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)
piv_chol = pivoted_cholesky.pivoted_cholesky(covar_matrix, 10)
woodbury_factor = pivoted_cholesky.woodbury_factor(
piv_chol,
torch.Tensor(2, 100).fill_(1))
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.Tensor(2, 100).fill_(1))
self.assertTrue(approx_equal(approx_solve, real_solve, 2e-4))
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 = pivoted_cholesky.woodbury_factor(piv_chol, torch.ones(100))
rhs_vector = torch.randn(100, 50)
shifted_covar_matrix = covar_matrix + torch.eye(size)
real_solve = shifted_covar_matrix.inverse().matmul(rhs_vector)
approx_solve = pivoted_cholesky.woodbury_solve(rhs_vector, piv_chol, woodbury_factor, torch.ones(100))
self.assertTrue(approx_equal(approx_solve, real_solve, 2e-4))
def test_solve_vector(self):
size = 100
train_x = Variable(torch.linspace(0, 1, size))
covar_matrix = RBFKernel()(train_x, train_x).data
piv_chol = pivoted_cholesky.pivoted_cholesky(covar_matrix, 10)
woodbury_factor = pivoted_cholesky.woodbury_factor(piv_chol, 1)
rhs_vector = torch.randn(100)
shifted_covar_matrix = covar_matrix + torch.eye(size)
real_solve = shifted_covar_matrix.inverse().matmul(rhs_vector)
approx_solve = pivoted_cholesky.woodbury_solve(rhs_vector, piv_chol, woodbury_factor, 1)
self.assertTrue(approx_equal(approx_solve, real_solve))
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 = pivoted_cholesky.woodbury_factor(piv_chol, torch.ones(2, 2, 3, 100))
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)
approx_solve = pivoted_cholesky.woodbury_solve(rhs_vector, piv_chol, woodbury_factor, torch.ones(2, 3, 100))
self.assertTrue(approx_equal(approx_solve, real_solve, 2e-4))
