spMC (version 0.3.2)

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 = "trm")

Value

An object of class pemt is returned.

Rdversion

1.1

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 $R_h$ 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 $R_h$ 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.

See Also

multi_tpfit_ml, tpfit_ml, image.pemt, plot.transiogram

Examples

data(ACM)

# Compute a 2-D section of a
# multi-directional transiogram
pemt(ACM$MAT3, ACM[, 1:3], 2,
     max.dist = c(200, 200, 20), 
     which.dire=c(1, 3), mle = "mdn")