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#'Plotting two probability density gaussian functions and the optimal linear
#'estimation (OLE) as result of combining them.
#'@author Eroteida Sanchez-Garcia - AEMET, \email{esanchezg@aemet.es}
#'@description This function plots two probability density gaussian functions
#'and the optimal linear estimation (OLE) as result of combining them.
#'@param pdf_1 A numeric array with a dimension named 'statistic', containg
#' two parameters: mean' and 'standard deviation' of the first gaussian pdf
#'@param pdf_2 A numeric array with a dimension named 'statistic', containg
#' two parameters: mean' and 'standard deviation' of the second gaussian pdf
#' to combining.
#'@param nsigma (optional) A numeric value for setting the limits of X axis.
#' (Default nsigma = 3).
#'@param legendPos (optional) A character value for setting the position of the
#' legend ("bottom", "top", "right" or "left")(Default 'bottom').
#'@param legendSize (optional) A numeric value for setting the size of the
#' legend text. (Default 1.0).
#'@param plotfile (optional) A filename where the plot will be saved.
#' (Default: the plot is not saved).
#'@param width (optional) A numeric value indicating the plot width in
#' units ("in", "cm", or "mm"). (Default width = 30).
#'@param height (optional) A numeric value indicating the plot height.
#' (Default height = 15).
#'@param units (optional) A character value indicating the plot size
#' unit. (Default units = 'cm').
#'@param dpi (optional) A numeric value indicating the plot resolution.
#' (Default dpi = 300).
#'
#'@return PlotPDFsOLE() returns a ggplot object containing the plot.
#'
#'@examples
#'# Example 1
#'pdf_1 <- c(1.1,0.6)
#'attr(pdf_1, "name") <- "NAO1"
#'dim(pdf_1) <- c(statistic = 2)
#'pdf_2 <- c(1,0.5)
#'attr(pdf_2, "name") <- "NAO2"
#'dim(pdf_2) <- c(statistic = 2)
#'
#'PlotPDFsOLE(pdf_1, pdf_2)
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PlotPDFsOLE <- function(pdf_1, pdf_2, nsigma = 3, legendPos = 'bottom',
legendSize = 1.0, plotfile = NULL, width = 30,
height = 15, units = "cm", dpi = 300) {
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if (!is.numeric(dpi)) {
stop("Parameter 'dpi' must be numeric.")
}
if (length(dpi) > 1) {
warning("Parameter 'dpi' has length greater than 1 and ",
"only the first element will be used.")
dpi <- dpi[1]
}
if (!is.character(units)) {
stop("Parameter 'units' must be character")
}
if (length(units) > 1) {
warning("Parameter 'units' has length greater than 1 and ",
"only the first element will be used.")
units <- units[1]
}
if(!(units %in% c("in", "cm", "mm"))) {
stop("Parameter 'units' must be equal to 'in', 'cm' or 'mm'.")
}
if (!is.numeric(height)) {
stop("Parameter 'height' must be numeric.")
}
if (length(height) > 1) {
warning("Parameter 'height' has length greater than 1 and ",
"only the first element will be used.")
height <- height[1]
}
if (!is.numeric(width)) {
stop("Parameter 'width' must be numeric.")
}
if (length(width) > 1) {
warning("Parameter 'width' has length greater than 1 and ",
"only the first element will be used.")
width <- width[1]
}
if (!is.character(plotfile)) {
stop("Parameter 'plotfile' must be a character string ",
"indicating the path and name of output png file.")
}
}
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if (!is.character(legendPos)) {
stop("Parameter 'legendPos' must be character")
}
if(!(legendPos %in% c("bottom", "top", "right", "left"))) {
stop("Parameter 'legendPos' must be equal to 'bottom', 'top', 'right' or 'left'.")
}
if (!is.numeric(legendSize)) {
stop("Parameter 'legendSize' must be numeric.")
}
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if (!is.numeric(nsigma)) {
stop("Parameter 'nsigma' must be numeric.")
}
if (length(nsigma) > 1) {
warning("Parameter 'nsigma' has length greater than 1 and ",
"only the first element will be used.")
nsigma <- nsigma[1]
}
if (!is.array(pdf_1)) {
stop("Parameter 'pdf_1' must be an array.")
}
if (!is.array(pdf_2)) {
stop("Parameter 'pdf_2' must be an array.")
}
if (!is.numeric(pdf_1)) {
stop("Parameter 'pdf_1' must be a numeric array.")
}
if (!is.numeric(pdf_2)) {
stop("Parameter 'pdf_2' must be a numeric array.")
}
if (is.null(names(dim(pdf_1))) ||
is.null(names(dim(pdf_2)))) {
stop("Parameters 'pdf_1' and 'pdf_2' ",
"should have dimmension names.")
}
if(!('statistic' %in% names(dim(pdf_1)))) {
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stop("Parameter 'pdf_1' must have dimension 'statistic'.")
}
if(!('statistic' %in% names(dim(pdf_2)))) {
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stop("Parameter 'pdf_2' must have dimension 'statistic'.")
}
if (length(dim(pdf_1)) != 1) {
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stop("Parameter 'pdf_1' must have only dimension 'statistic'.")
}
if (length(dim(pdf_2)) != 1) {
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stop("Parameter 'pdf_2' must have only dimension 'statistic'.")
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if ((dim(pdf_1)['statistic'] != 2) || (dim(pdf_2)['statistic'] != 2)) {
stop("Length of dimension 'statistic'",
"of parameter 'pdf_1' and 'pdf_2' must be equal to 2.")
}
if(!is.null(attr(pdf_1, "name"))){
if(!is.character(attr(pdf_1, "name"))){
stop("The 'name' attribute of parameter 'pdf_1' must be a character ",
"indicating the name of the variable of parameter 'pdf_1'.")
}
}
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if(!is.null(attr(pdf_2, "name"))){
if(!is.character(attr(pdf_2, "name"))){
stop("The 'name' attribute of parameter 'pdf_2' must be a character ",
"indicating the name of the variable of parameter 'pdf_2'.")
}
}
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if(is.null(attr(pdf_1, "name"))){
name1 <- "variable 1"
} else {
name1 <- attr(pdf_1, "name")
}
if(is.null(attr(pdf_2, "name"))){
name2 <- "Variable 2"
} else {
name2 <- attr(pdf_2, "name")
}
#-----------------------------------------------------------------------------
# Set parameters of gaussian distributions (mean and sd)
#-----------------------------------------------------------------------------
mean1 <- pdf_1[1]
sigma1 <- pdf_1[2]
mean2 <- pdf_2[1]
sigma2 <- pdf_2[2]
pdfBest <- CombinedPDFs(pdf_1, pdf_2)
meanBest <- pdfBest[1]
sigmaBest <- pdfBest[2]
#-----------------------------------------------------------------------------
# Plot the gaussian distributions
#-----------------------------------------------------------------------------
nameBest <- paste0(name1, " + ", name2)
graphicTitle <- "OPTIMAL LINEAR ESTIMATION"
xlimSup <- max(nsigma * sigmaBest + meanBest, nsigma * sigma1 + mean1,
nsigma * sigma2 + mean2)
xlimInf <- min(-nsigma * sigmaBest+meanBest, - nsigma * sigma1 + mean1,
-nsigma * sigma2 + mean2)
deltax <- (xlimSup - xlimInf) / 10000
x <- seq(xlimInf, xlimSup, deltax)
df1 <- data.frame(x = x, y = dnorm(x, mean = mean1, sd = sigma1),
type = name1)
df2 <- data.frame(x = x, y = dnorm(x, mean = mean2, sd = sigma2),
type = name2)
df3 <- data.frame(x = x, y = dnorm(x, mean = meanBest, sd = sigmaBest),
type = nameBest)
df123 <- rbind(df1, df2, df3)
label1 <- paste0(name1, ": N(mean=",round(mean1, 2), ", sd=", round(sigma1, 2),
label2 <- paste0(name2, ": N(mean=",round(mean2, 2), ", sd=", round(sigma2, 2),
labelBest <- paste0(nameBest, ": N(mean=",round(meanBest,2), ", sd=",
round(sigmaBest, 2), ")")
cols <- c("#DC3912", "#13721A", "#1F5094")
names(cols) <- c(name1, name2, nameBest)
g <- ggplot(df123) + geom_line(aes(x, y, colour = type), size = rel(1.2))
g <- g + scale_colour_manual(values = cols,
limits = c(name1, name2, nameBest),
labels = c(label1, label2, labelBest))
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g <- g + theme(plot.title=element_text(size=rel(1.1), colour="black",
face= "bold"),
axis.text.x = element_text(size=rel(1.2)),
axis.text.y = element_text(size=rel(1.2)),
axis.title.x = element_blank(),
legend.title = element_blank(),
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legend.position = legendPos,
legend.text = element_text(face = "bold", size=rel(legendSize)))
g <- g + ggtitle(graphicTitle)
g <- g + labs(y="probability", size=rel(1.9))
g <- g + stat_function(fun = dnorm_limit, args = list(mean=mean1, sd=sigma1),
fill = cols[name1], alpha=0.2, geom="area")
g <- g + stat_function(fun = dnorm_limit, args = list(mean=mean2, sd=sigma2),
fill = cols[name2], alpha=0.2, geom="area")
g <- g + stat_function(fun = dnorm_limit, args = list(mean=meanBest,
sd=sigmaBest),
fill = cols[nameBest], alpha=0.2, geom="area")
#-----------------------------------------------------------------------------
# Save to plotfile if needed, and return plot
#-----------------------------------------------------------------------------
if (!is.null(plotfile)) {
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ggsave(plotfile, g, width = width, height = height, units = units, dpi = dpi)
}
return(g)
}
# Auxiliar function to plot
CombinedPDFs <- function(pdf_1, pdf_2) {
mean_1 <- pdf_1[1]
sigma_1 <- pdf_1[2]
mean_2 <- pdf_2[1]
sigma_2 <- pdf_2[2]
a_1 <- (sigma_2^2)/((sigma_1^2)+(sigma_2^2))
a_2 <- (sigma_1^2)/((sigma_1^2)+(sigma_2^2))
pdf_mean <- a_1*mean_1 + a_2*mean_2
pdf_sigma <- sqrt((sigma_1^2)*(sigma_2^2)/((sigma_1^2)+(sigma_2^2)))
data <- c(pdf_mean, pdf_sigma)
dim(data) <- c(statistic = 2)
return(data)
}
dnorm_limit <- function(x,mean,sd){
y <- dnorm(x,mean,sd)
y[x<mean | x > mean+sd] <- NA
return(y)
}