def test_computes_periodic_function(self):
a = torch.tensor([[4, 1], [2, 2], [8, 0]], dtype=torch.float)
b = torch.tensor([[0, 0], [2, 1], [1, 0]], dtype=torch.float)
period = 1
kernel = CosineKernel().initialize(period_length=period)
kernel.eval()
actual = torch.zeros(3, 3)
for i in range(3):
for j in range(3):
actual[i, j] = torch.cos(math.pi * ((a[i] - b[j]) / period).norm(2, dim=-1))
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)
# diag
res = kernel(a, b).diag()
actual = actual.diag()
self.assertLess(torch.norm(res - actual), 1e-5)
# batch_dims
actual = torch.zeros(2, 3, 3)
for i in range(3):
for j in range(3):
for l in range(2):
actual[l, i, j] = torch.cos(math.pi * ((a[i, l] - b[j, l]) / period))
res = kernel(a, b, last_dim_is_batch=True).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)
# batch_dims + diag
res = kernel(a, b, last_dim_is_batch=True).diag()
actual = torch.cat([actual[i].diag().unsqueeze(0) for i in range(actual.size(0))])
self.assertLess(torch.norm(res - actual), 1e-5)
def test_batch_separate(self):
a = torch.tensor([[[4, 1], [2, 2], [8, 0]], [[2, 5], [6, 1], [0, 1]]], dtype=torch.float)
b = torch.tensor([[[0, 0], [2, 1], [1, 0]], [[1, 1], [2, 3], [1, 0]]], dtype=torch.float)
period = torch.tensor([1, 2], dtype=torch.float).view(2, 1, 1)
kernel = CosineKernel(batch_shape=torch.Size([2])).initialize(period_length=period)
kernel.eval()
actual = torch.zeros(2, 3, 3)
for k in range(2):
for i in range(3):
for j in range(3):
actual[k, i, j] = torch.cos(math.pi * ((a[k, i] - b[k, j]) / period[k]).norm(2, dim=-1))
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)
# diag
res = kernel(a, b).diag()
actual = torch.cat([actual[i].diag().unsqueeze(0) for i in range(actual.size(0))])
self.assertLess(torch.norm(res - actual), 1e-5)
# batch_dims
actual = torch.zeros(2, 2, 3, 3)
for k in range(2):
for i in range(3):
for j in range(3):
for l in range(2):
actual[k, l, i, j] = torch.cos(math.pi * ((a[k, i, l] - b[k, j, l]) / period[k]))
res = kernel(a, b, last_dim_is_batch=True).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)
# batch_dims + diag
res = kernel(a, b, last_dim_is_batch=True).diag()
actual = actual.diagonal(dim1=-2, dim2=-1)
self.assertLess(torch.norm(res - actual), 1e-5)
def test_computes_periodic_function(self):
a = torch.tensor([4, 2, 8], dtype=torch.float).view(3, 1)
b = torch.tensor([0, 2], dtype=torch.float).view(2, 1)
period = 1
kernel = CosineKernel().initialize(log_period_length=math.log(period))
kernel.eval()
actual = torch.zeros(3, 2)
for i in range(3):
for j in range(2):
actual[i, j] = torch.cos(math.pi * (a[i] - b[j]) / period)
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)
def test_batch(self):
a = torch.tensor([[4, 2, 8], [1, 2, 3]], dtype=torch.float).view(2, 3, 1)
b = torch.tensor([[0, 2, 1], [-1, 2, 0]], dtype=torch.float).view(2, 3, 1)
period = torch.tensor(1, dtype=torch.float).view(1, 1, 1)
kernel = CosineKernel().initialize(period_length=period)
kernel.eval()
actual = torch.zeros(2, 3, 3)
for k in range(2):
for i in range(3):
for j in range(3):
actual[k, i, j] = torch.cos(math.pi * ((a[k, i] - b[k, j]) / period))
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)