syten::Krylov Namespace Reference

Krylov subspace methods. More...

Namespaces
namespace	ClassicImpl
	Contains the classic Krylov implementation and helper functions.
namespace	Evolution
	Implementation of time evolution with recycling etc. using Krylov subspaces.
namespace	OrthoPolicies
	Orthonormalisation policies used by StandardKrylov and TensorNetworksKrylov.
namespace	SolverPolicies
	Solver policies to be used by StandardKrylov and TensorNetworksKrylov.
namespace	TensorNetworksImpl
	Implementation helpers for Krylov::TensorNetworks class.

Classes
struct	KrylovEvolver
	Helper class to model a Krylov time evolution. More...
class	NaiveExponential
	The plain exponential via application of the operator to the vector. More...
class	OperatorWrapper
	The OperatorWrapper class wraps a MPS/BTT operator, providing an interface complying to the exponentialLanczos template. More...
class	Standard
	The "Standard" Krylov method using the same solver and orthonormalisation policies as TensorNetworksKrylov but with the original Lanczos order. More...
class	StateWrapper
	The StateWrapper class wraps a MPS/BTT-state to provide an interface complying to exponentialLanczos template. More...
class	TensorNetworks
	Krylov implementation optimised for tensor network applications where calculating \( x^T \cdot A \cdot y \) does not require a matrix-vector application. More...

Functions
template<typename Vector , typename Matrix , typename... Pars>
IterativeExit	eigenLanczos (Vector &&vec, Matrix const &mat, IterativeConfig const &conf, Vector &evec)
	eigenLanczos shorthand for a Lanczos eigen-solver More...
template<typename Vector , typename Matrix , typename Scalar >
IterativeExit	expLanczos (Vector &&vec, Matrix const &mat, IterativeConfig const &conf, Scalar prefactor, Vector &result)
	expLanczos shorthand for an exponential Lanczos solver, calculates \(\exp(c H) v\) More...
template<typename Op >
auto	make_OperatorWrapper (Op &&o)
	make_OperatorWrapper simplifies OperatorWrapper construction by template type deduction More...
template<typename StateT , typename TruncT >
auto	make_StateWrapper (StateT &&state, TruncT &&trunc)
	make_StateWrapper simplifies StateWrapper construction by template type deduction More...
template<typename SType , typename TType >
SRDef	norm (StateWrapper< SType, TType > const &s)
	norm non-member norm function More...
template<typename SType , typename TType >
StateWrapper< SType, TType >	operator* (SDef prefactor, StateWrapper< SType, TType > const &s)
	operator * Multiplication of scalar w/ statewrapper. invokes StateWrapper::operator * More...
template<typename SType , typename TType , typename It >
void	orthogonalise_arithmetic (StateWrapper< SType, TType > &s, It first, It last, bool assume_norm_one=false)
template<typename SType , typename TType , typename It >
void	orthogonalise_variational (StateWrapper< SType, TType > &s, It first, It last)
template<typename SType , typename TType , typename It >
void	orthogonalise_variational_two_site (StateWrapper< SType, TType > &s, It first, It last)
template<typename SType , typename TType >
SDef	overlap (StateWrapper< SType, TType > const &a, StateWrapper< SType, TType > const &b)
	Overlap of two StateWrappers, first argument is complex-conjugated. More...

Detailed Description

Krylov subspace methods.

• classic_krylov.h, standard_krylov.h and tn_krylov.h provide Lanczos/Krylov implementations. classic_krylov.h is the currently oldest version and hopefully will be removed soon. standard_krylov.h and tn_krylov.h both provide nearly the same overall interface and crucially can make use of the same solver and orthonormalisation policies. standard_krylov.h only makes use of generic matrix-vector operations and assumes that \( \hat O |\psi\rangle \) is required to calculate \( \langle \psi | \hat O | \psi \rangle \) (true for generic matrix-vector algebra, e.g. tensors in DMRG). tn_krylov.h assumes that there is a cheaper way to calculate this product (true for MPS-MPO algebra, e.g. the Krylov time evolution method).
• solver_policies.h provides two solver policies which are used by standard_krylov.h and tn_krylov.h to turn the generated Krylov subspace into a useful result, i.e. either \( e^{\hat H t} |\psi\rangle \) or the eigenvalue-eigenvector pair for \( \hat H \).
• orthogonalise_policies.h in namespace syten::Krylov::OrthoPolicies are used by standard_krylov.h and tn_krylov.h to re-orthogonalise the generated subspaces. Not all policies are used by standard_krylov.h, as e.g. two-site variational orthonormalisation makes little sense for a DMRG tensor.
• common_krylov.h provides two simple-to-use entry points which can use either standard_krylov.h or classic_krylov.h.
• krylov_evolve.h provides the large-scale framework for Krylov time evolution including the recycling of subspaces in the namespace syten::Krylov::Evolution.