Sphere

class flow_matching.utils.manifolds.Sphere(*args, **kwargs)

Represents a hyperpshere in \(R^D\). Isometric to the product of 1-D spheres.

expmap(x: Tensor, u: Tensor) → Tensor

Computes exponential map \(\exp_x(u)\).

Parameters:

• x (Tensor) – point on the manifold

• u (Tensor) – tangent vector at point \(x\)

Raises:

NotImplementedError – if not implemented

Returns:

transported point

Return type:

Tensor

logmap(x: Tensor, y: Tensor) → Tensor

Computes logarithmic map \(\log_x(y)\).

Parameters:

• x (Tensor) – point on the manifold

• y (Tensor) – point on the manifold

Raises:

NotImplementedError – if not implemented

Returns:

tangent vector at point \(x\)

Return type:

Tensor

projx(x: Tensor) → Tensor

Project point \(x\) on the manifold.

Parameters:

x (Tensor) – point to be projected

Raises:

NotImplementedError – if not implemented

Returns:

projected point on the manifold

Return type:

Tensor

proju(x: Tensor, u: Tensor) → Tensor

Project vector \(u\) on a tangent space for \(x\).

Parameters:

• x (Tensor) – point on the manifold

• u (Tensor) – vector to be projected

Raises:

NotImplementedError – if not implemented

Returns:

projected tangent vector

Return type:

Tensor