Tensors

class geoopt.tensor.ManifoldTensor[source]

Same as torch.Tensor that has information about its manifold.

Other Parameters:
 manifold (geoopt.Manifold) – A manifold for the tensor, (default: geoopt.Euclidean)
dist(other: torch.Tensor, p: Union[int, float, bool, str] = 2, **kwargs) → torch.Tensor[source]

Return euclidean or geodesic distance between points on the manifold. Allows broadcasting.

Parameters:
  • other (tensor) –
  • p (str|int) – The norm to use. The default behaviour is not changed and is just euclidean distance. To compute geodesic distance, p should be set to "g"
Returns:
Return type:

scalar
expmap(u: torch.Tensor, **kwargs) → torch.Tensor[source]

Perform an exponential map \(\operatorname{Exp}_x(u)\).

Parameters:u (torch.Tensor) – tangent vector at point \(x\)
Returns:transported point
Return type:torch.Tensor
expmap_transp(u: torch.Tensor, v: torch.Tensor, **kwargs) → torch.Tensor[source]

Perform an exponential map and vector transport from point \(x\) with given direction \(u\).

Parameters:
  • u (torch.Tensor) – tangent vector at point \(x\)
  • v (torch.Tensor) – tangent vector at point \(x\) to be transported
Returns:

transported point
Return type:

torch.Tensor
inner(u: torch.Tensor, v: torch.Tensor = None, **kwargs) → torch.Tensor[source]

Inner product for tangent vectors at point \(x\).

Parameters:
  • u (torch.Tensor) – tangent vector at point \(x\)
  • v (Optional[torch.Tensor]) – tangent vector at point \(x\)
  • keepdim (bool) – keep the last dim?
Returns:

inner product (broadcasted)
Return type:

torch.Tensor
logmap(y: torch.Tensor, **kwargs) → torch.Tensor[source]

Perform an logarithmic map \(\operatorname{Log}_{x}(y)\).

Parameters:y (torch.Tensor) – point on the manifold
Returns:tangent vector
Return type:torch.Tensor
proj_() → torch.Tensor[source]

Inplace projection to the manifold.

Returns:same instance
Return type:tensor
proju(u: torch.Tensor, **kwargs) → torch.Tensor[source]

Project vector \(u\) on a tangent space for \(x\), usually is the same as egrad2rgrad().

Parameters:
  • torch.Tensor (u) – point on the manifold
  • torch.Tensor – vector to be projected
Returns:

projected vector
Return type:

torch.Tensor
retr(u: torch.Tensor, **kwargs) → torch.Tensor[source]

Perform a retraction from point \(x\) with given direction \(u\).

Parameters:u (torch.Tensor) – tangent vector at point \(x\)
Returns:transported point
Return type:torch.Tensor
retr_transp(u: torch.Tensor, v: torch.Tensor, **kwargs) → Tuple[torch.Tensor, torch.Tensor][source]

Perform a retraction + vector transport at once.

Parameters:
  • u (torch.Tensor) – tangent vector at point \(x\)
  • v (torch.Tensor) – tangent vector at point \(x\) to be transported
Returns:

transported point and vectors
Return type:

Tuple[torch.Tensor, torch.Tensor]

Notes

Sometimes this is a far more optimal way to preform retraction + vector transport

transp(y: torch.Tensor, v: torch.Tensor, **kwargs) → torch.Tensor[source]

Perform vector transport \(\mathfrak{T}_{x\to y}(v)\).

Parameters:
Returns:

transported tensor
Return type:

torch.Tensor
transp_follow_expmap(u: torch.Tensor, v: torch.Tensor, **kwargs) → torch.Tensor[source]

Perform vector transport following \(u\): \(\mathfrak{T}_{x\to\operatorname{Exp}(x, u)}(v)\).

Here, \(\operatorname{Exp}\) is the best possible approximation of the true exponential map. There are cases when the exact variant is hard or impossible implement, therefore a fallback, non-exact, implementation is used.

Parameters:
  • u (torch.Tensor) – tangent vector at point \(x\)
  • v (torch.Tensor) – tangent vector at point \(x\) to be transported
Returns:

transported tensor
Return type:

torch.Tensor
transp_follow_retr(u: torch.Tensor, v: torch.Tensor, **kwargs) → torch.Tensor[source]

Perform vector transport following \(u\): \(\mathfrak{T}_{x\to\operatorname{retr}(x, u)}(v)\).

This operation is sometimes is much more simpler and can be optimized.

Parameters:
  • u (torch.Tensor) – tangent vector at point \(x\)
  • v (torch.Tensor) – tangent vector at point \(x\) to be transported
Returns:

transported tensor
Return type:

torch.Tensor
unpack_tensor() → Union[torch.Tensor, Tuple[torch.Tensor]][source]

Construct a point on the manifold.

This method should help to work with product and compound manifolds. Internally all points on the manifold are stored in an intuitive format. However, there might be cases, when this representation is simpler or more efficient to store in a different way that is hard to use in practice.

Parameters:tensor (torch.Tensor) –
Returns:
Return type:torch.Tensor
class geoopt.tensor.ManifoldParameter[source]

Same as torch.nn.Parameter that has information about its manifold.

It should be used within torch.nn.Module to be recognized in parameter collection.

Other Parameters:
 manifold (geoopt.Manifold (optional)) – A manifold for the tensor if data is not a geoopt.ManifoldTensor