def test_asymmetry(self):
a = torch.Tensor([[0.1, 0.2, 0.7], [0.5, 0.5, 0.0]])
b = torch.Tensor([[0.4, 0.4, 0.2], [0.2, 0.1, 0.7]])
g_0 = gs_div(a, b, alpha=0, lmd=0.5)
g_1 = gs_div(b, a, alpha=0, lmd=0.5)
self.assertTrue(~torch.equal(g_0, g_1))
def test_non_centrosymmetricicy(self):
lmd = 0.2
a = torch.Tensor([[0.1, 0.2, 0.7], [0.5, 0.5, 0.0]])
b = torch.Tensor([[0.4, 0.4, 0.2], [0.2, 0.1, 0.7]])
g_0 = gs_div(a, b, alpha=0, lmd=lmd)
g_1 = gs_div(a, b, alpha=0, lmd=1 - lmd)
self.assertTrue(~torch.equal(g_0, g_1))
def test_monotonicity(self):
a = torch.Tensor([[0.1, 0.2, 0.7], [0.5, 0.5, 0.0]])
b = torch.Tensor([[0.4, 0.4, 0.2], [0.2, 0.1, 0.7]])
g_0 = gs_div(a, b, alpha=0, lmd=0.5)
g_1 = gs_div(a, b, alpha=1, lmd=0.5)
self.assertTrue(g_1 > g_0)
def symmetrized_gs_div(
input: torch.Tensor,
target: torch.Tensor,
alpha: float = -1,
lmd: float = 0.5,
reduction: Optional[str] = 'sum',
) -> torch.Tensor:
lhs = gs_div(input, target, alpha=alpha, lmd=lmd, reduction=reduction)
rhs = gs_div(target, input, alpha=alpha, lmd=lmd, reduction=reduction)
return (lhs + rhs) / 2
def test_lower_bound(self):
alpha_lower = -float('inf')
alpha_list = [-1, 0, 1, 2, 3, 4]
a = torch.Tensor([[0.1, 0.2, 0.7], [0.5, 0.5, 0.0]])
b = torch.Tensor([[0.4, 0.4, 0.2], [0.2, 0.1, 0.7]])
g_lower = gs_div(a, b, alpha=alpha_lower, lmd=0.5)
for alpha in alpha_list:
g = gs_div(a, b, alpha=alpha_lower, lmd=0.5)
self.assertTrue(g >= g_lower)
def test_subadditivity(self):
alpha = 0
beta = 1
a = torch.Tensor([[0.1, 0.2, 0.7], [0.5, 0.5, 0.0]])
b = torch.Tensor([[0.4, 0.4, 0.2], [0.2, 0.1, 0.7]])
g_0 = gs_div(a, b, alpha=alpha, lmd=0.5)
g_1 = gs_div(a, b, alpha=beta, lmd=0.5)
g_2 = gs_div(a, b, alpha=alpha + beta, lmd=0.5)
self.assertTrue(g_2 <= g_0 + g_1)
def test_value_0_2d(self):
a = torch.Tensor([[0.1, 0.2, 0.7], [0.5, 0.5, 0.0]])
b = torch.Tensor([[0.4, 0.4, 0.2], [0.2, 0.1, 0.7]])
g = gs_div(a, b, alpha=1, lmd=0.5)
self.assertTrue(torch.isinf(g).sum() == 0)
def test_alpha_minus_1(self):
a = torch.Tensor([1, 2, 3])
b = torch.Tensor([4, 5, 6])
g = gs_div(a, b, alpha=-1, lmd=0.5)
res = (a * torch.log(a / (0.5 * a + 0.5 * b))).sum()
self.assertIsNotNone(g)
self.assertEqual(g, res)
def test_alpha_1(self):
a = torch.Tensor([1, 2, 3])
b = torch.Tensor([4, 5, 6])
g = gs_div(a, b, alpha=1, lmd=0.5)
res = 0.5 * (a * torch.log(a / b)).sum()
self.assertIsNotNone(g)
self.assertAlmostEqual(g.item(), res.item(), 3)
def test_alpha_0(self):
a = torch.Tensor([1, 2, 3])
b = torch.Tensor([4, 5, 6])
g = gs_div(a, b, alpha=0, lmd=0.5)
res = (a * torch.log(
a / (0.5 * torch.sqrt(a) + 0.5 * torch.sqrt(b))**2)).sum()
self.assertIsNotNone(g)
self.assertEqual(g, res)