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#'Compute the trend
#'
#'Compute the linear trend or any degree of polynomial regression along the
#'forecast time. It returns the regression coefficients (including the intercept)
#'and the confidence intervals if needed. The detrended array is also provided.\cr
#'The confidence interval relies on the student-T distribution.\cr\cr
#'
#'@param data An numeric array including the dimension along which the trend
#' is computed.
#'@param time_dim A character string indicating the dimension along which to
#' compute the trend. The default value is 'sdate'.
#'@param interval A positive numeric indicating the unit length between two
#' points along 'time_dim' dimension. The default value is 1.
#'@param polydeg A positive integer indicating the degree of polynomial
#' regression. The default value is 1.
#'@param conf A logical value indicating whether to retrieve the confidence
#' intervals or not. The default value is TRUE.
#'@param conf.lev A numeric indicating the confidence level for the
#' regression 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
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#'\item{$trend}{
#' A numeric array with the first dimension 'stats', followed by the same
#' dimensions as parameter 'data' except the 'time_dim' dimension. The length
#' of the 'stats' dimension should be \code{polydeg + 1}, containing the
#' regression coefficients from the lowest order (i.e., intercept) to the
#' highest degree.
#'}
#'\item{$conf.lower}{
#' A numeric array with the first dimension 'stats', followed by the same
#' dimensions as parameter 'data' except the 'time_dim' dimension. The length
#' of the 'stats' dimension should be \code{polydeg + 1}, containing the
#' lower limit of the \code{conf.lev}\% confidence interval for all the
#' regression coefficients with the same order as \code{$trend}. Only present
#' \code{conf = TRUE}.
#'}
#'\item{$conf.upper}{
#' A numeric array with the first dimension 'stats', followed by the same
#' dimensions as parameter 'data' except the 'time_dim' dimension. The length
#' of the 'stats' dimension should be \code{polydeg + 1}, containing the
#' upper limit of the \code{conf.lev}\% confidence interval for all the
#' regression coefficients with the same order as \code{$trend}. Only present
#' \code{conf = TRUE}.
#'}
#'\item{$detrended}{
#' A numeric array with the same dimensions as paramter 'data', containing the
#' detrended values along the 'time_dim' dimension.
#'}
#'
#'@examples
#'# Load sample data as in Load() example:
#'example(Load)
#'months_between_startdates <- 60
#'trend <- Trend(sampleData$obs, polydeg = 2)
#'
#'@rdname Trend
#'@import multiApply
#'@export
Trend <- function(data, time_dim = 'sdate', interval = 1, polydeg = 1,
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)) <- time_dim
}
if(any(is.null(names(dim(data))))| any(nchar(names(dim(data))) == 0)) {
stop("Parameter 'data' must have dimension names.")
}
## time_dim
if (!is.character(time_dim) | length(time_dim) > 1) {
stop("Parameter 'time_dim' must be a character string.")
}
if (!time_dim %in% names(dim(data))) {
stop("Parameter 'time_dim' is not found in 'data' dimension.")
}
## interval
if (any(!is.numeric(interval) | interval <= 0 | length(interval) > 1)) {
stop("Parameter 'interval' must be a positive number.")
}
## polydeg
if (!is.numeric(polydeg) | polydeg %% 1 != 0 | polydeg < 0 |
length(polydeg) > 1) {
stop("Parameter 'polydeg' must be a positive integer.")
}
## 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 Trend
dim_names <- names(dim(data))
if (conf) {
output_dims <- list(trend = 'stats', conf.lower = 'stats',
conf.upper = 'stats', detrended = time_dim)
} else if (!conf) {
output_dims <- list(trend = 'stats', detrended = time_dim)
}
output <- Apply(list(data),
target_dims = time_dim,
fun = .Trend,
output_dims = output_dims,
time_dim = time_dim, interval = interval,
polydeg = polydeg, conf = conf,
conf.lev = conf.lev,
ncores = ncores)
#output <- lapply(output, .reorder, time_dim = time_dim, dim_names = dim_names)
return(output)
}
.Trend <- function(x, time_dim = 'sdate', interval = 1, polydeg = 1,
conf = TRUE, conf.lev = 0.95) {
mon <- seq(x) * interval
# remove NAs for potential poly()
NApos <- 1:length(x)
NApos[which(is.na(x))] <- NA
x2 <- x[!is.na(NApos)]
mon2 <- mon[!is.na(NApos)]
if (length(x2) > 0) {
# lm.out <- lm(x ~ mon, na.action = na.omit)
lm.out <- lm(x2 ~ poly(mon2, degree = polydeg, raw = TRUE), na.action = na.omit)
trend <- lm.out$coefficients #intercept, slope1, slope2,...
if (conf) {
conf.lower <- confint(lm.out, level = conf.lev)[, 1]
conf.upper <- confint(lm.out, level = conf.lev)[, 2]
}
detrended <- c()
detrended[is.na(x) == FALSE] <- x[is.na(x) == FALSE] - lm.out$fitted.values
} else {
trend <- rep(NA, polydeg + 1)
detrend <- NA
if (conf) {
conf.lower <- rep(NA, polydeg + 1)
conf.upper <- rep(NA, polydeg + 1)
}
}
if (conf) {
return(list(trend = trend, conf.lower = conf.lower, conf.upper = conf.upper,
detrended = detrended))
} else {
return(list(trend = trend, detrended = detrended))
}
}