[talweg.git] / pkg / R / plot.R

#' Plot curves
#'
#' Plot a range of curves in data
#'
#' @param data Object of class Data
#' @param indices Range of indices (integers or dates)
#'
#' @export
plotCurves <- function(data, indices=seq_len(data$getSize()))
{
	series = data$getSeries(indices)
	yrange = quantile(series, probs=c(0.025,0.975), na.rm=TRUE)
	par(mar=c(4.7,5,1,1), cex.axis=1.5, cex.lab=1.5)
	for (i in seq_along(indices))
	{
		plot(series[,i], type="l", ylim=yrange,
			xlab=ifelse(i==1,"Time (hours)",""), ylab=ifelse(i==1,"PM10",""))
		if (i < length(indices))
			par(new=TRUE)
	}
}

#' Plot error
#'
#' Draw error graphs, potentially from several runs of \code{computeForecast}
#'
#' @param err Error as returned by \code{computeError}
#' @param cols Colors for each error (default: 1,2,3,...)
#'
#' @seealso \code{\link{plotCurves}}, \code{\link{plotPredReal}},
#'   \code{\link{plotSimils}}, \code{\link{plotFbox}},
#'   \code{\link{computeFilaments}, }\code{\link{plotFilamentsBox}}, \code{\link{plotRelVar}}
#'
#' @export
plotError <- function(err, cols=seq_along(err))
{
	if (!is.null(err$abs))
		err = list(err)
	par(mfrow=c(2,2), mar=c(4.7,5,1,1), cex.axis=1.5, cex.lab=1.5, lwd=2)
	L = length(err)
	yrange = range( sapply(1:L, function(i) ( err[[i]]$abs$day ) ), na.rm=TRUE )
	for (i in seq_len(L))
	{
		plot(err[[i]]$abs$day, type="l", xlab=ifelse(i==1,"Time (hours)",""),
			ylab=ifelse(i==1,"Mean |y - y_hat|",""), ylim=yrange, col=cols[i])
		if (i < L)
			par(new=TRUE)
	}
	yrange = range( sapply(1:L, function(i) ( err[[i]]$abs$indices ) ), na.rm=TRUE )
	for (i in seq_len(L))
	{
		plot(err[[i]]$abs$indices, type="l", xlab=ifelse(i==1,"Time (days)",""),
			ylab=ifelse(i==1,"Mean |y - y_hat|",""), ylim=yrange, col=cols[i])
		if (i < L)
			par(new=TRUE)
	}
	yrange = range( sapply(1:L, function(i) ( err[[i]]$MAPE$day ) ), na.rm=TRUE )
	for (i in seq_len(L))
	{
		plot(err[[i]]$MAPE$day, type="l", xlab=ifelse(i==1,"Time (hours)",""),
			ylab=ifelse(i==1,"Mean MAPE",""), ylim=yrange, col=cols[i])
		if (i < L)
			par(new=TRUE)
	}
	yrange = range( sapply(1:L, function(i) ( err[[i]]$MAPE$indices ) ), na.rm=TRUE )
	for (i in seq_len(L))
	{
		plot(err[[i]]$MAPE$indices, type="l", xlab=ifelse(i==1,"Time (days)",""),
			ylab=ifelse(i==1,"Mean MAPE",""), ylim=yrange, col=cols[i])
		if (i < L)
			par(new=TRUE)
	}
}

#' Plot measured / predicted
#'
#' Plot measured curve (in black) and predicted curve (in blue)
#'
#' @param data Object return by \code{getData}
#' @param pred Object as returned by \code{computeForecast}
#' @param index Index in forecasts (integer or date)
#'
#' @export
plotPredReal <- function(data, pred, index)
{
	horizon = length(pred$getSerie(1))
	measure = data$getSerie( pred$getIndexInData(index)+1 )[1:horizon]
	prediction = pred$getSerie(index)
	yrange = range(measure, prediction)
	par(mar=c(4.7,5,1,1), cex.axis=1.5, cex.lab=1.5, lwd=3)
	plot(measure, type="l", ylim=yrange, xlab="Time (hours)", ylab="PM10")
	par(new=TRUE)
	plot(prediction, type="l", col="#0000FF", ylim=yrange, xlab="", ylab="")
}

#' Plot similarities
#'
#' Plot histogram of similarities (weights)
#'
#' @param pred Object as returned by \code{computeForecast}
#' @param index Index in forecasts (integer or date)
#'
#' @export
plotSimils <- function(pred, index)
{
	weights = pred$getParams(index)$weights
	if (is.null(weights))
		stop("plotSimils only works on 'Neighbors' forecasts")
	par(mar=c(4.7,5,1,1), cex.axis=1.5, cex.lab=1.5)
	hist(pred$getParams(index)$weights, nclass=20, main="", xlab="Weight", ylab="Count")
}

#' Functional boxplot
#'
#' Draw the functional boxplot on the left, and bivariate plot on the right
#'
#' @param data Object return by \code{getData}
#' @param indices integer or date indices to process
#'
#' @export
plotFbox <- function(data, indices=seq_len(data$getSize()))
{
	if (!requireNamespace("rainbow", quietly=TRUE))
		stop("Functional boxplot requires the rainbow package")

	series_matrix = data$getSeries(indices)
	# Remove series with NAs
	no_NAs_indices = sapply( 1:ncol(series_matrix),
		function(i) all(!is.na(series_matrix[,i])) )
	series_matrix = series_matrix[,no_NAs_indices]

	series_fds = rainbow::fds(seq_len(nrow(series_matrix)), series_matrix)
	par(mar=c(4.7,5,1,1), cex.axis=1.5, cex.lab=1.5)
	rainbow::fboxplot(series_fds, "functional", "hdr", xlab="Time (hours)", ylab="PM10",
		plotlegend=FALSE, lwd=2)
	rainbow::fboxplot(series_fds, "bivariate", "hdr", plotlegend=FALSE)
}

#' Compute filaments
#'
#' Get similar days in the past, as black as distances are small
#'
#' @param data Object as returned by \code{getData}
#' @param pred Object of class Forecast
#' @param index Index in forecast (integer or date)
#' @param limit Number of neighbors to consider
#' @param plot Should the result be plotted?
#'
#' @return A list with
#' \itemize{
#'   \item index : index of the current serie ('today')
#'   \item neighb_indices : indices of its neighbors
#'   \item colors : colors of neighbors curves (shades of gray)
#' }
#'
#' @export
computeFilaments <- function(data, pred, index, limit=60, plot=TRUE)
{
	ref_serie = data$getCenteredSerie( pred$getIndexInData(index) )
	if (any(is.na(ref_serie)))
		stop("computeFilaments requires a serie without NAs")

	# Compute colors for each neighbor (from darkest to lightest)
	sorted_dists = sort(-log(pred$getParams(index)$weights), index.return=TRUE)
	nn = min(limit, length(sorted_dists$x))
	min_dist = min(sorted_dists$x[1:nn])
	max_dist = max(sorted_dists$x[1:nn])
	color_values = floor(19.5*(sorted_dists$x[1:nn]-min_dist)/(max_dist-min_dist)) + 1
	colors = gray.colors(20,0.1,0.9)[color_values] #TODO: 20 == magic number

	if (plot)
	{
		# Complete series with (past and present) tomorrows
		ref_serie = c(ref_serie, data$getCenteredSerie( pred$getIndexInData(index)+1 ))
		centered_series = rbind(
			data$getCenteredSeries( pred$getParams(index)$indices ),
			data$getCenteredSeries( pred$getParams(index)$indices+1 ) )
		yrange = range( ref_serie, quantile(centered_series, probs=c(0.025,0.975), na.rm=TRUE) )
		par(mar=c(4.7,5,1,1), cex.axis=1.5, cex.lab=1.5, lwd=2)
		for (i in nn:1)
		{
			plot(centered_series[,sorted_dists$ix[i]], ylim=yrange, type="l", col=colors[i],
				xlab=ifelse(i==1,"Time (hours)",""), ylab=ifelse(i==1,"Centered PM10",""))
			par(new=TRUE)
		}
		# Also plot ref curve, in red
		plot(ref_serie, ylim=yrange, type="l", col="#FF0000", xlab="", ylab="")
		abline(v=24, lty=2, col=colors()[56], lwd=1)
	}

	list(
		"index"=pred$getIndexInData(index),
		"neighb_indices"=pred$getParams(index)$indices[sorted_dists$ix[1:nn]],
		"colors"=colors)
}

#' Functional boxplot on filaments
#'
#' Draw the functional boxplot on filaments obtained by \code{computeFilaments}
#'
#' @param data Object return by \code{getData}
#' @param fil Output of \code{computeFilaments}
#'
#' @export
plotFilamentsBox = function(data, fil)
{
	if (!requireNamespace("rainbow", quietly=TRUE))
		stop("Functional boxplot requires the rainbow package")

	series_matrix = rbind(
		data$getSeries(fil$neighb_indices), data$getSeries(fil$neighb_indices+1) )
	series_fds = rainbow::fds(seq_len(nrow(series_matrix)), series_matrix)
	par(mar=c(4.7,5,1,1), cex.axis=1.5, cex.lab=1.5)
	rainbow::fboxplot(series_fds, "functional", "hdr", xlab="Time (hours)", ylab="PM10",
		plotlegend=FALSE, lwd=2)

	# "Magic" found at http://stackoverflow.com/questions/13842560/get-xlim-from-a-plot-in-r
	usr <- par("usr")
	yr <- (usr[4] - usr[3]) / 27
	par(new=TRUE)
	plot(c(data$getSerie(fil$index),data$getSerie(fil$index+1)), type="l", lwd=2, lty=2,
		ylim=c(usr[3] + yr, usr[4] - yr), xlab="", ylab="")
	abline(v=24, lty=2, col=colors()[56])
}

#' Plot relative conditional variability / absolute variability
#'
#' Draw the relative conditional variability / absolute variability based on filaments
#' obtained by \code{computeFilaments}
#'
#' @param data Object return by \code{getData}
#' @param fil Output of \code{computeFilaments}
#'
#' @export
plotRelVar = function(data, fil)
{
	ref_var = c( apply(data$getSeries(fil$neighb_indices),1,sd),
		apply(data$getSeries(fil$neighb_indices+1),1,sd) )
	fdays = getNoNA2(data, 1, fil$index-1)
	global_var = c( apply(data$getSeries(fdays),1,sd), apply(data$getSeries(fdays+1),1,sd) )

	yrange = range(ref_var, global_var)
	par(mar=c(4.7,5,1,1), cex.axis=1.5, cex.lab=1.5)
	plot(ref_var, type="l", col=1, lwd=3, ylim=yrange,
		xlab="Time (hours)", ylab="Standard deviation")
	par(new=TRUE)
	plot(global_var, type="l", col=2, lwd=3, ylim=yrange, xlab="", ylab="")
	abline(v=24, lty=2, col=colors()[56])
}
Commit	Line	Data
98e958ca	1	#' Plot curves
e030a6e3	2	#'
af3b84f4	3	#' Plot a range of curves in data
e030a6e3 BA	4	#'
	5	#' @param data Object of class Data
	6	#' @param indices Range of indices (integers or dates)
	7	#'
	8	#' @export
1e20780e	9	plotCurves <- function(data, indices=seq_len(data$getSize()))
e030a6e3	10	{
98e958ca	11	series = data$getSeries(indices)
a5a3a294	12	yrange = quantile(series, probs=c(0.025,0.975), na.rm=TRUE)
e030a6e3 BA	13	par(mar=c(4.7,5,1,1), cex.axis=1.5, cex.lab=1.5)
	14	for (i in seq_along(indices))
	15	{
98e958ca	16	plot(series[,i], type="l", ylim=yrange,
4e25de2c	17	xlab=ifelse(i==1,"Time (hours)",""), ylab=ifelse(i==1,"PM10",""))
1e20780e	18	if (i < length(indices))
e030a6e3 BA	19	par(new=TRUE)
	20	}
	21	}
	22
af3b84f4	23	#' Plot error
3d69ff21	24	#'
af3b84f4	25	#' Draw error graphs, potentially from several runs of \code{computeForecast}
3d69ff21	26	#'
99f83c9a	27	#' @param err Error as returned by \code{computeError}
09cf9c19	28	#' @param cols Colors for each error (default: 1,2,3,...)
3d69ff21	29	#'
98e958ca BA	30	#' @seealso \code{\link{plotCurves}}, \code{\link{plotPredReal}},
	31	#' \code{\link{plotSimils}}, \code{\link{plotFbox}},
	32	#' \code{\link{computeFilaments}, }\code{\link{plotFilamentsBox}}, \code{\link{plotRelVar}}
3d69ff21 BA	33	#'
3d69ff21 BA	34	#' @export
09cf9c19	35	plotError <- function(err, cols=seq_along(err))
3d69ff21	36	{
09cf9c19 BA	37	if (!is.null(err$abs))
09cf9c19 BA	38	err = list(err)
4e95ec8f	39	par(mfrow=c(2,2), mar=c(4.7,5,1,1), cex.axis=1.5, cex.lab=1.5, lwd=2)
3d69ff21	40	L = length(err)
98e958ca	41	yrange = range( sapply(1:L, function(i) ( err[[i]]$abs$day ) ), na.rm=TRUE )
3d69ff21 BA	42	for (i in seq_len(L))
3d69ff21 BA	43	{
4e25de2c BA	44	plot(err[[i]]$abs$day, type="l", xlab=ifelse(i==1,"Time (hours)",""),
4e25de2c BA	45	ylab=ifelse(i==1,"Mean \|y - y_hat\|",""), ylim=yrange, col=cols[i])
3d69ff21 BA	46	if (i < L)
	47	par(new=TRUE)
	48	}
98e958ca	49	yrange = range( sapply(1:L, function(i) ( err[[i]]$abs$indices ) ), na.rm=TRUE )
3d69ff21 BA	50	for (i in seq_len(L))
3d69ff21 BA	51	{
4e25de2c BA	52	plot(err[[i]]$abs$indices, type="l", xlab=ifelse(i==1,"Time (days)",""),
4e25de2c BA	53	ylab=ifelse(i==1,"Mean \|y - y_hat\|",""), ylim=yrange, col=cols[i])
3d69ff21 BA	54	if (i < L)
	55	par(new=TRUE)
	56	}
98e958ca	57	yrange = range( sapply(1:L, function(i) ( err[[i]]$MAPE$day ) ), na.rm=TRUE )
3d69ff21 BA	58	for (i in seq_len(L))
3d69ff21 BA	59	{
4e25de2c BA	60	plot(err[[i]]$MAPE$day, type="l", xlab=ifelse(i==1,"Time (hours)",""),
4e25de2c BA	61	ylab=ifelse(i==1,"Mean MAPE",""), ylim=yrange, col=cols[i])
3d69ff21 BA	62	if (i < L)
	63	par(new=TRUE)
	64	}
98e958ca	65	yrange = range( sapply(1:L, function(i) ( err[[i]]$MAPE$indices ) ), na.rm=TRUE )
3d69ff21 BA	66	for (i in seq_len(L))
3d69ff21 BA	67	{
4e25de2c BA	68	plot(err[[i]]$MAPE$indices, type="l", xlab=ifelse(i==1,"Time (days)",""),
4e25de2c BA	69	ylab=ifelse(i==1,"Mean MAPE",""), ylim=yrange, col=cols[i])
3d69ff21 BA	70	if (i < L)
	71	par(new=TRUE)
	72	}
	73	}
	74
98e958ca BA	75	#' Plot measured / predicted
	76	#'
	77	#' Plot measured curve (in black) and predicted curve (in blue)
	78	#'
	79	#' @param data Object return by \code{getData}
	80	#' @param pred Object as returned by \code{computeForecast}
	81	#' @param index Index in forecasts (integer or date)
	82	#'
	83	#' @export
	84	plotPredReal <- function(data, pred, index)
	85	{
	86	horizon = length(pred$getSerie(1))
	87	measure = data$getSerie( pred$getIndexInData(index)+1 )[1:horizon]
	88	prediction = pred$getSerie(index)
	89	yrange = range(measure, prediction)
	90	par(mar=c(4.7,5,1,1), cex.axis=1.5, cex.lab=1.5, lwd=3)
4e25de2c	91	plot(measure, type="l", ylim=yrange, xlab="Time (hours)", ylab="PM10")
98e958ca BA	92	par(new=TRUE)
	93	plot(prediction, type="l", col="#0000FF", ylim=yrange, xlab="", ylab="")
	94	}
	95
	96	#' Plot similarities
	97	#'
	98	#' Plot histogram of similarities (weights)
	99	#'
	100	#' @param pred Object as returned by \code{computeForecast}
	101	#' @param index Index in forecasts (integer or date)
	102	#'
	103	#' @export
	104	plotSimils <- function(pred, index)
	105	{
	106	weights = pred$getParams(index)$weights
	107	if (is.null(weights))
	108	stop("plotSimils only works on 'Neighbors' forecasts")
	109	par(mar=c(4.7,5,1,1), cex.axis=1.5, cex.lab=1.5)
4e25de2c	110	hist(pred$getParams(index)$weights, nclass=20, main="", xlab="Weight", ylab="Count")
98e958ca BA	111	}
98e958ca BA	112
af3b84f4	113	#' Functional boxplot
3d69ff21	114	#'
af3b84f4	115	#' Draw the functional boxplot on the left, and bivariate plot on the right
3d69ff21 BA	116	#'
3d69ff21 BA	117	#' @param data Object return by \code{getData}
98e958ca	118	#' @param indices integer or date indices to process
3d69ff21 BA	119	#'
3d69ff21 BA	120	#' @export
98e958ca	121	plotFbox <- function(data, indices=seq_len(data$getSize()))
3d69ff21 BA	122	{
	123	if (!requireNamespace("rainbow", quietly=TRUE))
	124	stop("Functional boxplot requires the rainbow package")
	125
98e958ca BA	126	series_matrix = data$getSeries(indices)
98e958ca BA	127	# Remove series with NAs
af3b84f4 BA	128	no_NAs_indices = sapply( 1:ncol(series_matrix),
af3b84f4 BA	129	function(i) all(!is.na(series_matrix[,i])) )
99f83c9a	130	series_matrix = series_matrix[,no_NAs_indices]
3d69ff21 BA	131
3d69ff21 BA	132	series_fds = rainbow::fds(seq_len(nrow(series_matrix)), series_matrix)
fa8078f9	133	par(mar=c(4.7,5,1,1), cex.axis=1.5, cex.lab=1.5)
4e25de2c	134	rainbow::fboxplot(series_fds, "functional", "hdr", xlab="Time (hours)", ylab="PM10",
3d69ff21	135	plotlegend=FALSE, lwd=2)
98e958ca BA	136	rainbow::fboxplot(series_fds, "bivariate", "hdr", plotlegend=FALSE)
	137	}
	138
	139	#' Compute filaments
	140	#'
	141	#' Get similar days in the past, as black as distances are small
	142	#'
	143	#' @param data Object as returned by \code{getData}
8f84543c BA	144	#' @param pred Object of class Forecast
8f84543c BA	145	#' @param index Index in forecast (integer or date)
98e958ca BA	146	#' @param limit Number of neighbors to consider
	147	#' @param plot Should the result be plotted?
	148	#'
	149	#' @return A list with
	150	#' \itemize{
	151	#' \item index : index of the current serie ('today')
	152	#' \item neighb_indices : indices of its neighbors
	153	#' \item colors : colors of neighbors curves (shades of gray)
	154	#' }
	155	#'
	156	#' @export
8f84543c	157	computeFilaments <- function(data, pred, index, limit=60, plot=TRUE)
98e958ca	158	{
8f84543c	159	ref_serie = data$getCenteredSerie( pred$getIndexInData(index) )
98e958ca BA	160	if (any(is.na(ref_serie)))
	161	stop("computeFilaments requires a serie without NAs")
	162
98e958ca	163	# Compute colors for each neighbor (from darkest to lightest)
8f84543c BA	164	sorted_dists = sort(-log(pred$getParams(index)$weights), index.return=TRUE)
	165	nn = min(limit, length(sorted_dists$x))
	166	min_dist = min(sorted_dists$x[1:nn])
	167	max_dist = max(sorted_dists$x[1:nn])
	168	color_values = floor(19.5*(sorted_dists$x[1:nn]-min_dist)/(max_dist-min_dist)) + 1
98e958ca BA	169	colors = gray.colors(20,0.1,0.9)[color_values] #TODO: 20 == magic number
	170
	171	if (plot)
	172	{
	173	# Complete series with (past and present) tomorrows
8f84543c BA	174	ref_serie = c(ref_serie, data$getCenteredSerie( pred$getIndexInData(index)+1 ))
	175	centered_series = rbind(
	176	data$getCenteredSeries( pred$getParams(index)$indices ),
	177	data$getCenteredSeries( pred$getParams(index)$indices+1 ) )
	178	yrange = range( ref_serie, quantile(centered_series, probs=c(0.025,0.975), na.rm=TRUE) )
98e958ca BA	179	par(mar=c(4.7,5,1,1), cex.axis=1.5, cex.lab=1.5, lwd=2)
	180	for (i in nn:1)
	181	{
8f84543c	182	plot(centered_series[,sorted_dists$ix[i]], ylim=yrange, type="l", col=colors[i],
4e25de2c	183	xlab=ifelse(i==1,"Time (hours)",""), ylab=ifelse(i==1,"Centered PM10",""))
98e958ca BA	184	par(new=TRUE)
	185	}
	186	# Also plot ref curve, in red
	187	plot(ref_serie, ylim=yrange, type="l", col="#FF0000", xlab="", ylab="")
6d50a76f	188	abline(v=24, lty=2, col=colors()[56], lwd=1)
98e958ca BA	189	}
98e958ca BA	190
8f84543c BA	191	list(
	192	"index"=pred$getIndexInData(index),
	193	"neighb_indices"=pred$getParams(index)$indices[sorted_dists$ix[1:nn]],
	194	"colors"=colors)
fa8078f9 BA	195	}
fa8078f9 BA	196
af3b84f4	197	#' Functional boxplot on filaments
fa8078f9	198	#'
af3b84f4	199	#' Draw the functional boxplot on filaments obtained by \code{computeFilaments}
fa8078f9 BA	200	#'
fa8078f9 BA	201	#' @param data Object return by \code{getData}
98e958ca	202	#' @param fil Output of \code{computeFilaments}
fa8078f9 BA	203	#'
fa8078f9 BA	204	#' @export
4e25de2c	205	plotFilamentsBox = function(data, fil)
fa8078f9	206	{
98e958ca BA	207	if (!requireNamespace("rainbow", quietly=TRUE))
	208	stop("Functional boxplot requires the rainbow package")
	209
	210	series_matrix = rbind(
	211	data$getSeries(fil$neighb_indices), data$getSeries(fil$neighb_indices+1) )
	212	series_fds = rainbow::fds(seq_len(nrow(series_matrix)), series_matrix)
	213	par(mar=c(4.7,5,1,1), cex.axis=1.5, cex.lab=1.5)
4e25de2c	214	rainbow::fboxplot(series_fds, "functional", "hdr", xlab="Time (hours)", ylab="PM10",
98e958ca BA	215	plotlegend=FALSE, lwd=2)
98e958ca BA	216
fa8078f9 BA	217	# "Magic" found at http://stackoverflow.com/questions/13842560/get-xlim-from-a-plot-in-r
	218	usr <- par("usr")
	219	yr <- (usr[4] - usr[3]) / 27
98e958ca	220	par(new=TRUE)
a5a3a294	221	plot(c(data$getSerie(fil$index),data$getSerie(fil$index+1)), type="l", lwd=2, lty=2,
fa8078f9	222	ylim=c(usr[3] + yr, usr[4] - yr), xlab="", ylab="")
d5fe1f30	223	abline(v=24, lty=2, col=colors()[56])
3d69ff21	224	}
16b1c049	225
af3b84f4	226	#' Plot relative conditional variability / absolute variability
16b1c049	227	#'
af3b84f4 BA	228	#' Draw the relative conditional variability / absolute variability based on filaments
af3b84f4 BA	229	#' obtained by \code{computeFilaments}
16b1c049 BA	230	#'
16b1c049 BA	231	#' @param data Object return by \code{getData}
98e958ca	232	#' @param fil Output of \code{computeFilaments}
16b1c049 BA	233	#'
16b1c049 BA	234	#' @export
4e25de2c	235	plotRelVar = function(data, fil)
16b1c049	236	{
98e958ca BA	237	ref_var = c( apply(data$getSeries(fil$neighb_indices),1,sd),
	238	apply(data$getSeries(fil$neighb_indices+1),1,sd) )
	239	fdays = getNoNA2(data, 1, fil$index-1)
	240	global_var = c( apply(data$getSeries(fdays),1,sd), apply(data$getSeries(fdays+1),1,sd) )
16b1c049	241
af3b84f4	242	yrange = range(ref_var, global_var)
16b1c049	243	par(mar=c(4.7,5,1,1), cex.axis=1.5, cex.lab=1.5)
af3b84f4	244	plot(ref_var, type="l", col=1, lwd=3, ylim=yrange,
4e25de2c	245	xlab="Time (hours)", ylab="Standard deviation")
16b1c049	246	par(new=TRUE)
98e958ca	247	plot(global_var, type="l", col=2, lwd=3, ylim=yrange, xlab="", ylab="")
16b1c049 BA	248	abline(v=24, lty=2, col=colors()[56])
16b1c049 BA	249	}