def test_solve(self):
size = 100
train_x = torch.linspace(0, 1, size)
covar_matrix = RBFKernel()(train_x, train_x).evaluate()
piv_chol = pivoted_cholesky.pivoted_cholesky(covar_matrix, 10)
woodbury_factor, inv_scale, logdet = woodbury.woodbury_factor(
piv_chol, piv_chol, torch.ones(100), logdet=True)
self.assertTrue(
approx_equal(logdet, (piv_chol @ piv_chol.transpose(-1, -2) +
torch.eye(100)).logdet(), 2e-4))
rhs_vector = torch.randn(100, 50)
shifted_covar_matrix = covar_matrix + torch.eye(size)
real_solve = shifted_covar_matrix.inverse().matmul(rhs_vector)
scaled_inv_diag = (inv_scale / torch.ones(100)).unsqueeze(-1)
approx_solve = woodbury.woodbury_solve(rhs_vector,
piv_chol * scaled_inv_diag,
woodbury_factor,
scaled_inv_diag, inv_scale)
self.assertTrue(approx_equal(approx_solve, real_solve, 2e-4))
def test_solve(self):
size = 100
train_x = torch.cat(
[torch.linspace(0, 1, size).unsqueeze(0), torch.linspace(0, 0.5, size).unsqueeze(0)], 0
).unsqueeze(-1)
covar_matrix = RBFKernel()(train_x, train_x).evaluate()
piv_chol = pivoted_cholesky.pivoted_cholesky(covar_matrix, 10)
woodbury_factor = pivoted_cholesky.woodbury_factor(piv_chol, torch.ones(2, 100))
rhs_vector = torch.randn(2, 100, 5)
shifted_covar_matrix = covar_matrix + torch.eye(size)
real_solve = torch.cat(
[
shifted_covar_matrix[0].inverse().matmul(rhs_vector[0]).unsqueeze(0),
shifted_covar_matrix[1].inverse().matmul(rhs_vector[1]).unsqueeze(0),
],
0,
)
approx_solve = pivoted_cholesky.woodbury_solve(rhs_vector, piv_chol, woodbury_factor, torch.ones(2, 100))
self.assertTrue(approx_equal(approx_solve, real_solve, 2e-4))
def test_pivoted_cholesky(self):
size = 100
train_x = torch.cat(
[
torch.linspace(0, 1, size).unsqueeze(0),
torch.linspace(0, 0.5, size).unsqueeze(0),
torch.linspace(0, 0.25, size).unsqueeze(0),
torch.linspace(0, 1.25, size).unsqueeze(0),
torch.linspace(0, 1.5, size).unsqueeze(0),
torch.linspace(0, 1, size).unsqueeze(0),
torch.linspace(0, 0.5, size).unsqueeze(0),
torch.linspace(0, 0.25, size).unsqueeze(0),
torch.linspace(0, 1.25, size).unsqueeze(0),
torch.linspace(0, 1.25, size).unsqueeze(0),
torch.linspace(0, 1.5, size).unsqueeze(0),
torch.linspace(0, 1, size).unsqueeze(0),
],
0,
).unsqueeze(-1)
covar_matrix = RBFKernel()(train_x, train_x).evaluate().view(2, 2, 3, size, size)
piv_chol = pivoted_cholesky.pivoted_cholesky(covar_matrix, 10)
covar_approx = piv_chol @ piv_chol.transpose(-1, -2)
self.assertTrue(approx_equal(covar_approx, covar_matrix, 2e-4))
def test_solve(self):
size = 100
train_x = torch.cat(
[
torch.linspace(0, 1, size).unsqueeze(0),
torch.linspace(0, 0.5, size).unsqueeze(0),
torch.linspace(0, 0.25, size).unsqueeze(0),
torch.linspace(0, 1.25, size).unsqueeze(0),
torch.linspace(0, 1.5, size).unsqueeze(0),
torch.linspace(0, 1, size).unsqueeze(0),
torch.linspace(0, 0.5, size).unsqueeze(0),
torch.linspace(0, 0.25, size).unsqueeze(0),
torch.linspace(0, 1.25, size).unsqueeze(0),
torch.linspace(0, 1.25, size).unsqueeze(0),
torch.linspace(0, 1.5, size).unsqueeze(0),
torch.linspace(0, 1, size).unsqueeze(0),
],
0,
).unsqueeze(-1)
covar_matrix = RBFKernel()(train_x, train_x).evaluate().view(
2, 2, 3, size, size)
piv_chol = pivoted_cholesky.pivoted_cholesky(covar_matrix, 10)
woodbury_factor, inv_scale, logdet = woodbury.woodbury_factor(
piv_chol, piv_chol, torch.ones(2, 2, 3, 100), logdet=True)
actual_logdet = torch.stack([
mat.logdet() for mat in (piv_chol @ piv_chol.transpose(-1, -2) +
torch.eye(100)).view(-1, 100, 100)
], 0).view(2, 2, 3)
self.assertTrue(approx_equal(logdet, actual_logdet, 2e-4))
rhs_vector = torch.randn(2, 2, 3, 100, 5)
shifted_covar_matrix = covar_matrix + torch.eye(size)
real_solve = torch.cat(
[
shifted_covar_matrix[0, 0, 0].inverse().matmul(
rhs_vector[0, 0, 0]).unsqueeze(0),
shifted_covar_matrix[0, 0, 1].inverse().matmul(
rhs_vector[0, 0, 1]).unsqueeze(0),
shifted_covar_matrix[0, 0, 2].inverse().matmul(
rhs_vector[0, 0, 2]).unsqueeze(0),
shifted_covar_matrix[0, 1, 0].inverse().matmul(
rhs_vector[0, 1, 0]).unsqueeze(0),
shifted_covar_matrix[0, 1, 1].inverse().matmul(
rhs_vector[0, 1, 1]).unsqueeze(0),
shifted_covar_matrix[0, 1, 2].inverse().matmul(
rhs_vector[0, 1, 2]).unsqueeze(0),
shifted_covar_matrix[1, 0, 0].inverse().matmul(
rhs_vector[1, 0, 0]).unsqueeze(0),
shifted_covar_matrix[1, 0, 1].inverse().matmul(
rhs_vector[1, 0, 1]).unsqueeze(0),
shifted_covar_matrix[1, 0, 2].inverse().matmul(
rhs_vector[1, 0, 2]).unsqueeze(0),
shifted_covar_matrix[1, 1, 0].inverse().matmul(
rhs_vector[1, 1, 0]).unsqueeze(0),
shifted_covar_matrix[1, 1, 1].inverse().matmul(
rhs_vector[1, 1, 1]).unsqueeze(0),
shifted_covar_matrix[1, 1, 2].inverse().matmul(
rhs_vector[1, 1, 2]).unsqueeze(0),
],
0,
).view_as(rhs_vector)
scaled_inv_diag = (inv_scale / torch.ones(2, 3, 100)).unsqueeze(-1)
approx_solve = woodbury.woodbury_solve(rhs_vector,
piv_chol * scaled_inv_diag,
woodbury_factor,
scaled_inv_diag, inv_scale)
self.assertTrue(approx_equal(approx_solve, real_solve, 2e-4))
lambda0 = 0.5
n_cells_1d = 50
forward_cutoff = 400 # Only make 200 observations (Fourier and pointwise).
my_problem = ToyFourier2d.build_problem(n_cells_1d, forward_cutoff)
updatable_gp = UpdatableGP(kernel,
lambda0,
sigma0,
m0,
torch.tensor(my_problem.grid.cells).float(),
n_chunks=200)
lazy_cov = UpdatableCovLazyTensor(updatable_gp.covariance)
# Test getitem.
lazy_cov[0:10, 0:10].evaluate()
# Test pivoted Cholesky decomposition.
from gpytorch.utils.pivoted_cholesky import pivoted_cholesky
res = pivoted_cholesky(lazy_cov, max_iter=300, error_tol=0.01)
preconditioner = MatmulLazyTensor(res, res.t())
# Now test conjugate gradient inversion.
rhs = torch.rand((lazy_cov.n, 1))
ans = linear_cg(lazy_cov.matmul,
rhs,
tolerance=0.1,
max_iter=400,
preconditioner=preconditioner.matmul)
