def test_solve_qr_constant_noise(self, dtype=torch.float64, tol=1e-8):
size = 50
X = torch.rand((size, 2)).to(dtype=dtype)
y = torch.sin(torch.sum(X, 1)).unsqueeze(-1).to(dtype=dtype)
noise = 1e-2 * torch.ones(size, dtype=dtype)
lazy_tsr = RBFKernel().to(dtype=dtype)(X).evaluate_kernel().add_diag(noise)
precondition_qr, _, logdet_qr = lazy_tsr._preconditioner()
F = lazy_tsr._piv_chol_self
M = noise.diag() + F.matmul(F.t())
x_exact = torch.solve(y, M)[0]
x_qr = precondition_qr(y)
self.assertTrue(approx_equal(x_exact, x_qr, tol))
logdet = 2 * torch.cholesky(M).diag().log().sum(-1)
self.assertTrue(approx_equal(logdet, logdet_qr, tol))
def test_solve_qr(self, dtype=torch.float64, tol=1e-8):
size = 50
X = torch.rand((size, 2)).to(dtype=dtype)
y = torch.sin(torch.sum(X, 1)).unsqueeze(-1).to(dtype=dtype)
with settings.min_preconditioning_size(0):
noise = torch.DoubleTensor(size).uniform_(
math.log(1e-3), math.log(1e-1)).exp_().to(dtype=dtype)
lazy_tsr = RBFKernel().to(
dtype=dtype)(X).evaluate_kernel().add_diag(noise)
precondition_qr, _, logdet_qr = lazy_tsr._preconditioner()
F = lazy_tsr._piv_chol_self
M = noise.diag() + F.matmul(F.t())
x_exact = torch.solve(y, M)[0]
x_qr = precondition_qr(y)
self.assertTrue(approx_equal(x_exact, x_qr, tol))
logdet = 2 * torch.cholesky(M).diag().log().sum(-1)
self.assertTrue(approx_equal(logdet, logdet_qr, tol))
