retractions.h File Reference

Header file for several retractions of type I and II as well as simple vector transport. More...

#include <vector>
#include "../tensor.h"

Go to the source code of this file.

Classes
struct	xerus::HOSVDRetraction
	retraction that performs a HOSVD to project back onto the Manifold More...
class	xerus::TTTangentVector
	class to compactly represent tangent vectors of the manifold of constant TT-rank More...

Namespaces
	xerus
	The main namespace of xerus.

Typedefs
using	xerus::TTRetractionI = std::function< void(TTTensor &, const TTTangentVector &)>
using	xerus::TTRetractionII = std::function< void(TTTensor &, const TTTensor &)>
using	xerus::TTVectorTransport = std::function< void(const TTTensor &, TTTangentVector &)>

Functions
void	xerus::ALSRetractionI (TTTensor &_U, const TTTangentVector &_change)
	retraction that performs an ALS half-sweep to project back onto the Manifold. Automatically retains the ranks of _U More...
void	xerus::ALSRetractionII (TTTensor &_U, const TTTensor &_change)
	retraction that performs an ALS half-sweep to project back onto the Manifold. Automatically retains the ranks of _U More...
void	xerus::HOSVDRetractionI (TTTensor &_U, const TTTangentVector &_change)
	retraction that performs a HOSVD to project back onto the Manifold More...
void	xerus::HOSVDRetractionII (TTTensor &_U, const TTTensor &_change)
TTTangentVector	xerus::operator* (value_t _alpha, const TTTangentVector &_rhs)
void	xerus::ProjectiveVectorTransport (const TTTensor &_newBase, TTTangentVector &_tangentVector)
	simple vector transport by projecting onto the new tangent plane More...
void	xerus::SubmanifoldRetractionI (TTTensor &_U, const TTTangentVector &_change)
	retraction that performs componentwise addition of \( U_i \) and \( W_i \) where \( W_i \) is the i-th component of the riemannian tangential vector representation More...
void	xerus::SubmanifoldRetractionII (TTTensor &_U, const TTTensor &_change)
	retraction that performs componentwise addition of \( U_i \) and \( W_i \) where \( W_i \) is the i-th component of the riemannian tangential vector representation More...

Detailed Description

Header file for several retractions of type I and II as well as simple vector transport.

Definition in file retractions.h.