test_that("identical kernel estimates have zero divergence", {
    set.seed(11)
    x <- matrix(rnorm(80), ncol = 2)
    H <- diag(c(0.4, 0.5))
    expect_equal(biv_kld(x, x, Hx = H, Hy = H, grid_size = 25),
                 0, tolerance = 1e-12)
})

test_that("kernel estimator returns details and validates samples", {
    set.seed(12)
    x <- matrix(rnorm(80), ncol = 2)
    y <- matrix(rnorm(80, 0.25), ncol = 2)
    result <- biv_kld(x, y, bandwidth = "normal", grid_size = 25,
                      details = TRUE)
    expect_s3_class(result, "bivkld_estimate")
    expect_true(is.finite(result$estimate))
    expect_gte(result$estimate, 0)
    expect_error(biv_kld(x[, 1, drop = FALSE], y), "two columns")
    expect_error(biv_kld(rbind(x, c(NA, 0)), y), "finite")
})

test_that("pairwise matrix is directed and has a zero diagonal", {
    set.seed(13)
    groups <- list(
        A = matrix(rnorm(80), ncol = 2),
        B = matrix(rnorm(80, 0.5), ncol = 2),
        C = matrix(rnorm(80, -0.2), ncol = 2)
    )
    result <- biv_kld_matrix(groups, bandwidth = "normal", grid_size = 25)
    expect_s3_class(result, "bivkld_matrix")
    expect_equal(dim(result), c(3L, 3L))
    expect_equal(unname(diag(result)), rep(0, 3))
    expect_true(all(result >= 0))
    expect_named(attr(result, "bandwidth"), names(groups))
})