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#'Compute the Standardization of Precipitation-Evapotranspiration Index
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#'
#'The Standardization of the data is the last step of computing the SPEI
#'(Standarized Precipitation-Evapotranspiration Index). With this function the
#'data is fit to a probability distribution to transform the original values to
#'standardized units that are comparable in space and time and at different SPEI
#'time scales.
#'
#'Next, some specifications for the calculation of this indicator will be
#'discussed. To choose the time scale in which you want to accumulate the SPEI
#'(SPEI3, SPEI6...) is done using the accum parameter. The accumulation needs to
#'be performed in the previous step. However, since the accumulation is done for
#'the elapsed time steps, there will be no complete accumulations until reaching
#'the time instant equal to the value of the parameter. For this reason, in the
#'result, we will find that for the dimension where the accumulation has been
#'carried out, the values of the array will be NA since they do not include
#'complete accumulations. If there are NAs in the data and they are not removed with the
#'parameter 'na.rm', the standardization cannot be carried out for those
#'coordinates and therefore, the result will be filled with NA for the
#'specific coordinates. When NAs are not removed, if the length of the data for
#'a computational step is smaller than 4, there will not be enough data for
#'standarize and the result will be also filled with NAs for that coordinates.
#'About the distribution used to fit the data, there are only two possibilities:
#''log-logistic' and 'Gamma'. The 'Gamma' method only works when only
#'precipitation is provided and other variables are 0 because it is positive
#'defined (SPI indicator). For more information about SPEI, see functions
#'PeriodPET and PeriodAccumulation. This function is build to work be compatible
#'with other tools in that work with 's2dv_cube' object class. The input data
#'must be this object class. If you don't work with 's2dv_cube', see
#'PeriodStandardization. For more information on the SPEI indicator calculation,
#'see CST_PeriodPET and CST_PeriodAccumulation.
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#'
#'@param data An 's2dv_cube' that element 'data' stores a multidimensional
#' array containing the data to be standardized.
#'@param data_cor An 's2dv_cube' that element 'data' stores a multidimensional
#' array containing the data in which the standardization should be applied
#' using the fitting parameters from 'data'.
#'@param time_dim A character string indicating the name of the temporal
#' dimension. By default, it is set to 'syear'.
#'@param leadtime_dim A character string indicating the name of the temporal
#' dimension. By default, it is set to 'time'.
#'@param memb_dim A character string indicating the name of the dimension in
#' which the ensemble members are stored. When set it to NULL, threshold is
#' computed for individual members.
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#'@param accum An integer value indicating the number of
#' time steps (leadtime_dim dimension) that have been accumulated in the
#' previous step. When it is greater than 1, the result will be filled with
#' NA until the accum leadtime_dim dimension number due to the
#' accumulation to previous months. If it is 1, no accumulation is done.
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#'@param ref_period A list with two numeric values with the starting and end
#' points of the reference period used for computing the index. The default
#' value is NULL indicating that the first and end values in data will be
#' used as starting and end points.
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#'@param handle_infinity A logical value wether to return infinite values (TRUE)
#' or not (FALSE). When it is TRUE, the positive infinite values (negative
#' infinite) are substituted by the maximum (minimum) values of each
#' computation step, a subset of the array of dimensions time_dim, leadtime_dim
#' and memb_dim.
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#'@param method A character string indicating the standardization method used.
#' If can be: 'parametric' or 'non-parametric'. It is set to 'parametric' by
#' default.
#'@param distribution A character string indicating the name of the distribution
#' function to be used for computing the SPEI. The accepted names are:
#' 'log-Logistic' and 'Gamma'. It is set to 'log-Logistic' by default. The
#' 'Gamma' method only works when only precipitation is provided and other
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#' variables are 0 because it is positive defined (SPI indicator).
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#'@param na.rm A logical value indicating whether NA values should be removed
#' from data. It is FALSE by default. If it is FALSE and there are NA values,
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#' standardization cannot be carried out for those coordinates and therefore,
#' the result will be filled with NA for the specific coordinates. If it is
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#' TRUE, if the data from other dimensions except time_dim and leadtime_dim is
#' not reaching 4 values, it is not enough values to estimate the parameters
#' and the result will include NA.
#'@param ncores An integer value indicating the number of cores to use in
#' parallel computation.
#'
#'@return An object of class \code{s2dv_cube} containing the standardized data.
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#'If 'data_cor' is provided the array stored in element data will be of the same
#'dimensions as 'data_cor'. If 'data_cor' is not provided, the array stored in
#'element data will be of the same dimensions as 'data'.
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#'
#'@examples
#'dims <- c(syear = 6, time = 3, latitude = 2, ensemble = 25)
#'data <- NULL
#'data$data <- array(rnorm(600, -204.1, 78.1), dim = dims)
#'class(data) <- 's2dv_cube'
#'SPEI <- CST_PeriodStandardization(data = data, accum = 2)
#'@export
CST_PeriodStandardization <- function(data, data_cor = NULL, time_dim = 'syear',
leadtime_dim = 'time', memb_dim = 'ensemble',
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accum = 1, ref_period = NULL,
handle_infinity = FALSE,
method = 'parametric',
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distribution = 'log-Logistic',
na.rm = FALSE, ncores = NULL) {
# Check 's2dv_cube'
if (is.null(data)) {
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stop("Parameter 'data' cannot be NULL.")
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}
if (!inherits(data, 's2dv_cube')) {
stop("Parameter 'data' must be of 's2dv_cube' class.")
}
if (!is.null(data_cor)) {
if (!inherits(data_cor, 's2dv_cube')) {
stop("Parameter 'data_cor' must be of 's2dv_cube' class.")
}
}
std <- PeriodStandardization(data = data$data, data_cor = data_cor$data,
time_dim = time_dim, leadtime_dim = leadtime_dim,
memb_dim = memb_dim, accum = accum,
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ref_period = ref_period,
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handle_infinity = handle_infinity, method = method,
distribution = distribution,
na.rm = na.rm, ncores = ncores)
if (is.null(data_cor)) {
data$data <- std
data$attrs$Variable$varName <- paste0(data$attrs$Variable$varName, ' standardized')
return(data)
} else {
data_cor$data <- std
data_cor$attrs$Variable$varName <- paste0(data_cor$attrs$Variable$varName, ' standardized')
data_cor$attrs$Datasets <- c(data_cor$attrs$Datasets, data$attrs$Datasets)
data_cor$attrs$source_files <- c(data_cor$attrs$source_files, data$attrs$source_files)
return(data_cor)
}
}
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#'Compute the Standardization of Precipitation-Evapotranspiration Index
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#'
#'The Standardization of the data is the last step of computing the SPEI
#'indicator. With this function the data is fit to a probability distribution to
#'transform the original values to standardized units that are comparable in
#'space and time and at different SPEI time scales.
#'
#'Next, some specifications for the calculation of this indicator will be
#'discussed. To choose the time scale in which you want to accumulate the SPEI
#'(SPEI3, SPEI6...) is done using the accum parameter. The accumulation needs to
#'be performed in the previous step. However, since the accumulation is done for
#'the elapsed time steps, there will be no complete accumulations until reaching
#'the time instant equal to the value of the parameter. For this reason, in the
#'result, we will find that for the dimension where the accumulation has been
#'carried out, the values of the array will be NA since they do not include
#'complete accumulations. If there are NAs in the data and they are not removed with the
#'parameter 'na.rm', the standardization cannot be carried out for those
#'coordinates and therefore, the result will be filled with NA for the
#'specific coordinates. When NAs are not removed, if the length of the data for
#'a computational step is smaller than 4, there will not be enough data for
#'standarize and the result will be also filled with NAs for that coordinates.
#'About the distribution used to fit the data, there are only two possibilities:
#''log-logistic' and 'Gamma'. The 'Gamma' method only works when only
#'precipitation is provided and other variables are 0 because it is positive
#'defined (SPI indicator). For more information about SPEI, see functions
#'PeriodPET and PeriodAccumulation.
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#'
#'@param data A multidimensional array containing the data to be standardized.
#'@param data_cor A multidimensional array containing the data in which the
#' standardization should be applied using the fitting parameters from 'data'.
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#'@param dates An array containing the dates of the data with the same time
#' dimensions as the data. It is optional and only necessary for using the
#' parameter 'ref_period' to select a reference period directly from dates.
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#'@param time_dim A character string indicating the name of the temporal
#' dimension. By default, it is set to 'syear'.
#'@param leadtime_dim A character string indicating the name of the temporal
#' dimension. By default, it is set to 'time'.
#'@param memb_dim A character string indicating the name of the dimension in
#' which the ensemble members are stored. When set it to NULL, threshold is
#' computed for individual members.
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#'@param accum An integer value indicating the number of
#' time steps (leadtime_dim dimension) that have been accumulated in the
#' previous step. When it is greater than 1, the result will be filled with
#' NA until the accum leadtime_dim dimension number due to the
#' accumulation to previous months. If it is 1, no accumulation is done.
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#'@param ref_period A list with two numeric values with the starting and end
#' points of the reference period used for computing the index. The default
#' value is NULL indicating that the first and end values in data will be
#' used as starting and end points.
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#'@param handle_infinity A logical value wether to return infinite values (TRUE)
#' or not (FALSE). When it is TRUE, the positive infinite values (negative
#' infinite) are substituted by the maximum (minimum) values of each
#' computation step, a subset of the array of dimensions time_dim, leadtime_dim
#' and memb_dim.
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#'@param method A character string indicating the standardization method used.
#' If can be: 'parametric' or 'non-parametric'. It is set to 'parametric' by
#' default.
#'@param distribution A character string indicating the name of the distribution
#' function to be used for computing the SPEI. The accepted names are:
#' 'log-Logistic' and 'Gamma'. It is set to 'log-Logistic' by default. The
#' 'Gamma' method only works when only precipitation is provided and other
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#' variables are 0 because it is positive defined (SPI indicator).
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#'@param na.rm A logical value indicating whether NA values should be removed
#' from data. It is FALSE by default. If it is FALSE and there are NA values,
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#' standardization cannot be carried out for those coordinates and therefore,
#' the result will be filled with NA for the specific coordinates. If it is
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#' TRUE, if the data from other dimensions except time_dim and leadtime_dim is
#' not reaching 4 values, it is not enough values to estimate the parameters
#' and the result will include NA.
#'@param ncores An integer value indicating the number of cores to use in
#' parallel computation.
#'
#'@return A multidimensional array containing the standardized data.
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#'If 'data_cor' is provided the array will be of the same dimensions as
#''data_cor'. If 'data_cor' is not provided, the array will be of the same
#'dimensions as 'data'.
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#'
#'@examples
#'dims <- c(syear = 6, time = 2, latitude = 2, ensemble = 25)
#'dimscor <- c(syear = 1, time = 2, latitude = 2, ensemble = 25)
#'data <- array(rnorm(600, -194.5, 64.8), dim = dims)
#'datacor <- array(rnorm(100, -217.8, 68.29), dim = dimscor)
#'
#'SPEI <- PeriodStandardization(data = data, accum = 2)
#'SPEIcor <- PeriodStandardization(data = data, data_cor = datacor, accum = 2)
#'@import multiApply
#'@import ClimProjDiags
#'@import TLMoments
#'@import lmomco
#'@import lmom
#'@export
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PeriodStandardization <- function(data, data_cor = NULL, dates = NULL,
time_dim = 'syear', leadtime_dim = 'time',
memb_dim = 'ensemble', accum = 1,
ref_period = NULL, handle_infinity = FALSE,
method = 'parametric',
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distribution = 'log-Logistic',
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na.rm = FALSE, ncores = NULL) {
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# Check inputs
## data
if (!is.array(data)) {
stop("Parameter 'data' must be a numeric array.")
}
if (is.null(names(dim(data)))) {
stop("Parameter 'data' must have dimension names.")
}
## data_cor
if (!is.null(data_cor)) {
if (!is.array(data_cor)) {
stop("Parameter 'data_cor' must be a numeric array.")
}
if (is.null(names(dim(data_cor)))) {
stop("Parameter 'data_cor' must have dimension names.")
}
}
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## dates
if (!is.null(dates)) {
if (!(is.Date(dates)) & !(is.POSIXct(dates))) {
stop("Parameter 'dates' is not of the correct class, ",
"only 'Date' and 'POSIXct' classes are accepted.")
}
if (!time_dim %in% names(dim(dates)) | !leadtime_dim %in% names(dim(dates))) {
stop("Parameter 'dates' must have 'time_dim' and 'leadtime_dim' ",
"dimension.")
}
if (dim(data)[c(time_dim)] != dim(dates)[c(time_dim)]) {
stop("Parameter 'dates' needs to have the same length of 'time_dim' ",
"as 'data'.")
}
}
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## 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.")
}
if (!is.null(data_cor)) {
if (!time_dim %in% names(dim(data_cor))) {
stop("Parameter 'time_dim' is not found in 'data_cor' dimension.")
}
}
## leadtime_dim
if (!is.character(leadtime_dim) | length(leadtime_dim) != 1) {
stop("Parameter 'leadtime_dim' must be a character string.")
}
if (!leadtime_dim %in% names(dim(data))) {
stop("Parameter 'leadtime_dim' is not found in 'data' dimension.")
}
if (!is.null(data_cor)) {
if (!leadtime_dim %in% names(dim(data_cor))) {
stop("Parameter 'leadtime_dim' is not found in 'data_cor' 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(data))) {
stop("Parameter 'memb_dim' is not found in 'data' dimension.")
}
if (!is.null(data_cor)) {
if (!memb_dim %in% names(dim(data_cor))) {
stop("Parameter 'memb_dim' is not found in 'data_cor' dimension.")
}
}
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## data_cor (2)
if (!is.null(data_cor)) {
if (dim(data)[leadtime_dim] != dim(data_cor)[leadtime_dim]) {
stop("Parameter 'data' and 'data_cor' have dimension 'leadtime_dim' ",
"of different length.")
}
}
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## accum
if (accum > dim(data)[leadtime_dim]) {
stop(paste0("Cannot compute accumulation of ", accum, " months because ",
"loaded data has only ", dim(data)[leadtime_dim], " months."))
}
## ref_period
if (!is.null(ref_period)) {
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if (is.null(dates)) {
warning("Parameter 'dates' is not provided so 'ref_period' can't be ",
"used.")
ref_period <- NULL
} else if (length(ref_period) != 2) {
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warning("Parameter 'ref_period' must be of length two indicating the ",
"first and end years of the reference period. It will not ",
"be used.")
ref_period <- NULL
} else if (!all(sapply(ref_period, is.numeric))) {
warning("Parameter 'ref_period' must be a numeric vector indicating the ",
"'start' and 'end' years of the reference period. It will not ",
"be used.")
ref_period <- NULL
} else if (ref_period[[1]] > ref_period[[2]]) {
warning("In parameter 'ref_period' 'start' cannot be after 'end'. It ",
"will not be used.")
ref_period <- NULL
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} else if (!all(unlist(ref_period) %in% year(dates))) {
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warning("Parameter 'ref_period' contain years outside the dates. ",
"It will not be used.")
ref_period <- NULL
} else {
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years <- year(ClimProjDiags::Subset(dates, along = leadtime_dim,
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indices = 1))
ref_period[[1]] <- which(ref_period[[1]] == years)
ref_period[[2]] <- which(ref_period[[2]] == years)
}
}
## handle_infinity
if (!is.logical(handle_infinity)) {
stop("Parameter 'handle_infinity' must be a logical value.")
}
## method
if (!(method %in% c('parametric', 'non-parametric'))) {
stop("Parameter 'method' must be a character string containing one of ",
"the following methods: 'parametric' or 'non-parametric'.")
}
## distribution
if (!(distribution %in% c('log-Logistic', 'Gamma', 'PearsonIII'))) {
stop("Parameter 'distribution' must be a character string containing one ",
"of the following distributions: 'log-Logistic', 'Gamma' or ",
"'PearsonIII'.")
}
## na.rm
if (!is.logical(na.rm)) {
stop("Parameter 'na.rm' must be logical.")
}
## ncores
if (!is.null(ncores)) {
if (!is.numeric(ncores) | any(ncores %% 1 != 0) | any(ncores < 0) |
length(ncores) > 1) {
stop("Parameter 'ncores' must be a positive integer.")
}
}
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target_dims <- c(leadtime_dim, time_dim, memb_dim)
if (is.null(ref_period)) {
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ref_start <- NULL
ref_end <- NULL
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} else {
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ref_start <- ref_period[[1]]
ref_end <- ref_period[[2]]
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}
# Standardization
if (is.null(data_cor)) {
spei <- Apply(data = list(data),
target_dims = target_dims,
fun = .standardization,
leadtime_dim = leadtime_dim,
ref_period = ref_period, handle_infinity = handle_infinity,
method = method, distribution = distribution,
na.rm = na.rm, ncores = ncores)$output1
} else {
spei <- Apply(data = list(data, data_cor), target_dims = target_dims,
fun = .standardization,
leadtime_dim = leadtime_dim,
ref_period = ref_period, handle_infinity = handle_infinity,
method = method, distribution = distribution,
na.rm = na.rm, ncores = ncores)$output1
}
# add NA
if (!is.null(accum)) {
spei <- Apply(data = list(spei), target_dims = leadtime_dim,
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output_dims = leadtime_dim,
fun = function(x, accum, leadtime_dim) {
res <- c(rep(NA, accum-1), x)
return(res)
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}, accum = accum, leadtime_dim = leadtime_dim,
ncores = ncores)$output1
}
if (is.null(data_cor)) {
pos <- match(names(dim(data)), names(dim(spei)))
spei <- aperm(spei, pos)
} else {
pos <- match(names(dim(data_cor)), names(dim(spei)))
spei <- aperm(spei, pos)
}
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return(spei)
}
.standardization <- function(data, data_cor = NULL, leadtime_dim = 'time',
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ref_period = NULL, handle_infinity = FALSE,
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method = 'parametric', distribution = 'log-Logistic',
na.rm = FALSE) {
# data: [leadtime_dim, time_dim, memb_dim]
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dims <- dim(data)[-1]
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fit = 'ub-pwm'
coef = switch(distribution,
"Gamma" = array(NA, dim = 2, dimnames = list(c('alpha', 'beta'))),
"log-Logistic" = array(NA, dim = 3, dimnames = list(c('xi', 'alpha', 'kappa'))),
"PearsonIII" = array(NA, dim = 3, dimnames = list(c('mu', 'sigma', 'gamma'))))
if (is.null(data_cor)) {
# cross_val = TRUE
spei_mod <- data*NA
for (ff in 1:dim(data)[leadtime_dim]) {
data2 <- data[ff, , ]
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dim(data2) <- dims
if (method == 'non-parametric') {
bp <- matrix(0, length(data2), 1)
for (i in 1:length(data2)) {
bp[i,1] = sum(data2[] <= data2[i], na.rm = na.rm); # Writes the rank of the data
}
std_index <- qnorm((bp - 0.44)/(length(data2) + 0.12))
dim(std_index) <- dims
spei_mod[ff, , ] <- std_index
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} else {
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if (!is.null(ref_start) && !is.null(ref_end)) {
data_fit <- window(data2, ref_start, ref_end)
} else {
data_fit <- data2
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}
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for (nsd in 1:dim(data)[time_dim]) {
acu <- as.vector(data_fit[-nsd, ])
if (na.rm) {
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acu_sorted <- sort.default(acu, method = "quick")
} else {
acu_sorted <- sort.default(acu, method = "quick", na.last = TRUE)
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}
if (!any(is.na(acu_sorted)) & length(acu_sorted) != 0) {
acu_sd <- sd(acu_sorted)
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if (!is.na(acu_sd) & acu_sd != 0) {
if (distribution != "log-Logistic") {
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acu_sorted <- acu_sorted[acu_sorted > 0]
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}
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if (length(acu_sorted) >= 4) {
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f_params <- .std(data = acu_sorted, fit = fit,
distribution = distribution)
} else {
f_params <- NA
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}
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if (all(is.na(f_params))) {
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cdf_res <- NA
} else {
f_params <- f_params[which(!is.na(f_params))]
cdf_res = switch(distribution,
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"log-Logistic" = lmom::cdfglo(data2, f_params),
"Gamma" = lmom::cdfgam(data2, f_params),
"PearsonIII" = lmom::cdfpe3(data2, f_params))
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}
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std_index_cv <- array(qnorm(cdf_res), dim = dims)
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spei_mod[ff, nsd, ] <- std_index_cv[nsd, ]
}
}
}
}
}
} else {
# cross_val = FALSE
spei_mod <- data_cor*NA
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dimscor <- dim(data_cor)[-1]
for (ff in 1:dim(data)[leadtime_dim]) {
data_cor2 <- data_cor[ff, , ]
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dim(data_cor2) <- dimscor
if (method == 'non-parametric') {
bp <- matrix(0, length(data_cor2), 1)
for (i in 1:length(data_cor2)) {
bp[i,1] = sum(data_cor2[] <= data_cor2[i], na.rm = na.rm); # Writes the rank of the data
}
std_index <- qnorm((bp - 0.44)/(length(data_cor2) + 0.12))
dim(std_index) <- dimscor
spei_mod[ff, , ] <- std_index
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data2 <- data[ff, , ]
dim(data2) <- dims
if (!is.null(ref_start) && !is.null(ref_end)) {
data_fit <- window(data2, ref_start, ref_end)
} else {
data_fit <- data2
}
acu <- as.vector(data_fit)
if (na.rm) {
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acu_sorted <- sort.default(acu, method = "quick")
} else {
acu_sorted <- sort.default(acu, method = "quick", na.last = TRUE)
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}
if (!any(is.na(acu_sorted)) & length(acu_sorted) != 0) {
acu_sd <- sd(acu_sorted)
if (!is.na(acu_sd) & acu_sd != 0) {
if (distribution != "log-Logistic") {
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acu_sorted <- acu_sorted[acu_sorted > 0]
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if (length(acu_sorted) >= 4) {
f_params <- .std(data = acu_sorted, fit = fit,
distribution = distribution)
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if (all(is.na(f_params))) {
cdf_res <- NA
} else {
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f_params <- f_params[which(!is.na(f_params))]
cdf_res = switch(distribution,
"log-Logistic" = lmom::cdfglo(data_cor2, f_params),
"Gamma" = lmom::cdfgam(data_cor2, f_params),
"PearsonIII" = lmom::cdfpe3(data_cor2, f_params))
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std_index_cv <- array(qnorm(cdf_res), dim = dimscor)
spei_mod[ff, , ] <- std_index_cv
}
}
}
}
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}
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if (handle_infinity) {
# could also use "param_error" ?; we are giving it the min/max value of the grid point
spei_mod[is.infinite(spei_mod) & spei_mod < 0] <- min(spei_mod[!is.infinite(spei_mod)])
spei_mod[is.infinite(spei_mod) & spei_mod > 0] <- max(spei_mod[!is.infinite(spei_mod)])
}
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return(spei_mod)
}
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.std <- function(data, fit = 'pp-pwm', distribution = 'log-Logistic') {
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pwm = switch(fit,
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'pp-pwm' = pwm.pp(data, -0.35, 0, nmom = 3),
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pwm.ub(data, nmom = 3)
# TLMoments::PWM(data, order = 0:2)
)
lmom <- pwm2lmom(pwm)
if (!(!are.lmom.valid(lmom) || anyNA(lmom[[1]]) || any(is.nan(lmom[[1]])))) {
fortran_vec = c(lmom$lambdas[1:2], lmom$ratios[3])
params = switch(distribution,
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'log-Logistic' = tryCatch(lmom::pelglo(fortran_vec),
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error = function(e){parglo(lmom)$para}),
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'Gamma' = tryCatch(lmom::pelgam(fortran_vec),
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error = function(e){pargam(lmom)$para}),
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'PearsonIII' = tryCatch(lmom::pelpe3(fortran_vec),
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error = function(e){parpe3(lmom)$para}))
if (distribution == 'log-Logistic' && fit == 'max-lik') {
params = parglo.maxlik(data, params)$para
}
return(params)
} else {
return(NA)
}
}