Rotation group, also known as special orthogonal group, is a Riemannian manifold $$SO(p) = \lbrace Q \in \mathbf{R}^{p\times p}~\vert~ Q^\top Q = I, \textrm{det}(Q)=1 \rbrace $$ where the name originates from an observation that when \(p=2,3\) these matrices are rotation of shapes/configurations.
Arguments
- input
data matrices to be wrapped as
riemdataclass. Following inputs are considered,- array
a \((p\times p\times n)\) array where each slice along 3rd dimension is a rotation matrix.
- list
a length-\(n\) list whose elements are \((p\times p)\) rotation matrices.
Value
a named riemdata S3 object containing
- data
a list of \((p\times p)\) rotation matrices.
- size
size of each rotation matrix.
- name
name of the manifold of interests, "rotation"
Examples
#-------------------------------------------------------------------
# Checker for Two Types of Inputs
#-------------------------------------------------------------------
## DATA GENERATION
d1 = array(0,c(3,3,5))
d2 = list()
for (i in 1:5){
single = qr.Q(qr(matrix(rnorm(9),nrow=3)))
d1[,,i] = single
d2[[i]] = single
}
## RUN
test1 = wrap.rotation(d1)
test2 = wrap.rotation(d2)