image.multi_tpfit: Images with Multidimensional Transiograms

Description

The function plots $2$-D sections of a predicted multidimensional transiograms computed through ellipsoidal interpolation.

Usage

"image"(x, mpoints, which.dire, max.dist, main, mar, ask = TRUE, ..., nlevels = 10, contour = TRUE)

Arguments

an object of the class multi_tpfit, typically with the output of the function multi_tpfit.

mpoints

the number of points per axes. It controls the accuracy of images to plot.

which.dire

a vector with two chosen axial directions. If omitted, all $2$-D sections are plotted.

max.dist

a scalar or a vector of maximum length for the chosen axial directions.

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 over the image. Defaults to TRUE.

Value

Details

A multidimensional transiogram is a diagram which shows the transition probabilities for a single pair of categories. It is computed for any lag vector $h$ through $$\mbox{expm} (\Vert h \Vert R),$$ where entries of $R$ are ellipsoidally interpolated (see multi_tpfit).

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.