Computes Hill's index of diversity (Hill numbers) on different classes of numeric matrices using a moving window algorithm.
Hill(x, window = 3, alpha = 1, rasterOut=TRUE,
np = 1, na.tolerance=1.0, cluster.type = "SOCK",
debugging = FALSE)input data may be a matrix, a Spatial Grid Data Frame, a RasterLayer or a list of these objects. In the latter case, only the first element of the list will be considered.
the side of the square moving window, it must be a odd numeric value greater than 1 to ensure that the target pixel is in the centre of the moving window. Default value is 3.
Order of the Hill number to compute the index. If "alpha" is a vector with length greater than 1, then the index will be calculated over x for each value in the sequence.
Boolean, if TRUE output will be in RasterLayer format with x as template.
the number of processes (cores) which will be spawned. Default value is 1.
a numeric value \((0.0-1.0)\) which indicates the proportion of NA values that will be tolerated to calculate Hill's index in each moving window over x. If the relative proportion of NA's in a moving window is bigger than na.tolerance, then the value of the window will be set as NA, otherwise Rao's index will be calculated considering the non-NA values. Default values is 1.0 (i.e., no tolerance for NA's).
the type of cluster which will be created. The options are "MPI" (calls "makeMPIcluster"), "FORK" and "SOCK" (call "makeCluster"). Default type is "SOCK".
a boolean variable set to FALSE by default. If TRUE, additional messages will be printed. For debugging only.
A list of matrices of dimension dim(x) with length equal to the length of alpha.
Hill numbers (\({}^qD\)) are calculated on a numerical matrices as \({}^qD = (\sum_{i=1}^{R} {p^q}_i)^{1/(1-q)}\),where q is the order of the Hill number, R is the total number of categories (i.e., unique numerical values in a numerical matrix), p is the relative abundance of each category. When q=1, Shannon.R is called to calculate \(exp(H^1)\) instead of the indefinite \({}^1D\). if \(q > 2*10^9\), BerkgerParker.R is called to calculate \(1/{{}^\infty D}\). Hill numbers of low order weight more rare categories, whereas Hill numbers of higher order weight more dominant categories.
Hill, M.O. (1973). Diversity and evenness: a unifying notation and its consequences. Ecology 54, 427-431.
# NOT RUN {
#Minimal example; compute Hill's index with alpha 1:5
a <- matrix(c(10,10,10,20,20,20,20,30,30),ncol=3,nrow=3)
hill <- Hill(x=a,window=3,alpha=1:5)
# }
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