did.operators

Implements methods for computing approximate operators for the DID computation.

Module Contents

Functions

compute_kernel_cholesky(nystrom_points: torch.Tensor, kernel: did.kernels.Kernel, cholesky_reg: float)

Compute Cholesky decomposition of the kernel matrix for Nystrom points,

compute_operator(in_nystrom: torch.Tensor, in_points: torch.Tensor, in_cholesky_reg: float, out_nystrom: torch.Tensor, out_points: torch.Tensor, out_cholesky_reg: float, in_kernel: did.kernels.Kernel, out_kernel: did.kernels.Kernel, mask: torch.Tensor) → torch.Tensor

Computes the Nystrom approximation of the operator (without projection operator).

compute_operator_from_precomputed(in_points: torch.Tensor, out_points: torch.Tensor, r_in_inv: torch.Tensor, r_out_inv_t: torch.Tensor, in_nystrom: torch.Tensor, out_nystrom: torch.Tensor, mask: torch.Tensor, in_kernel: did.kernels.Kernel, out_kernel: did.kernels.Kernel)

Computes operators from common precomputed objects. Useful to avoid repeating computations.
did.operators.compute_kernel_cholesky(nystrom_points: torch.Tensor, kernel: did.kernels.Kernel, cholesky_reg: float)

Compute Cholesky decomposition of the kernel matrix for Nystrom points, i.e. sqrt(K(X_tilde, X_tilde)).

Parameters

  • nystrom_points (torch.Tensor) – Shape (n, d)

  • kernel (Kernel or callable) – Kernel on the space

  • cholesky_reg (float) – Regularization parameter for Cholesky decomposition.

Returns

Return type

torch.Tensor, (n, n)

did.operators.compute_operator(in_nystrom: torch.Tensor, in_points: torch.Tensor, in_cholesky_reg: float, out_nystrom: torch.Tensor, out_points: torch.Tensor, out_cholesky_reg: float, in_kernel: did.kernels.Kernel, out_kernel: did.kernels.Kernel, mask: torch.Tensor) → torch.Tensor

Computes the Nystrom approximation of the operator (without projection operator).

This method gives full implementation (without precomputation). See compute_operator_with_precomputation.

Parameters

  • in_nystrom (torch.Tensor) – Nystrom points on the input space (X).

  • in_points (torch.Tensor) – Coordinates of the sample points.

  • in_cholesky_reg (float) – Regularization parameter for Cholesky decomposition on input.

  • out_nystrom (torch.Tensor) – Nystrom points on the output space (Y).

  • out_points (torch.Tensor) – Values taken by the function.

  • out_cholesky_reg (float) – Regularization parameter for Cholesky decomposition on input.

  • in_kernel (Kernel or callable) – Kernel on the input space (X).

  • out_kernel (Kernel or callable) – Kernel on the output space (Y).

  • mask (torch.Tensor) – Mask function at sample points (mu).

Returns

Return type

F_hat, torch.Tensor

did.operators.compute_operator_from_precomputed(in_points: torch.Tensor, out_points: torch.Tensor, r_in_inv: torch.Tensor, r_out_inv_t: torch.Tensor, in_nystrom: torch.Tensor, out_nystrom: torch.Tensor, mask: torch.Tensor, in_kernel: did.kernels.Kernel, out_kernel: did.kernels.Kernel)

Computes operators from common precomputed objects. Useful to avoid repeating computations.

Parameters

  • in_points (torch.Tensor) – Coordinates of the sample points.

  • out_points (torch.Tensor) – Values taken by the function at the sample points.

  • r_in_inv (torch.Tensor) – Cholesky inverse of the kernel matrix over input Nyström points.

  • r_out_inv_t (torch.Tensor) – Cholesky inverse and transpose of the kernel matrix over output Nyström points.

  • in_nystrom (torch.Tensor) – Nystrom points on the input space.

  • out_nystrom (torch.Tensor) – Nystrom points on the output space.

  • mask (torch.Tensor) – Mask function at sample points (mu).

  • in_kernel (Kernel or callable) – Kernel on the input space (X).

  • out_kernel (Kernel or callable) – Kernel on the output space (Y).

Returns

torch.Tensor

Return type

representation of the Nyström approximation of the operator.