test_that("regularellipse() point satisfy on equation", {
  a <- 3
  b <- 5
  expect_equal(drop(regularellipse(0, a = a, b = b)), c(x = a, y = 0))
  expect_equal(drop(regularellipse(pi/2, a = a, b = b)), c(x = 0, y = b))


  locs <- regularellipse(seq(-2*pi, 2*pi, length.out = 100), a = a, b = b)
  expect_equal(locs[, "x"]^2/(a^2) + locs[, "y"]^2/(b^2), rep(1, 100))
})

test_that("conf_fixedtrace() warns when ordered boundary is intersected", {
  set.seed(345)
  ms <- rsymm_norm(n = 10, mean = diag(c(4,2,1)))
  ms <- normalise_trace(ms)
  expect_warning(cr <- conf_fixedtrace(ms, alpha = 0.05, B = 20, npts = 1000),
                 "not.*descending")
})

test_that("conf_fixedtrace() contains population mean about 95% of the time", {
  skip_if_fast_check()
  set.seed(345)
  popmeanincr <- replicate(100, {
     ms <- rsymm_norm(n = 30, mean = diag(c(4,2,1)))
     ms <- normalise_trace(ms)
     cr <- suppressWarnings(conf_fixedtrace(ms, alpha = 0.05, B = 100, npts = 1000))
     conf_fixedtrace_inregion(c(4,2,1)/7, cr)})
  expect_lt(abs(mean(popmeanincr) - 0.95),
            2*sd(popmeanincr)/sqrt(length(popmeanincr)))
})