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)
lengthscale = 2
period = 3
kernel = PeriodicKernel().initialize(log_lengthscale=math.log(lengthscale), log_period_length=math.log(period))
kernel.eval()
actual = torch.zeros(3, 2)
for i in range(3):
for j in range(2):
val = 2 * torch.pow(torch.sin(math.pi * (a[i] - b[j]) / 3), 2) / lengthscale
actual[i, j] = torch.exp(-val).item()
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, 2]], dtype=torch.float).view(2, 2, 1)
period = torch.tensor(1, dtype=torch.float).view(1, 1, 1)
lengthscale = torch.tensor(2, dtype=torch.float).view(1, 1, 1)
kernel = PeriodicKernel().initialize(lengthscale=lengthscale,
period_length=period)
kernel.eval()
actual = torch.zeros(2, 3, 2)
for k in range(2):
actual[k] = kernel(a[k], b[k]).evaluate()
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)
def test_computes_periodic_function(self):
a = torch.Tensor([4, 2, 8]).view(3, 1)
b = torch.Tensor([0, 2]).view(2, 1)
lengthscale = 2
period = 1
kernel = PeriodicKernel().initialize(log_lengthscale=math.log(lengthscale), log_period_length=math.log(period))
kernel.eval()
actual = torch.zeros(3, 2)
for i in range(3):
for j in range(2):
val = 2 * torch.pow(torch.sin(math.pi * (a[i] - b[j])), 2) / lengthscale
actual[i, j] = torch.exp(-val)[0]
res = kernel(Variable(a), Variable(b)).evaluate().data
self.assertLess(torch.norm(res - actual), 1e-5)
def test_batch_separate(self):
a = torch.tensor([[4, 2, 8], [1, 2, 3]], dtype=torch.float).view(2, 3, 1)
b = torch.tensor([[0, 2], [-1, 2]], dtype=torch.float).view(2, 2, 1)
period = torch.tensor([1, 2], dtype=torch.float).view(2, 1, 1)
lengthscale = torch.tensor([2, 1], dtype=torch.float).view(2, 1, 1)
kernel = PeriodicKernel(batch_shape=torch.Size([2])).initialize(lengthscale=lengthscale, period_length=period)
kernel.eval()
actual = torch.zeros(2, 3, 2)
for k in range(2):
for i in range(3):
for j in range(2):
val = 2 * torch.pow(torch.sin(math.pi * (a[k, i] - b[k, j]) / period[k]), 2) / lengthscale[k]
actual[k, i, j] = torch.exp(-val).item()
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)
def test_batch_separate(self):
a = torch.tensor([[4, 2, 8], [1, 2, 3]],
dtype=torch.float).view(2, 3, 1)
b = torch.tensor([[0, 2], [-1, 2]], dtype=torch.float).view(2, 2, 1)
period = torch.tensor([1, 2], dtype=torch.float).view(2, 1, 1)
lengthscale = torch.tensor([2, 1], dtype=torch.float).view(2, 1, 1)
kernel = PeriodicKernel(batch_shape=torch.Size([2])).initialize(
lengthscale=lengthscale, period_length=period)
kernel.eval()
actual = torch.zeros(2, 3, 2)
for k in range(2):
diff = a[k].unsqueeze(1) - b[k].unsqueeze(0)
diff = diff * math.pi / period[k].unsqueeze(-1)
actual[k] = diff.sin().pow(2).sum(dim=-1).div(
lengthscale[k]).mul(-2.0).exp_()
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)