lloca.utils.orthogonalize_3d

Orthogonalization of euclidean vectors.

Functions

orthogonalize_3d(vecs[, method, eps_norm, ...])

Wrapper for orthogonalization of euclidean vectors.

orthogonalize_cross_3d(vecs[, eps_norm])

Cross product orthogonalization algorithm for euclidean vectors.

orthogonalize_gramschmidt_3d(vecs[, eps_norm])

Gram-Schmidt orthogonalization algorithm for euclidean vectors.

regularize_collinear(vecs[, eps_reg])

If the cross product of two vectors is small, the vectors are collinear.
lloca.utils.orthogonalize_3d.orthogonalize_3d(vecs, method='gramschmidt', eps_norm=None, eps_reg=None, return_reg=False)[source]

Wrapper for orthogonalization of euclidean vectors.

Parameters:

  • vecs (list of torch.Tensor) – List of torch.tensor of shape (…, 3) Vectors to be orthogonalized

  • method (str) – Method for orthogonalization. Options are “cross” and “gramschmidt”.

  • eps_norm (float or None) – Numerical regularization for the normalization of the vectors. If None, use the smallest representable value for the vectors dtype.

  • eps_reg (float or None) – Controls the scale of the regularization for collinear vectors.

  • return_reg (bool) – If True, additionally return the number of regularized vectors for collinearity.

Returns:

  • orthogonal_vecs (list of torch.Tensor) – List of orthogonalized vectors of shape (…, 3)

  • reg_collinear (int) – Number of vectors that were regularized due to collinearity.

lloca.utils.orthogonalize_3d.orthogonalize_cross_3d(vecs, eps_norm=None)[source]

Cross product orthogonalization algorithm for euclidean vectors. This approach is equivalent to the Gram-Schmidt procedure for unlimited precision, but for limited precision it is more stable.

Parameters:

  • vecs (torch.Tensor) – Two vectors of shape (…, 2, 3).

  • eps_norm (float or None) – Numerical regularization for the normalization of the vectors.

Returns:

orthogonal_vecs – Three orthogonalized vectors of shape (…, 3, 3), where dim=-2 counts the vectors.

Return type:

torch.Tensor

lloca.utils.orthogonalize_3d.orthogonalize_gramschmidt_3d(vecs, eps_norm=None)[source]

Gram-Schmidt orthogonalization algorithm for euclidean vectors.

Parameters:

  • vecs (torch.Tensor) – Two vectors of shape (…, 2, 3).

  • eps_norm (float or None) – Numerical regularization for the normalization of the vectors.

Returns:

orthogonal_vecs – Three orthogonalized vectors of shape (…, 3, 3), where dim=-2 counts the vectors.

Return type:

torch.Tensor

lloca.utils.orthogonalize_3d.regularize_collinear(vecs, eps_reg=None)[source]

If the cross product of two vectors is small, the vectors are collinear. In this case, we add a small amount of noise to the second vector to regularize the orthogonalization.

Parameters:

  • vecs (list of torch.Tensor) – List with 2 vectors of shape (…, 3).

  • eps_reg (float or None) – Regularization epsilon, controls the scale of the noise added to the second vector. If None, use the smallest representable value for the vectors dtype.

Returns:

  • vecs (list of torch.Tensor) – List with 2 vectors of shape (…, 3), where the second vector is regularized if collinear.

  • reg_collinear (int) – Number of vectors that were regularized due to collinearity.