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#'Compute interquartile range, maximum-minimum, standard deviation and median
#'absolute deviation
#'
#'Compute interquartile range, maximum-minimum, standard deviation and median
#'absolute deviation along the list of dimensions provided by the compute_dim
#'argument (typically along the ensemble member and start date dimension).
#'The confidence interval is computed by bootstrapping by 100 times. The input
#'data can be the output of \code{Load()}, \code{Ano()}, or
#'\code{Ano_CrossValid()}, for example.
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#'
#'@param data A numeric vector or array with named dimensions to compute the
#' statistics. The dimensions should at least include 'compute_dim'.
#'@param compute_dim A vector of character strings of the dimension names along
#' which to compute the statistics. The default value is 'member'.
#'@param na.rm A logical value indicating if NAs should be removed (TRUE) or
#' kept (FALSE) for computation. The default value is TRUE.
#'@param conf A logical value indicating whether to compute the confidence
#' intervals or not. The default value is TRUE.
#'@param conf.lev A numeric value of the confidence level for the computation.
#' The default value is 0.95.
#'@param ncores An integer indicating the number of cores to use for parallel
#' computation. The default value is NULL.
#'
#'@return
#'A list of numeric arrays with the same dimensions as 'data' but without
#''compute_dim' and with the first dimension 'stats'. If 'conf' is TRUE, the
#'length of 'stats' is 3 corresponding to the lower limit of the confidence
#'interval, the spread, and the upper limit of the confidence interval. If
#''conf' is FALSE, the length of 'stats' is 1 corresponding to the spread.
#'\item{$iqr}{
#' InterQuartile Range.
#'}
#'\item{$maxmin}{
#' Maximum - Minimum.
#'}
#'\item{$sd}{
#' Standard Deviation.
#'}
#'\item{$mad}{
#' Median Absolute Deviation.
#'}
#'
#'@examples
#'# Load sample data as in Load() example:
#'example(Load)
#'clim <- Clim(sampleData$mod, sampleData$obs)
#'ano_exp <- Ano(sampleData$mod, clim$clim_exp)
#'runmean_months <- 12
#'smooth_ano_exp <- Smoothing(ano_exp, runmeanlen = runmean_months)
#'smooth_ano_exp_m_sub <- smooth_ano_exp - InsertDim(MeanDims(smooth_ano_exp, 'member',
#' na.rm = TRUE),
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#' lendim = dim(smooth_ano_exp)['member'],
#' name = 'member')
#'spread <- Spread(smooth_ano_exp_m_sub, compute_dim = c('member', 'sdate'))
#'
#'\donttest{
#'PlotVsLTime(Reorder(spread$iqr, c('dataset', 'stats', 'ftime')),
#' toptitle = "Inter-Quartile Range between ensemble members",
#' ytitle = "K", monini = 11, limits = NULL,
#' listexp = c('CMIP5 IC3'), listobs = c('ERSST'), biglab = FALSE,
#' hlines = c(0), fileout = 'tos_iqr.png')
#'PlotVsLTime(Reorder(spread$maxmin, c('dataset', 'stats', 'ftime')),
#' toptitle = "Maximum minus minimum of the members",
#' ytitle = "K", monini = 11, limits = NULL,
#' listexp = c('CMIP5 IC3'), listobs = c('ERSST'), biglab = FALSE,
#' hlines = c(0), fileout = 'tos_maxmin.png')
#'PlotVsLTime(Reorder(spread$sd, c('dataset', 'stats', 'ftime')),
#' toptitle = "Standard deviation of the members",
#' ytitle = "K", monini = 11, limits = NULL,
#' listexp = c('CMIP5 IC3'), listobs = c('ERSST'), biglab = FALSE,
#' hlines = c(0), fileout = 'tos_sd.png')
#'PlotVsLTime(Reorder(spread$mad, c('dataset', 'stats', 'ftime')),
#' toptitle = "Median Absolute Deviation of the members",
#' ytitle = "K", monini = 11, limits = NULL,
#' listexp = c('CMIP5 IC3'), listobs = c('ERSST'), biglab = FALSE,
#' hlines = c(0), fileout = 'tos_mad.png')
#'}
#'
#'@import multiApply
#'@importFrom stats IQR sd mad runif quantile
#'@export
Spread <- function(data, compute_dim = 'member', na.rm = TRUE,
conf = TRUE, conf.lev = 0.95, ncores = NULL) {
# Check inputs
## data
if (is.null(data)) {
stop("Parameter 'data' cannot be NULL.")
}
if (!is.numeric(data)) {
stop("Parameter 'data' must be a numeric array.")
}
if (is.null(dim(data))) { #is vector
dim(data) <- c(length(data))
names(dim(data)) <- compute_dim[1]
}
if(any(is.null(names(dim(data))))| any(nchar(names(dim(data))) == 0)) {
stop("Parameter 'data' must have dimension names.")
}
## compute_dim
if (!is.character(compute_dim)) {
stop("Parameter 'compute_dim' must be a character vector.")
}
if (any(!compute_dim %in% names(dim(data)))) {
stop("Parameter 'compute_dim' has some element not in 'data' dimension names.")
}
## na.rm
if (!is.logical(na.rm) | length(na.rm) > 1) {
stop("Parameter 'na.rm' must be one logical value.")
}
## conf
if (!is.logical(conf) | length(conf) > 1) {
stop("Parameter 'conf' must be one logical value.")
}
## conf.lev
if (!is.numeric(conf.lev) | conf.lev < 0 | conf.lev > 1 | length(conf.lev) > 1) {
stop("Parameter 'conf.lev' must be a numeric number between 0 and 1.")
}
## ncores
if (!is.null(ncores)) {
if (!is.numeric(ncores) | ncores %% 1 != 0 | ncores <= 0 |
length(ncores) > 1) {
stop("Parameter 'ncores' must be a positive integer.")
}
}
###############################
# Calculate Spread
output <- Apply(list(data),
target_dims = compute_dim,
fun = .Spread,
output_dims = list(iqr = 'stats', maxmin = 'stats',
sd = 'stats', mad = 'stats'),
na.rm = na.rm,
conf = conf, conf.lev = conf.lev,
ncores = ncores)
return(output)
}
.Spread <- function(data, compute_dim = 'member', na.rm = TRUE,
conf = TRUE, conf.lev = 0.95) {
# data: compute_dim. [member] or [member, sdate] for example
# Compute spread
res_iqr <- IQR(data, na.rm = na.rm)
res_maxmin <- max(data, na.rm = na.rm) - min(data, na.rm = na.rm)
res_sd <- sd(data, na.rm = na.rm)
res_mad <- mad(data, na.rm = na.rm)
# Compute conf (bootstrapping)
if (conf) {
# The output length is 3, [conf.low, spread, conf.high]
res_iqr <- rep(res_iqr, 3)
res_maxmin <- rep(res_maxmin, 3)
res_sd <- rep(res_sd, 3)
res_mad <- rep(res_mad, 3)
conf_low <- (1 - conf.lev) / 2
conf_high <- 1 - conf_low
# Create vector for saving bootstrap result
iqr_bs <- c()
maxmin_bs <- c()
sd_bs <- c()
mad_bs <- c()
# bootstrapping for 100 times
num <- length(data)
for (jmix in 1:100) {
drawings <- round(runif(num, 0.5, num + 0.5))
iqr_bs <- c(iqr_bs, IQR(data[drawings], na.rm = na.rm))
maxmin_bs <- c(maxmin_bs, max(data[drawings], na.rm = na.rm) -
min(data[drawings], na.rm = na.rm))
sd_bs <- c(sd_bs, sd(data[drawings], na.rm = na.rm))
mad_bs <- c(mad_bs, mad(data[drawings], na.rm = na.rm))
}
# Calculate confidence interval with the bootstrapping results
res_iqr[1] <- quantile(iqr_bs, conf_low, na.rm = na.rm)
res_iqr[3] <- quantile(iqr_bs, conf_high, na.rm = na.rm)
res_maxmin[1] <- res_maxmin[2] + (quantile(maxmin_bs, conf_low, na.rm = na.rm) -
quantile(maxmin_bs, conf_high, na.rm = na.rm)) / 2
res_maxmin[3] <- res_maxmin[2] - (quantile(maxmin_bs, conf_low, na.rm = na.rm) -
quantile(maxmin_bs, conf_high, na.rm = na.rm)) / 2
res_sd[1] <- quantile(sd_bs, conf_low, na.rm = na.rm)
res_sd[3] <- quantile(sd_bs, conf_high, na.rm = na.rm)
res_mad[1] <- res_mad[2] + (quantile(mad_bs, conf_low, na.rm = na.rm) -
quantile(mad_bs, conf_high, na.rm = na.rm))
res_mad[3] <- res_mad[2] - (quantile(mad_bs, conf_low, na.rm = na.rm) -
quantile(mad_bs, conf_high, na.rm = na.rm))
}
# Turn infinite to NA
res_maxmin[which(is.infinite(res_maxmin))] <- NA
return(invisible(list(iqr = as.array(res_iqr), maxmin = as.array(res_maxmin),
sd = as.array(res_sd), mad = as.array(res_mad))))