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# Display a Taylor diagram
# Taylor K.E. (2001)
# Summarizing multiple aspects of model performance in a single diagram
# Journal of Geophysical Research, 106: 7183-7192.
# version 1.0
# progr. Olivier.Eterradossi, 12/2007
# 2007-01-12 - modifications and Anglicizing - Jim Lemon
# version 2.0
# progr. initiale OLE, 8/01/2007
# rev. OLE 3/09/2008 : remove samples with NA's from mean, sd and cor calculations
# 2008-09-04 - integration and more anglicizing - Jim Lemon
# 2008-12-09 - added correlation radii, sd arcs to the pos.cor=FALSE routine
# and stopped the pos.cor=FALSE routine from calculating arcs for zero radius
# Jim Lemon
# 2010-4-30 - added the gamma.col argument for pos.cor=TRUE plots - Jim Lemon
# 2010-6-24 - added mar argument to pos.cor=TRUE plots - Jim Lemon
# 2012-1-31 - added the cex.axis argument - Jim Lemon
# 2019-02-22 - added cex.axis to Olivier's text calls plus adj and srt
taylor.diagram<-function(ref,model,add=FALSE,col="red",pch=19,pos.cor = TRUE,
xlab = "Standard deviation", ylab = "", main = "Taylor Diagram",
show.gamma = TRUE, ngamma = 3, gamma.col = 8, sd.arcs = 0, ref.sd = FALSE,
sd.method = "sample", grad.corr.lines = c(0.2, 0.4, 0.6, 0.8, 0.9),
pcex = 1, cex.axis = 1, normalize = FALSE, mar = c(4, 3, 4, 3), ...) {
grad.corr.full <- c(0, 0.2, 0.4, 0.6, 0.8, 0.9, 0.95, 0.99, 1)
# convert any list elements or data frames to vectors
R <- cor(ref, model, use = "pairwise")
if (is.list(ref))
ref <- unlist(ref)
if (is.list(model))
ref <- unlist(model)
SD <- function(x, subn) {
meanx <- mean(x, na.rm = TRUE)
devx <- x - meanx
ssd <- sqrt(sum(devx * devx, na.rm = TRUE)/(length(x[!is.na(x)]) -
subn))
return(ssd)
}
subn <- sd.method != "sample"
sd.r <- SD(ref, subn)
sd.f <- SD(model, subn)
if (normalize) {
sd.f <- sd.f/sd.r
sd.r <- 1
}
maxsd <- 1.5 * max(sd.f, sd.r)
oldpar <- par("mar", "xpd", "xaxs", "yaxs")
if (!add) {
par(mar = mar)
# display the diagram
if (pos.cor) {
if (nchar(ylab) == 0)
ylab = "Standard deviation"
plot(0, xlim = c(0, maxsd*1.1), ylim = c(0, maxsd*1.1), xaxs = "i",
yaxs = "i", axes = FALSE, main = main, xlab = "",
ylab = ylab, type = "n", cex = cex.axis, ...)
mtext(xlab,side=1,line=2.3)
if (grad.corr.lines[1]) {
for (gcl in grad.corr.lines) lines(c(0, maxsd *
gcl), c(0, maxsd * sqrt(1 - gcl^2)), lty = 3)
}
# add the axes
segments(c(0, 0), c(0, 0), c(0, maxsd), c(maxsd,
0))
axis.ticks <- pretty(c(0, maxsd))
axis.ticks <- axis.ticks[axis.ticks <= maxsd]
axis(1, at = axis.ticks,cex.axis=cex.axis)
axis(2, at = axis.ticks,cex.axis=cex.axis)
if (sd.arcs[1]) {
if (length(sd.arcs) == 1)
sd.arcs <- axis.ticks
for (sdarc in sd.arcs) {
xcurve <- cos(seq(0, pi/2, by = 0.03)) * sdarc
ycurve <- sin(seq(0, pi/2, by = 0.03)) * sdarc
lines(xcurve, ycurve, col = "blue", lty = 3)
}
}
if (show.gamma[1]) {
# if the user has passed a set of gamma values, use that
if (length(show.gamma) > 1) gamma <- show.gamma
# otherwise make up a set
else gamma <- pretty(c(0, maxsd), n = ngamma)[-1]
if (gamma[length(gamma)] > maxsd)
gamma <- gamma[-length(gamma)]
labelpos <- seq(45, 70, length.out = length(gamma))
# do the gamma curves
for (gindex in 1:length(gamma)) {
xcurve <- cos(seq(0, pi, by = 0.03)) * gamma[gindex] + sd.r
# find where to clip the curves
endcurve <- which(xcurve < 0)
endcurve <- ifelse(length(endcurve), min(endcurve) -
1, 105)
ycurve <- sin(seq(0, pi, by = 0.03)) * gamma[gindex]
maxcurve <- xcurve * xcurve + ycurve * ycurve
startcurve <- which(maxcurve > maxsd * maxsd)
startcurve <- ifelse(length(startcurve), max(startcurve) +
1, 0)
lines(xcurve[startcurve:endcurve], ycurve[startcurve:endcurve],
col = gamma.col)
if (xcurve[labelpos[gindex]] > 0)
boxed.labels(xcurve[labelpos[gindex]], ycurve[labelpos[gindex]],
gamma[gindex], border = FALSE)
}
}
# the outer curve for correlation
xcurve <- cos(seq(0, pi/2, by = 0.01)) * maxsd
ycurve <- sin(seq(0, pi/2, by = 0.01)) * maxsd
lines(xcurve, ycurve)
bigtickangles <- acos(seq(0.1, 0.9, by = 0.1))
medtickangles <- acos(seq(0.05, 0.95, by = 0.1))
smltickangles <- acos(seq(0.91, 0.99, by = 0.01))
segments(cos(bigtickangles) * maxsd, sin(bigtickangles) *
maxsd, cos(bigtickangles) * 0.97 * maxsd, sin(bigtickangles) *
0.97 * maxsd)
par(xpd = TRUE)
# the inner curve for reference SD
if (ref.sd) {
xcurve <- cos(seq(0, pi/2, by = 0.01)) * sd.r
ycurve <- sin(seq(0, pi/2, by = 0.01)) * sd.r
lines(xcurve, ycurve)
}
points(sd.r, 0, cex = pcex)
text(cos(c(bigtickangles, acos(c(0.95, 0.99)))) *
1.05 * maxsd, sin(c(bigtickangles, acos(c(0.95,
0.99)))) * 1.05 * maxsd, c(seq(0.1, 0.9, by = 0.1),
0.95, 0.99),cex=cex.axis)
text(maxsd * 0.8, maxsd * 0.8, "Correlation", srt = 315,cex=cex.axis)
segments(cos(medtickangles) * maxsd, sin(medtickangles) *
maxsd, cos(medtickangles) * 0.98 * maxsd, sin(medtickangles) *
0.98 * maxsd)
segments(cos(smltickangles) * maxsd, sin(smltickangles) *
maxsd, cos(smltickangles) * 0.99 * maxsd, sin(smltickangles) *
0.99 * maxsd)
}
else {
x <- ref
y <- model
R <- cor(x, y, use = "pairwise.complete.obs")
E <- mean(x, na.rm = TRUE) - mean(y, na.rm = TRUE)
xprime <- x - mean(x, na.rm = TRUE)
yprime <- y - mean(y, na.rm = TRUE)
sumofsquares <- (xprime - yprime)^2
Eprime <- sqrt(sum(sumofsquares)/length(complete.cases(x)))
E2 <- E^2 + Eprime^2
if (add == FALSE) {
# pourtour du diagramme (display the diagram)
maxray <- 1.5 * max(sd.f, sd.r)
plot(c(-maxray, maxray), c(0, maxray), type = "n",
asp = 1, bty = "n", xaxt = "n", yaxt = "n",
xlim=c(-1.1*maxray,1.1*maxray),
xlab = xlab, ylab = ylab, main = main, cex = cex.axis)
discrete <- seq(180, 0, by = -1)
listepoints <- NULL
for (i in discrete) {
listepoints <- cbind(listepoints, maxray *
cos(i * pi/180), maxray * sin(i * pi/180))
}
listepoints <- matrix(listepoints, 2, length(listepoints)/2)
listepoints <- t(listepoints)
lines(listepoints[, 1], listepoints[, 2])
# axes x,y
lines(c(-maxray, maxray), c(0, 0))
lines(c(0, 0), c(0, maxray))
# lignes radiales jusque R = +/- 0.8
for (i in grad.corr.lines) {
lines(c(0, maxray * i), c(0, maxray * sqrt(1 -
i^2)), lty = 3)
lines(c(0, -maxray * i), c(0, maxray * sqrt(1 -
i^2)), lty = 3)
}
# texte radial
for (i in grad.corr.full) {
text(1.05 * maxray * i, 1.05 * maxray * sqrt(1 -
i^2), i, cex = cex.axis,adj=cos(i)/2)
text(-1.05 * maxray * i, 1.05 * maxray * sqrt(1 -
i^2), -i, cex = cex.axis,adj=1-cos(i)/2)
}
# sd concentriques autour de la reference
seq.sd <- seq.int(0, 2 * maxray, by = (maxray/10))[-1]
for (i in seq.sd) {
xcircle <- sd.r + (cos(discrete * pi/180) *
i)
ycircle <- sin(discrete * pi/180) * i
for (j in 1:length(xcircle)) {
if ((xcircle[j]^2 + ycircle[j]^2) < (maxray^2)) {
points(xcircle[j], ycircle[j], col = "darkgreen",
pch = ".")
if (j == 10)
text(xcircle[j], ycircle[j], signif(i,
2), cex = cex.axis, col = "darkgreen",srt=90)
}
}
}
# sd concentriques autour de l'origine
seq.sd <- seq.int(0, maxray, length.out = 5)
for (i in seq.sd) {
xcircle <- cos(discrete * pi/180) * i
ycircle <- sin(discrete * pi/180) * i
if (i)
lines(xcircle, ycircle, lty = 3, col = "blue")
text(min(xcircle), -0.06 * maxray, signif(i,
2), cex = cex.axis, col = "blue")
text(max(xcircle), -0.06 * maxray, signif(i,
2), cex = cex.axis, col = "blue")
}
text(0, -0.14 * maxray, "Standard Deviation",
cex = cex.axis, col = "blue")
text(0, -0.22 * maxray, "Centered RMS Difference",
cex = cex.axis, col = "darkgreen")
points(sd.r, 0, pch = 22, bg = "darkgreen", cex = pcex)
text(0, 1.2 * maxray, "Correlation Coefficient",
cex = cex.axis)
}
S <- (2 * (1 + R))/(sd.f + (1/sd.f))^2
# Taylor<-S
}
}
# display the points
points(sd.f * R, sd.f * sin(acos(R)), pch = pch, col = col,
cex = pcex)
invisible(oldpar)
}
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