Nothing
## ----setup,include=FALSE------------------------------------------------------
orig_options <- options()
options(digits=3)
library(knitr)
opts_chunk$set(
concordance = TRUE,
fig.path = 'figure/',
fig.width = 5,
fig.height = 5,
fig.show = 'hold',
fig.align = 'center'
)
knit_hooks$set(document = function(x) {
sub('\\usepackage[]{color}', '\\usepackage{xcolor}', x, fixed = TRUE)
})
library(rotations)
## ----ex2----------------------------------------------------------------------
r <- pi/2
U <- c(0, 1 ,0)
W <- U*r
R <- as.SO3(W)
R
identical(R, as.SO3(U, r))
## ----ex3----------------------------------------------------------------------
mis.angle(R)*2/pi
mis.axis(R)
## ----ex4----------------------------------------------------------------------
as.Q4(U, r)
as.Q4(as.SO3(U, r))
## ----ex5----------------------------------------------------------------------
Rs <- ruars(n = 20, rangle = rcayley, kappa = 1, space = 'SO3')
Qs <- ruars(n = 20, rangle = rcayley, kappa = 1, space = 'Q4')
Rs <- ruars(n = 20, rangle = rcayley, nu = 1, space = 'SO3')
Qs <- ruars(n = 20, rangle = rcayley, nu = 1, space = 'Q4')
head(Rs,3)
## ----gridsearch---------------------------------------------------------------
# error function definition
L1.error <- function(sample, Shat) {
sum(rot.dist(sample, Shat, method = "intrinsic", p = 1))
}
cayley.sample <- ruars(n = 50, rangle = rcayley, nu = 1, space = "SO3")
# gradient based optimization
system.time(SL1 <- gradient.search(cayley.sample, L1.error))
# in-built function
system.time(S <- median(cayley.sample, type = "geometric"))
rot.dist(S, SL1$Shat)
## ----ex6----------------------------------------------------------------------
Rs <- ruars(50, rcayley, kappa = 10)
region(
x = Rs,
method = "direct",
type = "asymptotic",
estimator = "mean",
alp = 0.05
)
region(
x = Rs,
method = "direct",
type = "bootstrap",
estimator = "mean",
alp = 0.05,
m = 300
)
region(
x = Rs,
method = "direct",
type = "asymptotic",
estimator = "median",
alp = 0.05
)
region(
x = Rs,
method = "direct",
type = "bootstrap",
estimator = "median",
alp = 0.05,
m = 300
)
## ----ex7,fig.cap="The $x$-axis of a random sample from the Cayley-UARS distribution with $\\kappa=1$ and $n=50$. All four point estimates are displayed on the left and all three region methods along with the projected mean are on the right.",fig.lp="figure:eye1",out.width=".4\\textwidth",fig.pos="h",dev='png'----
plot(
x = Rs,
center = mean(Rs),
show_estimates = "all"
)
plot(
x = Rs,
center = mean(Rs),
show_estimates = "proj.mean",
mean_regions = "all",
alp = .05
)
## ----ex1----------------------------------------------------------------------
data(drill)
head(drill)
Subj1Wrist<-subset(drill, Subject == '1' & Joint == 'Wrist')
Subj1Wdata <- as.Q4(Subj1Wrist[,5:8])
mean(Subj1Wdata)
## ----ex21---------------------------------------------------------------------
data(nickel)
head(nickel[,1:6])
Location1<-subset(nickel, location==1)
Loc1data<-as.SO3(Location1[,5:13])
mean(Loc1data)
## ----summary------------------------------------------------------------------
Qs <- ruars(20, rcayley, space = 'Q4')
Rs <- as.SO3(Qs)
suppressMessages(require(onion))
onionQs <- as.quaternion(matrix(Qs,nrow=4, byrow = TRUE))
suppressMessages(require(orientlib))
orientRs <- rotvector(matrix(Rs, ncol = 9))
## ----resetoption, include=FALSE-----------------------------------------------
options(orig_options)
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