Tools for working with rotational data, including simulation from the most commonly used distributions on SO(3), methods for different Bayes, mean and median type estimators for the central orientation of a sample, confidence/credible regions for the central orientation based on those estimators and a novel visualization technique for rotation data. Most recently, functions to identify potentially discordant (outlying) values have been added.
*The Maxwell-Boltzmann distribution function has been added.
discord
has been added, which computes a measure of discord for random rotationstail.Q4
and tail.SO3
have been addedtype
argument in all of the Bayesian functionsmethod
argument in regions
function was changed from trans
to transformation
, a call to match.arg()
still allows for trans
type
argument in regions
function has been changed from theory
to asymptotic
print
method for Q4
objects now respects the digits
optioninteractive' has been added to
plot.SO3' and plot.Q4' which, when set to
TRUE', creates a sphere in 3D using `rgl' that can be manipulated by the usermethod
argument of the region
functions have been changed to "trans"
and "direct"
to align with the current names in my dissertation. "trans"
is short for "transformation," which is used to access the methods based on a transformation of a directional statistics result while "direct"
is used for the methods that rely on theory for SO(3) directly.Vignette added that introduces the package
Create a plot.Q4
function that uses plot.SO3
after casting the object to class SO3
The functions SO3
and Q4
have been deprecated. All of their functionality has been moved to as.SO3
and as.Q4
angle
and axis
have been renamed mis.angle
and mis.axis
, respectively, to avoid naming clashes with the graphics
package
The period.sep
naming convention has been adopted for all functions in package. The functions formerly known as sum_dist
, exp_skew
, cayley_kappa
, fisher_kappa
and vmises_kappa
are now called rotdist.sum
, skew.exp
, cayley.kappa
, fisher.kappa
and vmises.kappa
, respectively.
dist
renamed to rot.dist
to avoid clashes with stats
package
Fixes in documentation for Bayes point estimation
print.Q4
and print.SO3
no longer print the object class
print.SO3
now names the columns R11
through R33
to signify which element in the matrix each row corresponds to
is.SO3
more rigorously tests for conditions of SO3
Arithmetic for SO3
objects now is possible for samples of rotations
Multiple columns can be supplied to col
in plot
via grid.arrange. Each requested column is identified by its axis and one legend is printed when applicable. For example col=c(1,3)
will print two labelled eyeballs, one for the x- and one for the z-axis.
Quaternions are only unique up to their sign, that is if q is a quaternion the q=-q. So ==
has be redefined such that q==-q
will return TRUE
.
In 'dist' the 'method' argument now accepts the option 'extrinsic' and returns the same result had the 'projected' option been used.
The '['
operator has been redefined to maintain the SO3
or Q4
class of the object.
Addition +
and subtraction -
have been redefined for the multiplicative group SO(3). That is, for R1 and R2 in SO(3), R1+R2=R2R1, R1-R2=R2'R1 and -R1=R1'. Similarly for quaternions.
The head
and str
functions have been modified to properly handle objects of class 'SO3'
and 'Q4'
.
Functions for Bayesian analysis
type
, tuneS
, tuneK
, burnin
and B
. These arguments determine the transition probability form, tuning parameters for the central orientation, concentration parameter, burnin for the MCMC and total number of draws from the posterior, respectively. Currently only 'Cayley'
, 'Fisher'
and 'Mises'
are valid options for type
. See the respective help files for more details.MCMCSO3
implements a Gibbs-within-MCMC algorithm to get draws from the posterior distributions for the concentration parameter $S$ and concentration parameter $\kappa$. A list of four items is returned: S
is a B-by-p matrix where each row corresponds to a draw from the posterior for the central orientation S, kappa
is a vector of B draws from the posterior for the concentration parameter $\kappa$ and the transition probabilities for the central orientation and concentration are given by Saccept
and Kaccept
,respectively.bayes.mean
.region
by setting method='Bayes'
.