pemt: Multi-directional Transiograms Estimation

Description

The function computes the multi-directional transiograms without any ellipsoidal interpolation for $2$-D sections.

Usage

pemt(data, coords, mpoints, which.dire, max.dist, tolerance = pi/8, rotation = NULL, mle = "avg")

Arguments

data

a categorical data vector of length $n$.

coords

an $n x d$ matrix where each row denotes the $d$-D coordinates of data locations.

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.

tolerance

a numerical value for the tolerance angle (in radians). It's pi/8 by default.

rotation

a numerical vector of length $d - 1$ with rotation angles (in radians), in order to perform the main axes rotation when multidimensional transiogram is estimated. No rotation is performed by default. See multi_tpfit_ml.

mle

a character value to pass to the function tpfit_ml. It is "avg" by default.

Value

pemt is returned.

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 $h$.

In particular cases, some entries of the estimated matrix $R$ might be not finite, so that the exponential matrix is computable and the resulting transition probabilities are set to be NaN. If mle = "mlk", this problem may be partially solved.

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.