pemt {spMC}

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 \times 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.

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.

Value

An object of class pemt is returned.

Author(s)

Luca Sartore [e-mail]

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")