test_that("WW relabeling orders component medians and preserves likelihood", {
  draws <- rbind(
    c(alpha = 0.4, p = 0.2, k1 = 2, th1 = 3, k2 = 1.5, th2 = 0.7, loglik = -4),
    c(alpha = -0.3, p = 0.7, k1 = 1.2, th1 = 0.5, k2 = 2.5, th2 = 2, loglik = -5)
  )
  result <- ambs:::.relabel_posterior(draws, "ww")
  medians <- ambs:::.component_medians(result$draws, "ww")
  expect_true(all(medians[, "m1"] <= medians[, "m2"]))
  expect_equal(result$draws[, "loglik"], draws[, "loglik"])

  time <- c(0.2, 0.9, 1.8)
  status <- c(1, 0, 1)
  for (i in seq_len(nrow(draws))) {
    before <- draws[i, ]
    after <- result$draws[i, ]
    ll_before <- ambs:::.loglik_ww(
      before["alpha"], before["p"], 1 - before["p"],
      before["th1"], before["th2"], before["k1"], before["k2"],
      time, status
    )
    ll_after <- ambs:::.loglik_ww(
      after["alpha"], after["p"], 1 - after["p"],
      after["th1"], after["th2"], after["k1"], after["k2"],
      time, status
    )
    expect_equal(ll_after, ll_before, tolerance = 1e-12)
    for (type in c("s", "h", "d")) {
      expect_equal(
        ambs:::.curve_ww(before, time, type),
        ambs:::.curve_ww(after, time, type),
        tolerance = 1e-12
      )
    }
  }
})

test_that("LL relabeling orders locations and preserves likelihood", {
  draws <- rbind(
    c(alpha = 0.5, p = 0.25, mu1 = 2, mu2 = 0, sig1 = 0.2, sig2 = 0.8, loglik = -3),
    c(alpha = -0.4, p = 0.6, mu1 = -1, mu2 = 1, sig1 = 0.5, sig2 = 0.3, loglik = -6)
  )
  result <- ambs:::.relabel_posterior(draws, "ll")
  expect_true(all(result$draws[, "mu1"] <= result$draws[, "mu2"]))

  time <- c(0.3, 1, 3)
  status <- c(1, 1, 0)
  for (i in seq_len(nrow(draws))) {
    before <- draws[i, ]
    after <- result$draws[i, ]
    ll_before <- ambs:::.loglik_ll(
      before["alpha"], before["p"], 1 - before["p"],
      before["mu1"], before["mu2"], before["sig1"], before["sig2"],
      time, status
    )
    ll_after <- ambs:::.loglik_ll(
      after["alpha"], after["p"], 1 - after["p"],
      after["mu1"], after["mu2"], after["sig1"], after["sig2"],
      time, status
    )
    expect_equal(ll_after, ll_before, tolerance = 1e-12)
    for (type in c("s", "h", "d")) {
      expect_equal(
        ambs:::.curve_ll(before, time, type),
        ambs:::.curve_ll(after, time, type),
        tolerance = 1e-12
      )
    }
  }
})

test_that("relabeling requires exchangeable same-family priors", {
  symmetric <- ambs:::.default_prior("ww")
  asymmetric <- symmetric
  asymmetric$component2$k$meanlog <- asymmetric$component1$k$meanlog + 0.2
  expect_true(ambs:::.component_priors_exchangeable("ww", symmetric))
  expect_false(ambs:::.component_priors_exchangeable("ww", asymmetric))
  expect_error(
    ambs:::.validate_ident_request("ww", asymmetric, "relabel"),
    "exchangeable"
  )
  expect_error(
    ambs:::.validate_ident_request("gw", ambs:::.default_prior("gw"), "relabel"),
    "distribution family"
  )
})

test_that("known exact degeneracies are detected", {
  ww <- matrix(rep(c(alpha = 0, p = 0.5, k1 = 2, th1 = 1,
                     k2 = 2, th2 = 2, loglik = -1), 20), nrow = 20, byrow = TRUE)
  colnames(ww) <- c("alpha", "p", "k1", "th1", "k2", "th2", "loglik")
  gw <- matrix(rep(c(alpha = 0.4, p = 0.5, k1 = 1, th1 = 1,
                     k2 = 1, th2 = 1, loglik = -1), 20), nrow = 20, byrow = TRUE)
  colnames(gw) <- colnames(ww)
  ll <- matrix(rep(c(alpha = 0.4, p = 0.5, mu1 = 1, mu2 = 1,
                     sig1 = 0.5, sig2 = 0.5, loglik = -1), 20), nrow = 20, byrow = TRUE)
  colnames(ll) <- c("alpha", "p", "mu1", "mu2", "sig1", "sig2", "loglik")

  for (case in list(list(ww, "ww"), list(gw, "gw"), list(ll, "ll"))) {
    diagnosed <- ambs:::.diagnose_identifiability(case[[1]], case[[2]], c(0.2, 1, 2))
    expect_equal(diagnosed$known_degeneracy$probability, 1)
    expect_equal(diagnosed$status, "non_identifiable")
  }
})

test_that("overlap and boundary diagnostics flag weak identification", {
  draws <- matrix(rep(c(alpha = 0.5, p = 0.99, mu1 = 1, mu2 = 1.01,
                        sig1 = 0.5, sig2 = 0.6, loglik = -1), 20),
                  nrow = 20, byrow = TRUE)
  colnames(draws) <- c("alpha", "p", "mu1", "mu2", "sig1", "sig2", "loglik")
  diagnosed <- ambs:::.diagnose_identifiability(draws, "ll", c(0.2, 1, 2))
  expect_equal(diagnosed$weight_boundary$probability, 1)
  expect_true(diagnosed$component_overlap$probability > 0)
  expect_equal(diagnosed$status, "weak")
})

test_that("public ident interface records raw and relabeled draws", {
  set.seed(27)
  fit <- suppressWarnings(alpmixsurv(
    c(0.4, 0.8, 1.2, 2), c(1, 1, 0, 1), model = "ll",
    mcmc = list(nburn = 10, nsamp = 20), ident = "auto"
  ))
  expect_equal(nrow(fit$posterior_raw), 20)
  expect_equal(fit$identifiability$method, "median-based posterior relabeling")
  expect_true(all(fit$posterior[, "mu1"] <= fit$posterior[, "mu2"]))

  fit_none <- suppressWarnings(alpmixsurv(
    c(0.4, 0.8, 1.2, 2), c(1, 1, 0, 1), model = "ll",
    mcmc = list(nburn = 2, nsamp = 4), ident = "none"
  ))
  expect_equal(fit_none$posterior, fit_none$posterior_raw)
  expect_equal(fit_none$identifiability$status, "not_assessed")
})