UARS: Generic UARS Distribution

In rotations: Working with Rotation Data

Generic UARS Distribution

Description

Density, distribution function and random generation for the the generic uniform axis-random spin (UARS) class of distributions.

Usage

duars(R, dangle, S = id.SO3, kappa = 1, ...)

puars(R, pangle = NULL, S = id.SO3, kappa = 1, ...)

ruars(n, rangle, S = NULL, kappa = 1, space = "SO3", ...)

Arguments

R	Value at which to evaluate the UARS density.
dangle	The function to evaluate the angles from, e.g. dcayley, dvmises, dfisher, dhaar.
S	central orientation of the distribution.
kappa	concentration parameter.
...	additional arguments.
pangle	The form of the angular density, e.g. pcayley, pvmises, pfisher, phaar.
n	number of observations. If length(n)>1, the length is taken to be the number required.
rangle	The function from which to simulate angles, e.g. rcayley, rvmises, rhaar, rfisher.
space	indicates the desired representation: matrix ("SO3") or quaternion ("Q4").

Details

For the rotation R with central orientation S and concentration κ the UARS density is given by

f(R|S,κ)=4π C(acos[tr(S'R)-1]/2|κ)/[3-tr(S'R)]

where C(r|κ) is one of the Angular-distributions.

bingham09

Value

duars	gives the density
puars	gives the distribution function. If pangle is left empty, the empirical CDF is returned.
ruars	generates random deviates

See Also

For more on the angular distribution options see Angular-distributions.

Examples

#Generate random rotations from the Cayley-UARS distribution with central orientation
#rotated about the y-axis through pi/2 radians
S <- as.SO3(c(0, 1, 0), pi/2)
Rs <- ruars(20, rangle = rcayley, kappa = 1, S = S)

rs <- mis.angle(Rs-S)                          #Find the associated misorientation angles
frs <- duars(Rs, dcayley, kappa = 10, S = S)   #Compute UARS density evaluated at each rotations
plot(rs, frs)

cdf <- puars(Rs, pcayley, S = S)               #By supplying 'pcayley', it is used to compute the
plot(rs, cdf)                                  #the CDF

ecdf <- puars(Rs, S = S)                       #No 'puars' arguement is supplied so the empirical
plot(rs, ecdf)                                 #cdf is returned

rotations documentation built on June 25, 2022, 1:06 a.m.