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. References: Bingham, Melissa A. and Nordman, Dan J. and Vardeman, Steve B. (2009)
*The Maxwell-Boltzmann distribution function has been added.
discordhas been added, which computes a measure of discord for random rotations
tail.SO3have been added
typeargument in all of the Bayesian functions
regionsfunction was changed from
transformation, a call to
match.arg()still allows for
regionsfunction has been changed from
Q4objects now respects the
interactive' has been added toplot.SO3' and
plot.Q4' which, when set toTRUE', creates a sphere in 3D using `rgl' that can be manipulated by the user
methodargument of the
regionfunctions have been changed to
"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
plot.Q4 function that uses
plot.SO3 after casting the object to class
Q4 have been deprecated. All of their functionality has been moved to
axis have been renamed
mis.axis, respectively, to avoid naming clashes with the
period.sep naming convention has been adopted for all functions in package. The functions formerly known as
vmises_kappa are now called
dist renamed to
rot.dist to avoid clashes with
Fixes in documentation for Bayes point estimation
print.SO3 no longer print the object class
print.SO3 now names the columns
R33 to signify which element in the matrix each row corresponds to
is.SO3 more rigorously tests for conditions of
SO3 objects now is possible for samples of rotations
Multiple columns can be supplied to
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
In 'dist' the 'method' argument now accepts the option 'extrinsic' and returns the same result had the 'projected' option been used.
'[' operator has been redefined to maintain the
Q4 class of the object.
+ 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.
str functions have been modified to properly handle objects of class
Functions for Bayesian analysis
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
'Mises'are valid options for
type. See the respective help files for more details.
MCMCSO3implements 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:
Sis a B-by-p matrix where each row corresponds to a draw from the posterior for the central orientation S,
kappais 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