center {rotations}

Center rotation data

Description

This function will take the sample Rs and return the sample Rs centered at S. That is, the ith observation of Rs denoted R_i is returned as S^\top R_i. If S is the true center then the projected mean should be close to the 3-by-3 identity matrix.

Usage

center(x, S)

## S3 method for class 'SO3'
center(x, S)

## S3 method for class 'Q4'
center(x, S)

Arguments

x

n\times p matrix where each row corresponds to a random rotation in matrix (p=9) or quaternion (p=4) form.

S

the rotation or a matrix of n\times p rotations about which to center each row of x.

Value

The sample centered about S

Examples

Rs <- ruars(5, rcayley)
cRs <- center(Rs, mean(Rs))
mean(cRs)                      #Close to identity matrix

all.equal(cRs, Rs - mean(Rs))  #TRUE, center and '-' have the same effect
                               #See ?"-.SO3" for more details

center(Rs,Rs)                  #n-Identity matrices: If the second argument is of the same dimension
                               #as Rs then each row is centered around the corresponding
                               #row in the first argument