def test_ard(self):
a = torch.tensor([[1, 2], [3, 4]], dtype=torch.float)
b = torch.tensor([[1, 4], [1, 4]], dtype=torch.float)
lengthscales = torch.tensor([1, 2], dtype=torch.float).view(1, 1, 2)
kernel = MaternKernel(nu=2.5, ard_num_dims=2)
kernel.initialize(lengthscale=lengthscales)
kernel.eval()
dist = torch.tensor([[1, 1], [2, 2]], dtype=torch.float)
dist.mul_(math.sqrt(5))
actual = (dist ** 2 / 3 + dist + 1).mul(torch.exp(-dist))
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-3)
# diag
res = kernel(a, b).diag()
actual = actual.diag()
self.assertLess(torch.norm(res - actual), 1e-5)
# batch_dims
dist = torch.tensor([[[0, 0], [2, 2]], [[1, 1], [0, 0]]], dtype=torch.float)
dist.mul_(math.sqrt(5))
actual = (dist ** 2 / 3 + dist + 1).mul(torch.exp(-dist))
res = kernel(a, b, batch_dims=(0, 2)).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)
# batch_dims + diag
res = kernel(a, b, batch_dims=(0, 2)).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_ard_batch(self):
a = torch.tensor([[[1, 2, 3], [2, 4, 3]], [[2, -1, 2], [2, -1, 0]]], dtype=torch.float)
b = torch.tensor([[[1, 4, 3]], [[2, -1, 0]]], dtype=torch.float)
lengthscales = torch.tensor([[[1, 2, 1]]], dtype=torch.float)
kernel = MaternKernel(nu=2.5, batch_size=2, ard_num_dims=3)
kernel.initialize(lengthscale=lengthscales)
kernel.eval()
dist = torch.tensor([[[1], [1]], [[2], [0]]], dtype=torch.float).mul_(math.sqrt(5))
actual = (dist ** 2 / 3 + dist + 1).mul(torch.exp(-dist))
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-3)
def test_ard(self):
a = torch.tensor([[1, 2], [3, 4]], dtype=torch.float)
b = torch.tensor([1, 4], dtype=torch.float).view(1, 2)
lengthscales = torch.tensor([1, 2], dtype=torch.float).view(1, 1, 2)
kernel = MaternKernel(nu=2.5, ard_num_dims=2)
kernel.initialize(log_lengthscale=torch.log(lengthscales))
kernel.eval()
dist = torch.tensor([[1], [2]], dtype=torch.float)
dist.mul_(math.sqrt(5))
actual = (dist**2 / 3 + dist + 1).mul(torch.exp(-dist))
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-3)
def test_ard_separate_batch(self):
a = torch.tensor([[[1, 2, 3], [2, 4, 3]], [[2, -1, 2], [2, -1, 0]]],
dtype=torch.float)
b = torch.tensor([[[1, 4, 3]], [[2, -1, 0]]],
dtype=torch.float).repeat(1, 2, 1)
lengthscales = torch.tensor([[[1, 2, 1]], [[2, 1, 0.5]]],
dtype=torch.float)
kernel = MaternKernel(nu=2.5, batch_size=2, ard_num_dims=3)
kernel.initialize(log_lengthscale=torch.log(lengthscales))
kernel.eval()
dist = torch.tensor([[[1, 1], [1, 1]], [[4, 4], [0, 0]]],
dtype=torch.float).mul_(math.sqrt(5))
actual = (dist**2 / 3 + dist + 1).mul(torch.exp(-dist))
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-3)
# 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
dist = torch.tensor(
[
[[0, 0], [1, 1]],
[[1, 1], [0, 0]],
[[0, 0], [0, 0]],
[[0, 0], [0, 0]],
[[0, 0], [0, 0]],
[[4, 4], [0, 0]],
],
dtype=torch.float,
)
dist.mul_(math.sqrt(5))
actual = (dist**2 / 3 + dist + 1).mul(torch.exp(-dist))
res = kernel(a, b, batch_dims=(0, 2)).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)
# batch_dims + diag
res = kernel(a, b, batch_dims=(0, 2)).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_ard_separate_batch(self):
a = torch.tensor([[[1, 2, 3], [2, 4, 3]], [[2, -1, 2], [2, -1, 0]]],
dtype=torch.float)
b = torch.tensor([[[1, 4, 3]], [[2, -1, 0]]],
dtype=torch.float).repeat(1, 2, 1)
lengthscales = torch.tensor([[[1, 2, 1]], [[2, 1, 0.5]]],
dtype=torch.float)
kernel = MaternKernel(nu=2.5,
batch_shape=torch.Size([2]),
ard_num_dims=3)
kernel.initialize(lengthscale=lengthscales)
kernel.eval()
dist = torch.tensor([[[1, 1], [1, 1]], [[4, 4], [0, 0]]],
dtype=torch.float).mul_(math.sqrt(5))
actual = (dist**2 / 3 + dist + 1).mul(torch.exp(-dist))
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-3)
# 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
dist = torch.tensor([
[[[0.0, 0.0], [1.0, 1.0]], [[0.0, 0.0], [0.0, 0.0]]],
[[[1.0, 1.0], [0.0, 0.0]], [[0.0, 0.0], [0.0, 0.0]]],
[[[0.0, 0.0], [0.0, 0.0]], [[4.0, 4.0], [0.0, 0.0]]],
])
dist.mul_(math.sqrt(5))
dist = dist.view(3, 2, 2, 2).transpose(0, 1)
actual = (dist**2 / 3 + dist + 1).mul(torch.exp(-dist))
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 create_kernel_ard(self, num_dims, **kwargs):
kernel = MaternKernel(nu=0.5, ard_num_dims=num_dims, **kwargs)
kernel.initialize(lengthscale=5.0)
return kernel
def create_kernel_no_ard(self, **kwargs):
kernel = MaternKernel(nu=0.5, **kwargs)
kernel.initialize(lengthscale=5.0)
return kernel