def test_kernel(self, seed=1, n=500):
print("test kernel")
torch.random.manual_seed(seed)
# input data
x = torch.linspace(-10, 10, 201).view(-1, 1)
nf = 2.0 * torch.mean(x[1:] - x[:-1])
print('nyquist frequency: ', nf)
# generating kernel values
kernel = RBFKernel()
kernel._set_lengthscale(3.)
k = kernel(x, torch.zeros(1, 1)).evaluate()
k = k.detach()
# extracting approximate spectral density
omega = torch.linspace(0, 1. / nf, n)
tau = x.data
s = torch.zeros(n)
for ii in range(n):
s[ii] = torch.dot(
k.data.squeeze(),
torch.cos(2 * math.pi * tau.squeeze() * omega[ii]))
# reconstructing kernel using mean
kernel_rec = SpectralGPKernel(integration='U',
num_locs=n,
omega_max=1. / nf)
# check that the generated omegas are computed properly
self.assertEqual((omega - kernel_rec.omega.squeeze()).norm().item(),
0.)
kernel_output = kernel_rec.compute_kernel_values(
tau, s, integration='U').view(-1)
# fig, ax = plt.subplots(nrows=1, ncols=2)
# ax[0].plot(x.numpy(), kernel_output.numpy(), label='Integration Output')
# ax[0].plot(x.numpy(), k.numpy(), label='True K')
# ax[0].legend()
# ax[0].set_xlabel('x')
# ax[0].set_ylabel('K(x,0)')
# true_s = (2*math.pi*kernel.lengthscale**2)**(0.5) * torch.exp(-2*(math.pi * kernel.lengthscale * omega)**2)
# ax[1].plot(omega.numpy(), s.numpy() * (0.5 * nf.numpy()), label = 'DTFT')
# ax[1].plot(omega.numpy(), true_s.squeeze(0).detach().numpy(), label = 'True')
# ax[1].legend()
# ax[1].set_xlabel('omega')
# ax[1].set_ylabel('S(omega)')
# plt.show()
relative_error = (kernel_output.view(-1) -
k.view(-1)).norm() / k.norm()
print('relative error: ', relative_error)
self.assertLess(relative_error, 1e-3)
def test_kernel_forwards(self, seed=1, n=500):
print("test kernel")
torch.random.manual_seed(seed)
# input data
x = torch.linspace(-100, 100, 201).view(-1, 1)
# generating kernel values
kernel = RBFKernel()
kernel._set_lengthscale(3.)
k = kernel(x, torch.zeros(1, 1)).evaluate()
k = k.detach()
# reconstructing kernel using mean
kernel_rec = SpectralGPKernel(integration='U', num_locs=n)
