gradient.search {rotations}

Gradient optimization for rotation data

Description

Gradient based optimization for user defined central orientation of a rotation sample.

Usage

gradient.search(
  sample,
  error,
  minerr = 1e-05,
  start = mean(sample),
  theta = NULL
)

Arguments

sample

sample of rotations.

error

user defined function to observed distance between sample and estimate, has to have parameters for the sample and the estimate.

minerr

minimal distance to consider for convergence.

start

starting value for the estimation.

theta

size of the grid considered.

Value

list of

• Shat estimate of the main direction

• iter number of iterations necessary for convergence

• theta final size of the grid

• minerr error used for convergence

• error numeric value of total sample's distance from main direction

Examples

# minimize L1 norm:
L1.error <- function(sample, Shat) {
  sum(rot.dist(sample, Shat, method = "intrinsic", p = 1))
}

cayley.sample <- ruars(n = 10, rangle = rcayley, nu = 1, space = 'SO3')
SL1 <- gradient.search(cayley.sample, L1.error, start = id.SO3)

# visually no perceptible difference between median estimates from in-built function and 
# gradient based search (for almost all starting values)


plot(cayley.sample, center=SL1$Shat, show_estimates="all")