image.pemt: Images with Multi-directional Transiograms

Description

The function plots $2$-D sections of a multidirectional transiogram computed without any ellipsoidal interpolation.

Usage

"image"(x, main, mar, ask = TRUE, ...,  nlevels = 10, contour = FALSE)

Arguments

an object of class pemt.

main

the main title (on top) whose font and size are fixed.

mar

a scalar or a numerical vector of the form c(bottom, left, top, right) which gives the number of margin lines to be specified on the four sides of image to plot. See par(mar=.).

ask

a logical value; if TRUE, the user is asked for input, before each plot. See par(ask=.).

...

other arguments to pass to the function image.

nlevels

the number of levels to pass to the function contour.

contour

logical. If TRUE, the function contour is used to draw contour lines of the theoretical multidimensional transiogram over images. This permits to compare the model probabilities with the pseudo-empirical ones. Defaults to FALSE.

Value

Details

A multidimensional transiogram is a diagram which shows the transition probabilities for a single pair of categories. The probability is computed for any lag vector $h$ through $$\mbox{expm} (\Vert h \Vert R_h),$$ where entries of $R$ are not ellipsoidally interpolated, but they are estimated for the direction specified by the vector $h$.

The exponential matrix is evaluated by the scaling and squaring algorithm.

References

Carle, S. F., Fogg, G. E. (1997) Modelling Spatial Variability with One and Multidimensional Continuous-Lag Markov Chains. Mathematical Geology, 29(7), 891-918.

Higham, N. J. (2008) Functions of Matrices: Theory and Computation. Society for Industrial and Applied Mathematics.

Sartore, L. (2010) Geostatistical models for 3-D data. M.Phil. thesis, Ca' Foscari University of Venice.