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################################
#### Median direction
#### Tsagris Michail 1/2016
#### mtsagris@yahoo.gr
#### References: Fisher, N. I. (1985). Spherical medians.
#### Journal of the Royal Statistical Society. Series B, 47(2): 342-348.
#### Fisher, N. I., Lewis, T., & Embleton, B. J. (1987).
#### Statistical analysis of spherical data. Cambridge university press.
################################
mediandir_2 <- function(x) {
## x is the directional data
funa <- function(pa) {
pa <- pa / sqrt( sum(pa^2) )
a <- x %*% pa
a[ abs(a) > 1 ] <- 1
mean( acos( a ) )
}
suppressWarnings({
bar <- nlm( funa, Rfast::colMedians(x), iterlim = 10000 )
ini <- bar$estimate/sqrt( sum(bar$estimate^2) )
bar <- optim( ini, funa, control = list(maxit = 10000) )
})
med <- bar$par
med / sqrt( sum(med^2) )
}
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