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#'Computes Root Mean Square Error
#'
#'Computes the root mean square error for an array of forecasts, var_exp and
#'an array of observations, var_obs, which should have the same dimensions
#'except along the posloop dimension where the lengths can be different, with
#'the number of experiments/models for var_exp (nexp) and the number of
#'obserational datasets for var_obs (nobs).\cr
#'The RMSE is computed along the posRMS dimension which should correspond to
#'the startdate dimension.\cr
#'If compROW is given, the RMSE is computed only if rows along the compROW
#'dimension are complete between limits[1] and limits[2], i.e. there are no
#'NAs between limits[1] and limits[2]. This option can be activated if the
#'user wishes to account only for the forecasts for which observations are
#'available at all leadtimes.\cr
#'Default: limits[1] = 1 and limits[2] = length(compROW dimension).\cr
#'The confidence interval relies on a chi2 distribution.\cr\cr
#'.RMS provides the same functionality but taking a matrix of ensemble
#'members as input (exp).
#'
#'@param var_exp Matrix of experimental data.
#'@param var_obs Matrix of observational data, same dimensions as var_exp
#' except along posloop dimension, where the length can be nobs instead of
#' nexp.
#'@param posloop Dimension nobs and nexp.
#'@param posRMS Dimension along which RMSE are to be computed (the dimension
#' of the start dates).
#'@param compROW Data taken into account only if (compROW)th row is complete.\cr
#' Default = NULL.
#'@param limits Complete between limits[1] & limits[2]. Default = NULL.
#'@param siglev Confidence level of the computed confidence interval. 0.95
#' by default.
#'@param conf Whether to compute confidence interval or not. TRUE by default.
#'@param exp N by M matrix of N forecasts from M ensemble members.
#'@param obs Vector of the corresponding observations of length N.
#'
#'@return
#'RMS: Array with dimensions:\cr
#'c(length(posloop) in var_exp, length(posloop) in var_obs, 1 or 3, all
#' other dimensions of var_exp & var_obs except posRMS).\cr
#'The 3rd dimension corresponds to the lower limit of the 95\% confidence
#' interval (only present if \code{conf = TRUE}), the RMSE, and the upper
#' limit of the 95\% confidence interval (only present if
#' \code{conf = TRUE}).\cr\cr
#'.RMS:
#'\item{$rms}{
#'The root mean square error,
#'}
#'\item{$conf_low}{
#' Corresponding to the lower limit of the \code{siglev}\% confidence interval
#' (only present if \code{conf = TRUE}) for the rms.
#'}
#'\item{$conf_high}{
#' Corresponding to the upper limit of the \code{siglev}\% confidence interval
#' (only present if \code{conf = TRUE}) for the rms.
#'}
#'
#'@keywords datagen
#'@author History:\cr
#'0.1 - 2011-05 (V. Guemas) - Original code\cr
#'1.0 - 2013-09 (N. Manubens) - Formatting to R CRAN\cr
#'1.1 - 2017-02 (A. Hunter) - Adapted to veriApply()
#'@examples
#'# Load sample data as in Load() example:
#'example(Load)
#'clim <- Clim(sampleData$mod, sampleData$obs)
#'ano_exp <- Ano(sampleData$mod, clim$clim_exp)
#'ano_obs <- Ano(sampleData$obs, clim$clim_obs)
#'runmean_months <- 12
#'dim_to_smooth <- 4 # Smooth along lead-times
#'smooth_ano_exp <- Smoothing(ano_exp, runmean_months, dim_to_smooth)
#'smooth_ano_obs <- Smoothing(ano_obs, runmean_months, dim_to_smooth)
#'dim_to_mean <- 2 # Mean along members
#'# Discard start-dates for which some leadtimes are missing
#'required_complete_row <- 3
#'leadtimes_per_startdate <- 60
#'rms <- RMS(Mean1Dim(smooth_ano_exp, dim_to_mean),
#' Mean1Dim(smooth_ano_obs, dim_to_mean),
#' compROW = required_complete_row,
#' limits = c(ceiling((runmean_months + 1) / 2),
#' leadtimes_per_startdate - floor(runmean_months / 2)))
#' \donttest{
#'PlotVsLTime(rms, toptitle = "Root Mean Square Error", ytitle = "K",
#' monini = 11, limits = NULL, listexp = c('CMIP5 IC3'),
#' listobs = c('ERSST'), biglab = FALSE, hlines = c(0),
#' fileout = 'tos_rms.eps')
#' }
#'# The following example uses veriApply combined with .RMS instead of RMS
#' \dontrun{
#'require(easyVerification)
#'RMS2 <- s2dverification:::.RMS
#'rms2 <- veriApply("RMS2",
#' smooth_ano_exp,
#' # see ?veriApply for how to use the 'parallel' option
#' Mean1Dim(smooth_ano_obs, dim_to_mean),
#' tdim = 3, ensdim = 2)
#' }
#'
#'@rdname RMS
#'@export
RMS <- function(var_exp, var_obs, posloop = 1, posRMS = 2, compROW = NULL,
limits = NULL, siglev = 0.95, conf = TRUE) {
#
# Remove data along compROW dim if there is at least one NA between limits
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#
if (is.null(compROW) == FALSE) {
if (is.null(limits) == TRUE) {
limits <- c(1, dim(var_obs)[compROW])
}
outrows <- (is.na(Mean1Dim(var_obs, compROW, narm = FALSE, limits)))
outrows <- InsertDim(outrows, compROW, dim(var_obs)[compROW])
var_obs[which(outrows)] <- NA
}
#
# Enlarge var_exp & var_obs to 10 dim + move posloop & posRMS to 1st & 2nd
# pos
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#
dimsvar <- dim(var_exp)
for (iind in 1:length(dimsvar)) {
if (iind != posloop & dim(var_obs)[iind] != dimsvar[iind]) {
stop("var_exp & var_obs must have same dimensions except along posloop")
}
}
if (dimsvar[posRMS] < 2 ) {
stop("At least 2 values required to compute RMSE")
}
enlvarexp <- Enlarge(var_exp, 10)
enlvarobs <- Enlarge(var_obs, 10)
nexp <- dimsvar[posloop]
nobs <- dim(var_obs)[posloop]
posaperm <- numeric(10)
posaperm[1] <- posloop
posaperm[2] <- posRMS
posaperm[3:10] <- seq(1, 10)[-c(posloop, posRMS)]
permvarexp <- aperm(enlvarexp, posaperm)
permvarobs <- aperm(enlvarobs, posaperm)
dimsaperm <- dim(permvarexp)
#
# RMS & its confidence interval computation
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#
if (conf) {
nvals <- 3
dim_rms <- 2
conf_low <- (1 - siglev) / 2
conf_high <- 1 - conf_low
} else {
nvals <- 1
dim_rms <- 1
}
enlrms <- array(dim = c(nexp, nobs, nvals, dimsaperm[3:10]))
for (jexp in 1:nexp) {
for (jobs in 1:nobs) {
dif <- array(dim = dimsaperm[-1])
dif[, , , , , , , , ] <- permvarexp[jexp, , , , , , , ,
, ] - permvarobs[jobs, , , , , , , , , ]
enlrms[jexp, jobs, dim_rms, , , , , , , , ] <- Mean1Dim(dif ** 2, 1,
narm = TRUE) ** 0.5
if (conf) {
eno <- Eno(dif, 1)
for (j3 in 1:dimsaperm[3]){
for (j4 in 1:dimsaperm[4]){
for (j5 in 1:dimsaperm[5]){
for (j6 in 1:dimsaperm[6]){
for (j7 in 1:dimsaperm[7]){
for (j8 in 1:dimsaperm[8]){
for (j9 in 1:dimsaperm[9]){
for (j10 in 1:dimsaperm[10]){
ndat <- length(sort(dif[, j3, j4, j5, j6, j7, j8, j9,
j10]))
enlrms[jexp, jobs, 1, j3, j4, j5, j6, j7, j8, j9,
j10] <- (eno[j3, j4, j5, j6, j7, j8, j9,
j10] * enlrms[jexp, jobs, 2, j3, j4, j5, j6, j7,
j8, j9, j10] ** 2 / qchisq(conf_high, eno[j3, j4, j5,
j6, j7, j8, j9, j10] - 1)) ** 0.5
enlrms[jexp, jobs, 3, j3, j4, j5, j6, j7, j8, j9,
j10] <- (eno[j3, j4, j5, j6, j7, j8, j9,
j10] * enlrms[jexp, jobs, 2, j3, j4, j5, j6, j7,
j8, j9, j10] ** 2 / qchisq(conf_low, eno[j3, j4, j5,
j6, j7, j8, j9, j10] - 1)) ** 0.5
}
}
}
}
}
}
}
}
}
}
}
dim(enlrms) <- c(nexp, nobs, nvals, dimsvar[-c(posloop, posRMS)])
#
# Output
# ~~~~~~~~
#
enlrms
}
#'@rdname RMS
#'@importFrom stats qchisq
#'@export
.RMS <- function(exp, obs, siglev = 0.95, conf = TRUE) {
#
# RMS & its confidence interval computation
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#
if (conf) {
conf_low <- (1 - siglev) / 2
conf_high <- 1 - conf_low
}
dif <- rowMeans(exp) - obs
enlrms <- mean(dif ** 2, na.rm = TRUE) ** 0.5
if (conf) {
eno <- Eno(dif, 1)
ndat <- length(sort(dif))
conf_int <- c((eno * enlrms ** 2 / qchisq(conf_high, eno - 1)) ** 0.5,
(eno * enlrms ** 2 / qchisq(conf_low, eno - 1)) ** 0.5)
names(conf_int) <- c("conf_low","conf_high")
} else {
conf_int <- c()
names(conf_int) <- c()
}
results <- c(enlrms, conf_int)
names(results) <- c("rms", names(conf_int))
return(results)
}
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