RMangle: Anisotropy matrix given by angle

In RandomFields: Simulation and Analysis of Random Fields

Description

RMangle delivers an anisotropy matrix for the argument Aniso in RMmodel in two dimensions. RMangle requires one or two stretching values, passed by ratio or diag, and an angle.

In two dimensions and with angle equal to a and diag equal to (d1, d2) the anisotropy matrix A is

A = diag(d1, d2) %*% matrix(ncol=2, c(cos(a), sin(a), -sin(a), cos(a)))

In three dimensions and with angle equal to a, second angle L and diag equal to (d1, d2, d3) the anisotropy matrix A is

A = diag(d1, d2, d3) %*% matrix(ncol=3, c(cos(a) * cos(L), sin(a) * cos(L), sin(L), -sin(a), cos(a), 0, -cos(a) * sin(L), -sin(a) * sin(L), cos(L) )) i.e. Ax turns a vector x first in the x-z plane, then in the x-y plane.

Usage

RMangle(angle, lat.angle, ratio, diag) 

Arguments

angle	angle a
lat.angle	second angle; in 3 dimensions only
ratio	equivalent to diag=c(1, 1/ratio); in 2 dimensions only
diag	the diagonal components of the matrix

Value

RMangle returns an object of class RMmodel.

See Also

RMtrafo, RMmodel

Examples

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again

model <- RMexp(Aniso=RMangle(angle=pi/4, ratio=3))
plot(model, dim=2)

x <- seq(0, 2, 0.05)
z <- RFsimulate(x, x, model=model)
plot(z)


model <- RMexp(Aniso=RMangle(angle=pi/4, lat.angle=pi/8, diag=c(1,2,3)))
x <- seq(0, 2, 0.2)
z <- RFsimulate(x, x, x, model=model)
plot(z, MARGIN.slices=3)


## next model gives an example how to estimate the parameters back
n <- 20
x <- runif(n, 0, 10)
y <- runif(n, 0, 10)
coords <- expand.grid(x, y)
model <- RMexp(Aniso=RMangle(angle=pi/4, diag=c(1/4, 1/12)))
d <- RFsimulate(model, x=coords[, 1], y=coords[, 2], n=10)
estmodel <- RMexp(Aniso=RMangle(angle=NA, diag=c(NA, NA)))
system.time(RFfit(estmodel, data=d, modus_operandi='sloppy'))

RandomFields documentation built on Jan. 19, 2022, 1:06 a.m.