rotations (version 1.6.3)

UARS: 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").

Value

duars

gives the density

puars

gives the distribution function. If pangle is left empty, the empirical CDF is returned.

ruars

generates random deviates

Details

For the rotation R with central orientation S and concentration $\kappa$ the UARS density is given by $$f(R|S,\kappa )=\frac{4\pi }{3-tr(S^{\mathrm{\top }}R)}C({\cos }^{-1}[tr(S^{\mathrm{\top }}R)-1]/2|\kappa )$$ where $C(r|\kappa )$ is one of the Angular-distributions.

bingham09

See Also

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

Examples

# NOT RUN {
#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
# }