Hill: Hill's index of diversity - Hill numbers (D)

In rasterdiv: Diversity Indices for Numerical Matrices

Hill's index of diversity - Hill numbers (D)

Description

Computes Hill's index of diversity (Hill numbers) on different classes of numeric matrices using a moving window algorithm.

Usage

Hill(x, window = 3, alpha = 1, rasterOut=TRUE, 
	np = 1, na.tolerance=1.0, cluster.type = "SOCK", 
	debugging = FALSE)

Arguments

x	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.
window	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.
alpha	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.
rasterOut	Boolean, if TRUE output will be in RasterLayer format with x as template.
np	the number of processes (cores) which will be spawned. Default value is 1.
na.tolerance	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).
cluster.type	the type of cluster which will be created. The options are "MPI" (calls "makeMPIcluster"), "FORK" and "SOCK" (call "makeCluster"). Default type is "SOCK".
debugging	a boolean variable set to FALSE by default. If TRUE, additional messages will be printed. For debugging only.

Details

Hill numbers ({}^qD) are calculated on a numerical matrices as {}^qD = (∑_{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/{{}^∞ D}. Hill numbers of low order weight more rare categories, whereas Hill numbers of higher order weight more dominant categories.

Value

A list of matrices of dimension dim(x) with length equal to the length of alpha.

Note

Linux users need to install libopenmpi for MPI parallel computing. Linux Ubuntu users may try: apt-get update; apt-get upgrade; apt-get install mpi; apt-get install libopenmpi-dev; apt-get install r-cran-rmpi

Microsoft Windows users may need some additional work to use "MPI", see:
https://bioinfomagician.wordpress.com/2013/11/18/installing-rmpi-mpi-for-r-on-mac-and-windows/

Author(s)

Marcantonio Matteo [e-mail]
Martina Iannacito [e-mail]
Duccio Rocchini [e-mail]

References

Hill, M.O. (1973). Diversity and evenness: a unifying notation and its consequences. Ecology 54, 427-431.

See Also

BergerParker Shannon

Examples

#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)

rasterdiv documentation built on Nov. 24, 2022, 9:07 a.m.