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#'Compute the correlation coefficient between an array of forecast and their corresponding observation
#'
#'Calculate the correlation coefficient (Pearson, Kendall or Spearman) for
#'an array of forecast and an array of observation. The correlations are
#'computed along time_dim, the startdate dimension. If comp_dim is given,
#'the correlations are computed only if obs along the comp_dim dimension are
#'complete between limits[1] and limits[2], i.e., there is no NA between
#'limits[1] and limits[2]. This option can be activated if the user wants to
#'account only for the forecasts which the corresponding observations are
#'available at all leadtimes.\cr
#'The confidence interval is computed by the Fisher transformation and the
#'significance level relies on an one-sided student-T distribution.\cr
#'
#'@param exp A named numeric array of experimental data, with at least two
#' dimensions 'time_dim' and 'memb_dim'.
#'@param obs A named numeric array of observational data, same dimensions as
#' parameter 'exp' except along memb_dim.
#'@param time_dim A character string indicating the name of dimension along
#' which the correlations are computed. The default value is 'sdate'.
#'@param memb_dim A character string indicating the name of member (nobs/nexp)
#' dimension. The default value is 'member'.
#'@param comp_dim A character string indicating the name of dimension along which
#' obs is taken into account only if it is complete. The default value
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#' is NULL.
#'@param limits A vector of two integers indicating the range along comp_dim to
#' be completed. The default is c(1, length(comp_dim dimension)).
#'@param method A character string indicating the type of correlation:
#' 'pearson', 'spearman', or 'kendall'. The default value is 'pearson'.
#'@param pval A logical value indicating whether to compute or not the p-value
#' of the test Ho: Corr = 0. The default value is TRUE.
#'@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
#'A list containing the numeric arrays with dimension:\cr
#' c(nexp, nobs, all other dimensions of exp except time_dim).\cr
#'nexp is the number of experiment (i.e., memb_dim in exp), and nobs is the
#'number of observation (i.e., memb_dim in obs).\cr
#'\item{$corr}{
#' The correlation coefficient.
#'}
#'\item{$p.val}{
#' The p-value. Only present if \code{pval = TRUE}.
#'}
#'\item{$conf.lower}{
#' The lower confidence interval. Only present if \code{conf = TRUE}.
#'}
#'\item{$conf.upper}{
#' The upper confidence interval. Only present if \code{conf = TRUE}.
#'}
#'
#'@examples
#'# Load sample data as in Load() example:
#'example(Load)
#'clim <- Clim(sampleData$mod, sampleData$obs)
#'corr <- Corr(clim$clim_exp, clim$clim_obs, time_dim = 'ftime')
#'# Renew the example when Ano and Smoothing is ready
#'
#'@rdname Corr
#'@import multiApply
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#'@importFrom stats cor pt qnorm
#'@export
Corr <- function(exp, obs, time_dim = 'sdate', memb_dim = 'member',
comp_dim = NULL, limits = NULL,
method = 'pearson', pval = TRUE, conf = TRUE,
conf.lev = 0.95, ncores = NULL) {
# Check inputs
## exp and obs (1)
if (is.null(exp) | is.null(obs)) {
stop("Parameter 'exp' and 'obs' cannot be NULL.")
}
if (!is.numeric(exp) | !is.numeric(obs)) {
stop("Parameter 'exp' and 'obs' must be a numeric array.")
}
if (is.null(dim(exp)) | is.null(dim(obs))) {
stop(paste0("Parameter 'exp' and 'obs' must be at least two dimensions ",
"containing time_dim and memb_dim."))
}
if(any(is.null(names(dim(exp))))| any(nchar(names(dim(exp))) == 0) |
any(is.null(names(dim(obs))))| any(nchar(names(dim(obs))) == 0)) {
stop("Parameter 'exp' and 'obs' must have dimension names.")
}
if(!all(names(dim(exp)) %in% names(dim(obs))) |
!all(names(dim(obs)) %in% names(dim(exp)))) {
stop("Parameter 'exp' and 'obs' must have same dimension name")
}
## 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(exp)) | !time_dim %in% names(dim(obs))) {
stop("Parameter 'time_dim' is not found in 'exp' or 'obs' dimension.")
}
## memb_dim
if (!is.character(memb_dim) | length(memb_dim) > 1) {
stop("Parameter 'memb_dim' must be a character string.")
}
if (!memb_dim %in% names(dim(exp)) | !memb_dim %in% names(dim(obs))) {
stop("Parameter 'memb_dim' is not found in 'exp' or 'obs' dimension.")
}
## comp_dim
if (!is.null(comp_dim)) {
if (!is.character(comp_dim) | length(comp_dim) > 1) {
stop("Parameter 'comp_dim' must be a character string.")
}
if (!comp_dim %in% names(dim(exp)) | !comp_dim %in% names(dim(obs))) {
stop("Parameter 'comp_dim' is not found in 'exp' or 'obs' dimension.")
}
}
## limits
if (!is.null(limits)) {
if (is.null(comp_dim)) {
stop("Paramter 'comp_dim' cannot be NULL if 'limits' is assigned.")
}
if (!is.numeric(limits) | any(limits %% 1 != 0) | any(limits < 0) |
length(limits) != 2 | any(limits > dim(exp)[comp_dim])) {
stop(paste0("Parameter 'limits' must be a vector of two positive ",
"integers smaller than the length of paramter 'comp_dim'."))
}
}
## method
if (!(method %in% c("kendall", "spearman", "pearson"))) {
stop("Parameter 'method' must be one of 'kendall', 'spearman' or 'pearson'.")
}
## pval
if (!is.logical(pval) | length(pval) > 1) {
stop("Parameter 'pval' 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.")
}
}
## exp and obs (2)
name_exp <- sort(names(dim(exp)))
name_obs <- sort(names(dim(obs)))
name_exp <- name_exp[-which(name_exp == memb_dim)]
name_obs <- name_obs[-which(name_obs == memb_dim)]
if(!all(dim(exp)[name_exp] == dim(obs)[name_obs])) {
stop(paste0("Parameter 'exp' and 'obs' must have same length of ",
"all dimension expect 'memb_dim'."))
}
if (dim(exp)[time_dim] < 3) {
stop("The length of time_dim must be at least 3 to compute correlation.")
}
###############################
# Sort dimension
name_exp <- names(dim(exp))
name_obs <- names(dim(obs))
order_obs <- match(name_exp, name_obs)
###############################
# Calculate Corr
# Remove data along comp_dim dim if there is at least one NA between limits
if (!is.null(comp_dim)) {
if (is.null(limits)) {
limits <- c(1, dim(obs)[comp_dim])
}
pos <- which(names(dim(obs)) == comp_dim)
obs_sub <- Subset(obs, pos, list(limits[1]:limits[2]))
outrows <- is.na(MeanDims(obs_sub, pos, na.rm = FALSE))
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outrows <- InsertDim(outrows, pos, dim(obs)[comp_dim])
obs[which(outrows)] <- NA
}
res <- Apply(list(exp, obs),
target_dims = list(c(time_dim, memb_dim),
c(time_dim, memb_dim)),
fun = .Corr,
time_dim = time_dim, method = method,
pval = pval, conf = conf, conf.lev = conf.lev,
ncores = ncores)
return(res)
}
.Corr <- function(exp, obs, time_dim = 'sdate', method = 'pearson',
conf = TRUE, pval = TRUE, conf.lev = 0.95) {
# exp: [sdate, member_exp]
# obs: [sdate, member_obs]
n_exp <- as.numeric(dim(exp)[2])
n_obs <- as.numeric(dim(obs)[2])
CORR <- array(dim = c(n_exp = n_exp, n_obs = n_obs))
eno_expand <- array(dim = c(n_exp = n_exp, n_obs = n_obs))
p.val <- array(dim = c(n_exp = n_exp, n_obs = n_obs))
# ens_mean
for (i in 1:n_obs) {
CORR[, i] <- sapply(1:n_exp,
function(x) {
if (any(!is.na(exp[, x])) && sum(!is.na(obs[, i])) > 2) {
cor(exp[, x], obs[, i],
use = "pairwise.complete.obs",
method = method)
} else {
CORR[, i] <- NA
}
})
}
# if (pval) {
# for (i in 1:n_obs) {
# p.val[, i] <- try(sapply(1:n_exp,
# function(x) {(cor.test(exp[, x], obs[, i],
# use = "pairwise.complete.obs",
# method = method)$p.value)/2}), silent = TRUE)
# if (class(p.val[, i]) == 'character') {
# p.val[, i] <- NA
# }
# }
# }
if (pval | conf) {
if (method == "kendall" | method == "spearman") {
tmp <- apply(obs, 2, rank)
names(dim(tmp))[1] <- time_dim
eno <- Eno(tmp, time_dim)
} else if (method == "pearson") {
eno <- Eno(obs, time_dim)
}
for (i in 1:n_exp) {
eno_expand[i, ] <- eno
}
}
#############old#################
#This doesn't return error but it's diff from cor.test() when method is spearman and kendall
if (pval) {
t <-sqrt(CORR * CORR * (eno_expand - 2) / (1 - (CORR ^ 2)))
p.val <- pt(t, eno_expand - 2, lower.tail = FALSE)
}
###################################
if (conf) {
conf.lower <- (1 - conf.lev) / 2
conf.upper <- 1 - conf.lower
conflow <- tanh(atanh(CORR) + qnorm(conf.lower) / sqrt(eno_expand - 3))
confhigh <- tanh(atanh(CORR) + qnorm(conf.upper) / sqrt(eno_expand - 3))
}
if (pval & conf) {
res <- list(corr = CORR, p.val = p.val,
conf.lower = conflow, conf.upper = confhigh)
} else if (pval & !conf) {
res <- list(corr = CORR, p.val = p.val)
} else if (!pval & conf) {
res <- list(corr = CORR,
conf.lower = conflow, conf.upper = confhigh)
} else {
res <- list(corr = CORR)
}
return(res)
}