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```
#' @title Spatial variance indicator
#'
#' @description This functions computes the spatial variance of spatial data.
#' It also computes a null value obtained by randomizing
#' the matrix.
#'
#' @param input A matrix or a list of matrices. The matrix
#' values can be logical, with \code{FALSE} (empty) or \code{TRUE} (occupied)
#' values. The entries can also be continuous (like NDVI or EVI data).
#'
#' @param subsize Dimension of the submatrix used to coarse-grain the
#' original matrix. This must be an integer less than size of the full
#' matrix. Coarse-graining reduces the size of the matrix by a factor
#' \code{subsize} in each dimension of the matrix. Variance is calculated
#' on the coarse-grained matrix.
#'
#' @param nreplicates Number of replicates to produce to estimate null
#' distribution of index.
#'
#' @return A list (or a list of lists if input was a list of matrices) with
#' components:
#' \itemize{
#' \item `value`: Spatial variance of the matrix
#' }
#' If nreplicates is above 2, then the list has the following additional
#' components :
#' \itemize{
#' \item `null_mean`: Mean spatial variance of the null distribution
#' \item `null_sd`: SD of spatial variance in the null distribution
#' \item `z_score`: Z-score of the observed value in the null distribution
#' (value minus the null mean and divided by null
#' standard deviation)
#' \item `pval`: p-value based on the rank of the observed spatial variance
#' in the null distribution. A low p-value means that
#' the indicator value is significantly higher than the
#' null values.
#' }
#'
#' @details
#'
#' Spatial variance is a measure of fluctuations in space. Based on the theory
#' of critical slowing down, when systems approach critical points
#' they are expected to show increased fluctuations in space. Thus, increasing
#' spatial variance is proposed as an early warning signal of impending
#' critical transitions.
#'
#' For example, many high resolution spatial data are classified as FALSE (empty)
#' or TRUE (occupied by plant). In such cases, spatial variance captures just
#' the variance in data, but not that of spatial structure.
#' To resolve the issue, this function employs a method called coarse-graining,
#' proposed in Kefi et al (2014), and described in detail in
#' Sankaran et al. (2017). One must specify a subsize above one for
#' binary valued data sets to obtain meaningful values.
#'
#' \code{subsize} has to be an integer. It has to be less than or equal to
#' half of matrix size (N). \code{subsize} must also be preferably a
#' divisor of N. If it is not a divisor of N, the remainder rows and columns
#' are discarded when computing coarse-graining matrices.
#'
#' Null model evaluations are also done on coarse-grained matrices.
#'
#' @references
#'
#' Guttal, V., and Jayaprakash, C. (2009). Spatial variance and
#' spatial skewness: leading indicators of regime shifts in spatial
#' ecological systems. Theoretical Ecology, 2(1), 3-12.
#'
#' Kefi, S., Guttal, V., Brock, W.A., Carpenter, S.R., Ellison, A.M.,
#' Livina, V.N., et al. (2014). Early Warning Signals of Ecological
#' Transitions: Methods for Spatial Patterns. PLoS ONE, 9, e92097.
#'
#' Sankaran, S., Majumder, S., Kefi, S., and Guttal, V. (2017). Implication
#' of being discrete and spatial in detecting early warning signals
#' of regime shifts. Ecological Indicators.
#'
#' @examples
#'
#' data(serengeti)
#' \dontrun{
#' indicator_variance(serengeti, nreplicates = 499)
#' }
#'
#'@export
indicator_variance <- function(input,
subsize = 5,
nreplicates = 999) {
check_mat(input) # checks data input
if (is.list(input)) {
# Returns a list of lists
return( lapply(input, indicator_variance, subsize, nreplicates) )
} else {
# We alter the raw_variance function so it includes coarse_graining
# in case subsize is above 1.
indicf <- raw_variance
if ( subsize > 1 ) {
indicf <- with_coarse_graining(raw_variance, subsize)
}
# Compute and return indicator
return( compute_indicator_with_null(input, nreplicates, indicf) )
}
}
raw_variance <- function(mat) { var(as.vector(mat)) }
```

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