def test_computes_sum_three_radial_basis_function_gradient(self):
softplus = torch.nn.functional.softplus
a = torch.tensor([4, 2, 8], dtype=torch.float).view(3, 1)
b = torch.tensor([0, 2, 2], dtype=torch.float).view(3, 1)
lengthscale = 2
param = math.log(math.exp(lengthscale) - 1) * torch.ones(3, 3)
param.requires_grad_()
diffs = a.expand(3, 3) - b.expand(3, 3).transpose(0, 1)
actual_output = (-0.5 * (diffs / softplus(param))**2).exp()
actual_output.backward(torch.eye(3))
actual_param_grad = param.grad.sum() * 3
kernel_1 = RBFKernel().initialize(lengthscale=lengthscale)
kernel_2 = RBFKernel().initialize(lengthscale=lengthscale)
kernel_3 = RBFKernel().initialize(lengthscale=lengthscale)
kernel = AdditiveKernel(kernel_1, kernel_2, kernel_3)
kernel.eval()
output = kernel(a, b).evaluate()
output.backward(gradient=torch.eye(3))
res = (kernel.kernels[0].raw_lengthscale.grad +
kernel.kernels[1].raw_lengthscale.grad +
kernel.kernels[2].raw_lengthscale.grad)
self.assertLess(torch.norm(res - actual_param_grad), 2e-5)
def test_computes_sum_of_three_radial_basis_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
kernel_1 = RBFKernel().initialize(lengthscale=lengthscale)
kernel_2 = RBFKernel().initialize(lengthscale=lengthscale)
kernel_3 = RBFKernel().initialize(lengthscale=lengthscale)
kernel = AdditiveKernel(kernel_1, kernel_2, kernel_3)
actual = (torch.tensor([[16, 4], [4, 0], [64, 36]],
dtype=torch.float).mul_(-0.5).div_(lengthscale**
2).exp() * 3)
kernel.eval()
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 2e-5)
