test_that("Euclidean implementations satisfy the metric properties", {
  X = rbind(c(0, 0), c(1, 0), c(1, 2), c(-1, 1))

  Dfast = EuclideanMulticore_Distance(X)
  expect_distance_structure(Dfast)
  expect_positive_off_diagonal(Dfast)
  expect_triangle_inequality(Dfast)

  Dweighted = EuclideanGPU_Distance(
    X, Weights = c(1, 3), backend = "cpu", OutputType = "mat"
  )
  expect_distance_structure(Dweighted)
  expect_positive_off_diagonal(Dweighted)
  expect_triangle_inequality(Dweighted)

  # A zero weight removes a coordinate and can collapse different vectors.
  collapsed = EuclideanGPU_Distance(
    rbind(c(0, 0), c(0, 1), c(2, 1)),
    Weights = c(1, 0), backend = "cpu", OutputType = "mat"
  )
  expect_distance_structure(collapsed)
  expect_triangle_inequality(collapsed)
  expect_equal(collapsed[1, 2], 0)
})

test_that("fractional Minkowski behavior changes at p = 1", {
  X = rbind(c(0, 0), c(1, 0), c(1, 1))

  D1 = Fractional_Distance(X, p = 1)
  D2 = Fractional_Distance(X, p = 2)
  expect_distance_structure(D1)
  expect_distance_structure(D2)
  expect_positive_off_diagonal(D1)
  expect_positive_off_diagonal(D2)
  expect_triangle_inequality(D1)
  expect_triangle_inequality(D2)

  Dhalf = Fractional_Distance(X, p = 1 / 2)
  expect_distance_structure(Dhalf)
  expect_equal(Dhalf[1, 3], 4)
  expect_triangle_violation(Dhalf)
})

test_that("squared Euclidean and correlation dispatcher routes are classified correctly", {
  line = matrix(c(0, 1, 2), ncol = 1L)
  squared = DistanceMatrix(line, method = "sqeuclidean")
  expect_distance_structure(squared)
  expect_positive_off_diagonal(squared)
  expect_equal(squared[1, 3], 4)
  expect_triangle_violation(squared)
  expect_positive_off_diagonal(sqrt(squared))
  expect_triangle_inequality(sqrt(squared))

  # These three mean-zero unit vectors have pairwise Pearson correlations
  # cos(60 degrees), cos(60 degrees), and cos(120 degrees).
  u = c(1, -1, 0) / sqrt(2)
  v = c(1, 1, -2) / sqrt(6)
  angles = c(0, pi / 3, 2 * pi / 3)
  X = outer(cos(angles), u) + outer(sin(angles), v)

  correlation_dissimilarity = DistanceMatrix(X, method = "pearsond")
  expect_distance_structure(correlation_dissimilarity)
  expect_equal(correlation_dissimilarity[1, 2], 0.5, tolerance = 1e-12)
  expect_equal(correlation_dissimilarity[2, 3], 0.5, tolerance = 1e-12)
  expect_equal(correlation_dissimilarity[1, 3], 1.5, tolerance = 1e-12)
  expect_triangle_violation(correlation_dissimilarity)

  correlation_metric = DistanceMatrix(X, method = "pearsonm")
  expect_distance_structure(correlation_metric)
  expect_positive_off_diagonal(correlation_metric)
  expect_triangle_inequality(correlation_metric)

  encoded_examples = rbind(
    c(1, 2, 3, 4, 5),
    c(1, 3, 2, 5, 4),
    c(5, 4, 3, 2, 1),
    c(2, 1, 4, 3, 5)
  )
  for (method in c("pearsonm", "spearmanm", "kendallm")) {
    D = DistanceMatrix(encoded_examples, method = method)
    expect_distance_structure(D)
    expect_positive_off_diagonal(D)
    expect_triangle_inequality(D)
  }

  original = c(1, 2, 4, 8)
  affine = rbind(original, 2 * original + 5, c(8, 4, 2, 1))
  for (method in c(
    "pearsond", "spearmand", "kendalld",
    "pearsonm", "spearmanm", "kendallm"
  )) {
    expect_equal(
      DistanceMatrix(affine, method = method)[1, 2],
      0,
      tolerance = 1e-12,
      info = method
    )
  }
})

test_that("cosine output is a dissimilarity rather than a metric", {
  angles = c(0, pi / 3, 2 * pi / 3)
  X = cbind(cos(angles), sin(angles))
  D = Cosine_Distance(X)

  expect_distance_structure(D)
  expect_equal(D[1, 2], 0.5, tolerance = 1e-12)
  expect_equal(D[2, 3], 0.5, tolerance = 1e-12)
  expect_equal(D[1, 3], 1.5, tolerance = 1e-12)
  expect_triangle_violation(D)

  scale_collapse = Cosine_Distance(rbind(c(1, 0), c(2, 0)))
  expect_equal(scale_collapse[1, 2], 0, tolerance = 1e-12)

  zero_convention = Cosine_Distance(rbind(c(0, 0), c(0, 0), c(1, 0)))
  expect_equal(zero_convention[1, 2], 0)
  expect_equal(zero_convention[1, 3], 1)
})

test_that("squared Mahalanobis output is non-metric but its square root is metric", {
  X = matrix(c(0, 1, 2), ncol = 1L)
  squared = Mahalanobis_Distance(X, cov = matrix(1, 1L, 1L))

  expect_distance_structure(squared)
  expect_equal(squared[1, 3], 4)
  expect_triangle_violation(squared)
  expect_positive_off_diagonal(sqrt(squared))
  expect_triangle_inequality(sqrt(squared))

  expect_error(
    Mahalanobis_Distance(diag(2), cov = diag(c(1, -1)), inverted = TRUE),
    "positive definite"
  )
})

test_that("the similarity transformation enforces its Euclidean condition", {
  theta = c(0, pi / 6, pi / 3)
  unit_vectors = cbind(cos(theta), sin(theta))
  S = tcrossprod(unit_vectors)
  D = TransformSimilarity2MetricDistance(S)

  expect_distance_structure(D)
  expect_positive_off_diagonal(D)
  expect_triangle_inequality(D)

  Sduplicate = matrix(
    c(1, 1, 0.5,
      1, 1, 0.5,
      0.5, 0.5, 1),
    nrow = 3L, byrow = TRUE
  )
  Dduplicate = TransformSimilarity2MetricDistance(Sduplicate)
  expect_equal(Dduplicate[1, 2], 0)
  expect_triangle_inequality(Dduplicate)

  Sbad = matrix(
    c(1, 0.99, 0.19,
      0.99, 1, 0.99,
      0.19, 0.99, 1),
    nrow = 3L, byrow = TRUE
  )
  expect_error(
    TransformSimilarity2MetricDistance(Sbad),
    "positive semidefinite"
  )
})

test_that("Endres-Schindelin and Hellinger satisfy distribution-metric cases", {
  distributions = list(
    c(1, 0, 0),
    c(0.5, 0.5, 0),
    c(0, 1, 0),
    c(0.2, 0.3, 0.5)
  )

  Des = pairwise_property_matrix(
    distributions,
    function(a, b) endresSchindelin_Distribution(a, b)
  )
  expect_distance_structure(Des)
  expect_positive_off_diagonal(Des, tolerance = 1e-12)
  expect_triangle_inequality(Des, tolerance = 1e-12)
  expect_equal(
    endresSchindelin_Distribution(c(1, 2, 3), c(2, 4, 6)),
    0,
    tolerance = 1e-14
  )

  hellinger = getFromNamespace(".hellinger_distance", "BIDistances")
  Dh = pairwise_property_matrix(distributions, hellinger)
  expect_distance_structure(Dh)
  expect_positive_off_diagonal(Dh, tolerance = 1e-12)
  expect_triangle_inequality(Dh, tolerance = 1e-12)
})

test_that("generalized Jaccard is a metric on non-negative vectors", {
  X = rbind(
    c(0, 0, 0),
    c(1, 0, 0),
    c(0, 1, 0),
    c(1, 1, 1),
    c(2, 1, 0)
  )
  D = Jaccard_Distance(X)

  expect_distance_structure(D)
  expect_positive_off_diagonal(D, tolerance = 1e-12)
  expect_triangle_inequality(D, tolerance = 1e-12)
  expect_equal(D[1, 2], 1)
  expect_equal(D[2, 3], 1)
  expect_equal(D[2, 5], 2 / 3, tolerance = 1e-12)

  two_zero_rows = Jaccard_Distance(rbind(c(0, 0), c(0, 0)))
  expect_equal(two_zero_rows[1, 2], 0)
})

test_that("tf-idf distance is a pseudometric on the original rows", {
  annotations = rbind(
    gene_a = c(1, 1, 0),
    gene_b = c(1, 0, 1),
    gene_c = c(1, 1, 1)
  )
  tfidf = Tfidf_dist(annotations)
  expect_distance_structure(tfidf$Distance)
  expect_triangle_inequality(tfidf$Distance)
  expect_equal(tfidf$Distance["gene_a", "gene_b"], 0)
  expect_false(identical(annotations[1, ], annotations[2, ]))
  expect_named(tfidf$TfidfWeights, rownames(annotations))

  expect_error(
    Tfidf_dist(rbind(c(0, 0), c(1, 0))),
    "at least one positive annotation"
  )
  expect_error(Tfidf_dist(matrix(c(1, -1), nrow = 1L)), "non-negative")
})

test_that("Gini distance is a pseudometric on the original rows", {
  skip_if_not_installed("ineq")

  gini_data = rbind(
    c(0, 1, 2),
    c(2, 1, 0),
    c(0, 0, 3),
    c(1, 1, 1)
  )
  Dgini = Gini_Distance(gini_data)
  expect_distance_structure(Dgini)
  expect_triangle_inequality(Dgini)
  expect_equal(Dgini[1, 2], 0, tolerance = 1e-12)
})

test_that("shared-neighbor distance is a metric on neighbor sets", {
  X = matrix(c(0, 1, 2, 3), ncol = 1L)
  D = SharedNeighbor_Distance(
    X, k = 1L, NThreads = 1L, ComputationInR = TRUE
  )

  expect_distance_structure(D)
  expect_triangle_inequality(D)
  # Rows one and three have the same one-element nearest-neighbor set {2}.
  expect_equal(D[1, 3], 0)
})

test_that("toroidal distance is metric after periodic identification", {
  points = rbind(c(0, 0), c(9, 0), c(5, 5), c(3, 8))
  D = ToroidalEuclidean_Distance(Lines = 10, Columns = 10, Points = points)

  expect_distance_structure(D)
  expect_positive_off_diagonal(D)
  expect_triangle_inequality(D)
  expect_equal(D[1, 2], 1)

  periodic_collapse = ToroidalEuclidean_Distance(
    Lines = 10, Columns = 10,
    Points = rbind(c(0, 0), c(10, 0))
  )
  expect_equal(periodic_collapse[1, 2], 0)
})

test_that("MSM and TWED satisfy deterministic metric cases", {
  msm_series = list(c(0, 0), c(0, 1), c(1, 1), c(2, -1, 0))
  Dmsm = pairwise_property_matrix(
    msm_series,
    function(a, b) MSMD_Distance(a, b, ParameterC = 1)
  )
  expect_distance_structure(Dmsm)
  expect_positive_off_diagonal(Dmsm)
  expect_triangle_inequality(Dmsm)

  twed_series = list(
    list(values = c(0, 0), time = c(1, 2)),
    list(values = c(0, 1), time = c(1, 2)),
    list(values = c(1, 1), time = c(1, 2)),
    list(values = c(0, 1, 0), time = c(1, 2, 3))
  )
  Dtwed = pairwise_property_matrix(
    twed_series,
    function(a, b) {
      TWED_Distance(
        a$values, b$values, a$time, b$time,
        Nu = 1, Lambda = 1, Degree = 2
      )$TWED
    }
  )
  expect_distance_structure(Dtwed)
  expect_positive_off_diagonal(Dtwed)
  expect_triangle_inequality(Dtwed)

  expect_error(TWED_Distance(1:2, 1:2, c(1, 1), c(1, 2)), "strictly increasing")
  expect_error(TWED_Distance(1:2, 1:2, c(0, 1), c(1, 2)), "positive timestamps")
  expect_error(TWED_Distance(1:2, 1:2, 1:2, 1:2, Nu = 0), "greater than 0")
  expect_error(TWED_Distance(1:2, 1:2, 1:2, 1:2, Degree = 0.5), "greater than or equal to 1")
})

test_that("Kullback-Leibler outputs are divergences rather than metrics", {
  p = c(0.8, 0.2)
  q = c(0.5, 0.5)
  dpq = Kullback_Leibler_div(
    p, q, sym = FALSE, PDF = TRUE, Eps = 1e-12
  )$KLD
  dqp = Kullback_Leibler_div(
    q, p, sym = FALSE, PDF = TRUE, Eps = 1e-12
  )$KLD
  expect_false(isTRUE(all.equal(dpq, dqp, tolerance = 1e-12)))

  distributions = list(
    rep(1 / 3, 3),
    c(0.2, 0.4, 0.4),
    c(1 / 7, 3 / 7, 3 / 7)
  )
  symmetric_kld = pairwise_property_matrix(
    distributions,
    function(a, b) {
      Kullback_Leibler_div(
        a, b, sym = TRUE, PDF = TRUE, Eps = 1e-12
      )$KLD
    }
  )
  expect_distance_structure(symmetric_kld)
  expect_triangle_violation(symmetric_kld, tolerance = 1e-12)
})

test_that("Wasserstein is metric on empirical distributions but not ordered rows", {
  skip_if_not_installed("transport")

  X = rbind(
    c(0, 1, 2),
    c(2, 1, 0),
    c(1, 2, 3),
    c(0, 0, 4)
  )
  D = Wasserstein_Distance(X, p = 1)
  expect_distance_structure(D)
  expect_triangle_inequality(D)
  expect_equal(D[1, 2], 0, tolerance = 1e-12)
})