"exo\")\n",
+ "p2 = computeForecast(data, indices_ch, \"Neighbors\", \"Zero\", horizon=H, simtype=\"endo\")\n",
+ "p3 = computeForecast(data, indices_ch, \"Neighbors\", \"Zero\", horizon=H, simtype=\"mix\")\n",
+ "p4 = computeForecast(data, indices_ch, \"Neighbors2\", \"Zero\", horizon=H, simtype=\"exo\")\n",
+ "p5 = computeForecast(data, indices_ch, \"Neighbors2\", \"Zero\", horizon=H, simtype=\"endo\")\n",
+ "p6 = computeForecast(data, indices_ch, \"Neighbors2\", \"Zero\", horizon=H, simtype=\"mix\")\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "e1 = computeError(data, p1, H)\n",
+ "e2 = computeError(data, p2, H)\n",
+ "e3 = computeError(data, p3, H)\n",
+ "e4 = computeError(data, p4, H)\n",
+ "e5 = computeError(data, p5, H)\n",
+ "e6 = computeError(data, p6, H)\n",
+ "plotError(list(e1,e2,e3,e4,e5,e6), cols=c(1,2,colors()[258], 4,5,6))"
]
},
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"e_nn_exo = computeError(data, p_nn_exo, 3)\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"options(repr.plot.width=9, repr.plot.height=4)\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"par(mfrow=c(1,2))\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"par(mfrow=c(1,2))\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"par(mfrow=c(1,2))\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"par(mfrow=c(1,2))\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"# Fenêtres sélectionnées dans ]0,10] / endo à gauche, exo à droite\n",
},
{
"cell_type": "markdown",
- "metadata": {},
+ "metadata": {
+ "deletable": true,
+ "editable": true
+ },
"source": [
"\n",
"\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"p_nn_exo = computeForecast(data, indices_ep, \"Neighbors\", \"Neighbors\",\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"e_nn_exo = computeError(data, p_nn_exo, 3)\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"options(repr.plot.width=9, repr.plot.height=4)\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"par(mfrow=c(1,2))\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"par(mfrow=c(1,2))\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"par(mfrow=c(1,2))\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"par(mfrow=c(1,2))\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"# Fenêtres sélectionnées dans ]0,10] / endo à gauche, exo à droite\n",
},
{
"cell_type": "markdown",
- "metadata": {},
+ "metadata": {
+ "deletable": true,
+ "editable": true
+ },
"source": [
"\n",
"\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"p_nn_exo = computeForecast(data, indices_np, \"Neighbors\", \"Neighbors\",\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"e_nn_exo = computeError(data, p_nn_exo, 3)\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"options(repr.plot.width=9, repr.plot.height=4)\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"par(mfrow=c(1,2))\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"par(mfrow=c(1,2))\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"par(mfrow=c(1,2))\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"par(mfrow=c(1,2))\n",
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
"outputs": [],
"source": [
"# Fenêtres sélectionnées dans ]0,10] / endo à gauche, exo à droite\n",
},
{
"cell_type": "markdown",
- "metadata": {},
+ "metadata": {
+ "deletable": true,
+ "editable": true
+ },
"source": [
"\n",
"\n",
projects / talweg.git / commitdiff