Specialized TensorNetwork class used to represent TTTensor and TToperators. More...

#include <performanceData.h>

Inheritance diagram for xerus::TTNetwork< isOperator >:

Collaboration diagram for xerus::TTNetwork< isOperator >:

[legend]

Public Member Functions
	TTNetwork ()
	Constructs an order zero TTNetwork. More...

	TTNetwork (const TTNetwork &_cpy)=default
	TTNetworks are default copy constructable. More...

	TTNetwork (TTNetwork &&_mov) noexcept=default
	TTNetworks are default move constructable. More...

	TTNetwork (const size_t _degree)
	Constructs an zero initialized TTNetwork with the given degree and ranks all equal to one. More...

	TTNetwork (Tensor::DimensionTuple _dimensions)
	Constructs an zero initialized TTNetwork with the given dimensions and ranks all equal to one. More...

	TTNetwork (const Tensor &_tensor, const double _eps=EPSILON, const size_t _maxRank=std::numeric_limits< size_t >::max())
	Constructs a TTNetwork from the given Tensor. More...

	TTNetwork (const Tensor &_tensor, const double _eps, const RankTuple &_maxRanks)
	Constructs a TTNetwork from the given Tensor. More...

void	assume_core_position (const size_t _pos)
	stores _pos as the current core position without verifying of ensuring that this is the case More...

void	canonicalize_left ()
	Move the core to the left. More...

void	canonicalize_right ()
	Move the core to the left. More...

std::pair< TensorNetwork, TensorNetwork >	chop (const size_t _position) const
	Splits the TTNetwork into two parts by removing the node. More...

Tensor &	component (const size_t _idx)
	Complete access to a specific component of the TT decomposition. More...

virtual void	contract_unconnected_subnetworks () override
	Contracts all nodes that are not connected to any external links. More...

size_t	degrees_of_freedom ()
	calculates the number of degrees of freedom of the manifold of fixed tt-rank that the given TTTensor is part of More...

virtual void	fix_mode (const size_t _mode, const size_t _slatePosition) override
	Fixes a specific mode to a specific value, effectively reducing the order by one. More...

virtual value_t	frob_norm () const override
	Calculates the frobenious norm of the TensorNetwork. More...

const Tensor &	get_component (const size_t _idx) const
	Read access to a specific component of the TT decomposition. More...

virtual TensorNetwork *	get_copy () const override
	Returns a new copy of the network. More...

template<>
TTNetwork< true >	identity (const std::vector< size_t > &_dimensions)

void	move_core (const size_t _position, const bool _keepRank=false)
	Move the core to a new position. More...

virtual void	operator*= (const value_t _factor) override
	Calculates the entrywise multiplication of this TensorNetwork with a constant _factor. More...

TTNetwork &	operator+= (const TTNetwork &_other)
	Adds a given TTNetwork to this one. More...

TTNetwork &	operator-= (const TTNetwork &_other)
	Subtracts the _other TTNetwork entrywise from this one. More...

virtual void	operator/= (const value_t _divisor) override
	Calculates the entrywise divison of this TensorNetwork by a constant _divisor. More...

TTNetwork &	operator= (const TTNetwork &_other)=default
	TTNetworks are default assignable. More...

TTNetwork &	operator= (TTNetwork &&_other)=default
	TTNetworks are default move-assignable. More...

size_t	rank (const size_t _i) const
	Gets the rank of a specific egde of the TTNetwork. More...

std::vector< size_t >	ranks () const
	Gets the ranks of the TTNetwork. More...

virtual void	require_correct_format () const override
	Tests whether the network resembles that of a TTTensor and checks consistency with the underlying tensor objects. More...

virtual void	resize_mode (const size_t _mode, const size_t _newDim, const size_t _cutPos=~0ul) override
	Resizes a specific mode of the TensorNetwork. More...

void	round (const std::vector< size_t > &_maxRanks, const double _eps=EPSILON)
	Reduce all ranks up to a given accuracy and maximal number. More...

void	round (const size_t _maxRank)
	Reduce all ranks to the given number. More...

void	round (const int _maxRank)
	Reduce all ranks to the given number. More...

void	round (const value_t _eps)
	Reduce all ranks up to a given accuracy. More...

void	set_component (const size_t _idx, Tensor _T)
	Sets a specific component of the TT decomposition. More...

void	soft_threshold (const double _tau, const bool _preventZero=false)
	Applies the soft threshholding operation to all ranks. More...

void	soft_threshold (const std::vector< double > &_taus, const bool _preventZero=false)
	Applies soft threshholding operations to all ranks. More...

virtual bool	specialized_contraction (std::unique_ptr< internal::IndexedTensorMoveable< TensorNetwork >> &_out, internal::IndexedTensorReadOnly< TensorNetwork > &&_me, internal::IndexedTensorReadOnly< TensorNetwork > &&_other) const override
	(Internal) Calculates the contraction between _me and _other and stores the result in _out. Requires that *this is the tensorObjectReadOnly of _me. More...

template<>
bool	specialized_contraction_f (std::unique_ptr< internal::IndexedTensorMoveable< TensorNetwork >> &, internal::IndexedTensorReadOnly< TensorNetwork > &&, internal::IndexedTensorReadOnly< TensorNetwork > &&)

template<>
bool	specialized_contraction_f (std::unique_ptr< internal::IndexedTensorMoveable< TensorNetwork >> &_out, internal::IndexedTensorReadOnly< TensorNetwork > &&_me, internal::IndexedTensorReadOnly< TensorNetwork > &&_other)

virtual void	specialized_evaluation (internal::IndexedTensorWritable< TensorNetwork > &&_me, internal::IndexedTensorReadOnly< TensorNetwork > &&_other) override
	(Internal) Evaluates _other into _me. Requires that *this is the tensorObjectReadOnly of _me. More...

virtual bool	specialized_sum (std::unique_ptr< internal::IndexedTensorMoveable< TensorNetwork >> &_out, internal::IndexedTensorReadOnly< TensorNetwork > &&_me, internal::IndexedTensorReadOnly< TensorNetwork > &&_other) const override
	(Internal) Calculates the sum between _me and _other and stores the result in _out. Requires that *this is the tensorObjectReadOnly of _me. More...

template<bool B = isOperator, typename std::enable_if< B, int >::type = 0>
void	transpose ()
	Transpose the TTOperator. More...

void	use_dense_representations ()
	Converts all components to use dense representations. More...

Public Member Functions inherited from xerus::TensorNetwork
	TensorNetwork ()
	Constructs an order zero TensorNetwork. More...

	TensorNetwork (const TensorNetwork &_cpy)=default
	Copy Constructor. More...

	TensorNetwork (TensorNetwork &&_mv) noexcept=default
	Move Constructor. More...

	TensorNetwork (Tensor _other)
	Constructs the trivial TensorNetwork containing the given Tensor as single node. More...

	TensorNetwork (std::unique_ptr< Tensor > &&_tensor)
	Constructs the trivial TensorNetwork containing the given Tensor as single node. The TN takes the ownership of the pointer. More...

	TensorNetwork (size_t _degree)
	Constructs the trivial TensorNetwork containing a Tensor with the given degree. More...

	TensorNetwork (const ZeroNode _nodeStatus)
	(Internal) Constructs an order zero TensorNetwork. More...

virtual	~TensorNetwork ()=default
	Destructor. More...

void	contract (const size_t _nodeId1, const size_t _nodeId2)
	Contracts the nodes with indices _nodeId1 and _nodeId2. More...

size_t	contract (const std::set< size_t > &_ids)
	Contracts the nodes with with indices included in the given set _ids. More...

double	contraction_cost (const size_t _nodeId1, const size_t _nodeId2) const
	Approximates the cost of contraction two given nodes. More...

size_t	datasize () const
	Calculates the storage requirement of the current representation. More...

size_t	degree () const
	Gets the degree of the TensorNetwork. More...

void	draw (const std::string &_filename) const
	Draws a graph representation of the TensorNetwork. More...

std::pair< size_t, size_t >	find_common_edge (const size_t _nodeA, const size_t _nodeB) const
	Finds the position of a single common edge between two nodes. More...

	operator Tensor () const
	Explicit cast to Tensor. More...

template<typename... args>
internal::IndexedTensor< TensorNetwork >	operator() (args... _args)
	Indexes the TensorNetwork for read/write use. More...

template<typename... args>
internal::IndexedTensorReadOnly< TensorNetwork >	operator() (args... _args) const
	Indexes the TensorNetwork for read only use. More...

internal::IndexedTensor< TensorNetwork >	operator() (const std::vector< Index > &_indices)
	Indexes the TensorNetwork for read/write use. More...

internal::IndexedTensor< TensorNetwork >	operator() (std::vector< Index > &&_indices)
	Indexes the TensorNetwork for read/write use. More...

internal::IndexedTensorReadOnly< TensorNetwork >	operator() (const std::vector< Index > &_indices) const
	Indexes the TensorNetwork for read only use. More...

internal::IndexedTensorReadOnly< TensorNetwork >	operator() (std::vector< Index > &&_indices) const
	Indexes the TensorNetwork for read only use. More...

TensorNetwork &	operator= (const TensorNetwork &_cpy)=default
	TensorNetworks are copy assignable. More...

TensorNetwork &	operator= (TensorNetwork &&_mv)=default
	TensorNetworks are move assignable. More...

value_t	operator[] (const size_t _position) const
	Read the value at a specific position. More...

value_t	operator[] (const std::vector< size_t > &_positions) const
	Read the value at a specific position. More...

void	reduce_representation ()
	Contracts all nodes that are joined by a full-rank edge. More...

virtual void	remove_slate (const size_t _mode, const size_t _slatePosition)
	removes the given _slatePosition from the _mode. this reduces the given dimension by one More...

void	require_valid_network (const bool _check_erased=true) const
	Sanity checks the network. More...

void	reshuffle_nodes (const std::function< size_t(size_t)> &_f)
	reshuffled the nodes according to the given function More...

virtual void	round_edge (const size_t _nodeA, const size_t _nodeB, const size_t _maxRank, const double _eps, const double _softThreshold)
	Thresholds the rank between two given nodes. More...

void	sanitize ()
	Removes all erased nodes from the TensorNetwork. More...

void	swap_external_links (const size_t _i, const size_t _j)
	Swaps the external indices _i and _j, effectively changing those indices for the represented Tensor (e.g. a transposition for matrices). More...

virtual void	transfer_core (const size_t _from, const size_t _to, const bool _allowRankReduction=true)
	Transfers the core from one given node to another. More...

Static Public Member Functions
static size_t	degrees_of_freedom (const std::vector< size_t > &_dimensions, const std::vector< size_t > &_ranks)
	calculates the number of degrees of freedom of the manifold of fixed tt-rank _ranks with the given _dimensions More...

static TTNetwork XERUS_warn_unused	dirac (std::vector< size_t > _dimensions, const std::vector< size_t > &_position)
	: Returns a TTNetwork with a single entry equals oen and all other zero. More...

static TTNetwork XERUS_warn_unused	dirac (std::vector< size_t > _dimensions, const size_t _position)
	: Returns a Tensor with a single entry equals oen and all other zero. More...

template<bool B = isOperator, typename std::enable_if< B, int >::type = 0>
static TTNetwork XERUS_warn_unused	identity (const std::vector< size_t > &_dimensions)
	: Construct a TTOperator with the given dimensions representing the identity. More...

static TTNetwork XERUS_warn_unused	kronecker (const std::vector< size_t > &_dimensions)
	: Returns a TTNetwork representation of the kronecker delta. More...

static TTNetwork XERUS_warn_unused	ones (const std::vector< size_t > &_dimensions)
	: Returns a the (rank one) TT-Tensor with all entries equal to one. More...

template<class distribution = std::normal_distribution<value_t>, class generator = std::mt19937_64>
static TTNetwork XERUS_warn_unused	random (std::vector< size_t > _dimensions, const std::vector< size_t > &_ranks, distribution &_dist=xerus::misc::defaultNormalDistribution, generator &_rnd=xerus::misc::randomEngine)
	Transforms a given TensorNetwork to a TTNetwork. More...

template<class distribution = std::normal_distribution<value_t>, class generator = std::mt19937_64>
static TTNetwork XERUS_warn_unused	random (const std::vector< size_t > &_dimensions, const size_t _rank, distribution &_dist=xerus::misc::defaultNormalDistribution, generator &_rnd=xerus::misc::randomEngine)
	Random constructs a TTNetwork with the given dimensions and ranks limited by the given rank. More...

template<class distribution = std::normal_distribution<value_t>, class generator = std::mt19937_64>
static TTNetwork XERUS_warn_unused	random (const std::vector< size_t > &_dimensions, const std::vector< size_t > &_ranks, const std::function< void(Tensor &)> &_modifySingularValues, distribution &_dist=xerus::misc::defaultNormalDistribution, generator &_rnd=xerus::misc::randomEngine)
	Random constructs a TTNetwork with the given dimensions and ranks. More...

static std::vector< size_t >	reduce_to_maximal_ranks (std::vector< size_t > _ranks, const std::vector< size_t > &_dimensions)
	Reduces the given ranks to the maximal possible. More...

static bool	specialized_contraction_f (std::unique_ptr< internal::IndexedTensorMoveable< TensorNetwork >> &_out, internal::IndexedTensorReadOnly< TensorNetwork > &&_me, internal::IndexedTensorReadOnly< TensorNetwork > &&_other)

static bool	specialized_sum_f (std::unique_ptr< internal::IndexedTensorMoveable< TensorNetwork >> &_out, internal::IndexedTensorReadOnly< TensorNetwork > &&_me, internal::IndexedTensorReadOnly< TensorNetwork > &&_other)

Static Public Member Functions inherited from xerus::TensorNetwork
static void	add_network_to_network (internal::IndexedTensorWritable< TensorNetwork > &&_base, internal::IndexedTensorReadOnly< TensorNetwork > &&_toInsert)
	Inserts all nodes from _toInsert into _base, creating links where demanded by the indices. More...

static void	link_traces_and_fix (internal::IndexedTensorWritable< TensorNetwork > &&_base)
	Finds traces defined by the indices and internally links the corresponding indices. Also applys all fixed indices. More...

Public Attributes
bool	canonicalized
	Flag indicating whether the TTNetwork is canonicalized. More...

size_t	corePosition
	The position of the core. More...

Public Attributes inherited from xerus::TensorNetwork
std::vector< size_t >	dimensions
	Dimensions of the external indices, i.e. the dimensions of the tensor represented by the network. More...

std::vector< Link >	externalLinks
	The open links of the network in order. More...

std::vector< TensorNode >	nodes
	The nodes constituting the network. The order determines the ids of the nodes. More...

Static Public Attributes
static constexpr const size_t	N = isOperator?2:1
	The number of external links in each node, i.e. one for TTTensors and two for TTOperators. More...

Protected Member Functions
bool	exceeds_maximal_ranks () const
	Tests whether any rank exceeds the theoretic maximal value it should have. More...

size_t	num_ranks () const
	Return the number of ranks, i.e. 0 for degree zero and degree()/N-1 otherwise. More...

Protected Member Functions inherited from xerus::TensorNetwork
std::vector< Link >	init_from_dimension_array ()
	: Sets the externalLinks and returns an Link vector for a node, assuming that this node is the only node there is and all given dimensions are open. More...

void	perform_traces (const size_t _nodeId)
	Performs all traces in the given node. More...

TensorNetwork	stripped_subnet (const std::function< bool(size_t)> &_idF=[](size_t){ return true;}) const
	Creates a dataless copy of a subnet. More...

Static Protected Member Functions
static void	construct_train_from_full (TensorNetwork &_out, const Tensor &_A, const double _eps)
	Constructs a TTNetwork in _out by decomposing the given Tensor _A. More...

Additional Inherited Members
Public Types inherited from xerus::TensorNetwork
using	RankTuple = std::vector< size_t >
	: Represention of the ranks of a TensorNetwork. More...

Protected Types inherited from xerus::TensorNetwork
enum	ZeroNode : bool { ZeroNode::None, ZeroNode::Add }
	Internal indicator to prevent the creation of an degree zero node in TensorNetwork constructor. More...

Detailed Description

template<bool isOperator>
class xerus::TTNetwork< isOperator >

Specialized TensorNetwork class used to represent TTTensor and TToperators.

TTTensors correspond to isOperator=FALSE and TTOperators correspond to isOperator=FALSE.

Definition at line 37 of file performanceData.h.

Constructor & Destructor Documentation

◆ TTNetwork() [1/7]

template<bool isOperator>

xerus::TTNetwork< isOperator >::TTNetwork ( )

explicit

Constructs an order zero TTNetwork.

This is an empty TensorNetwork. Internally the network contains one order zero node with entry zero.

Definition at line 46 of file ttNetwork.cpp.

◆ TTNetwork() [2/7]

template<bool isOperator>

xerus::TTNetwork< isOperator >::TTNetwork ( const TTNetwork< isOperator > & _cpy )

default

TTNetworks are default copy constructable.

◆ TTNetwork() [3/7]

template<bool isOperator>

xerus::TTNetwork< isOperator >::TTNetwork ( TTNetwork< isOperator > && _mov )

defaultnoexcept

TTNetworks are default move constructable.

◆ TTNetwork() [4/7]

template<bool isOperator>

xerus::TTNetwork< isOperator >::TTNetwork ( const size_t _degree )

explicit

Constructs an zero initialized TTNetwork with the given degree and ranks all equal to one.

Naturally for TTOperators the degree must be even.

Definition at line 55 of file ttNetwork.cpp.

◆ TTNetwork() [5/7]

template<bool isOperator>

xerus::TTNetwork< isOperator >::TTNetwork ( Tensor::DimensionTuple _dimensions )

explicit

Constructs an zero initialized TTNetwork with the given dimensions and ranks all equal to one.

Naturally for TTOperators the degree must be even.

Definition at line 58 of file ttNetwork.cpp.

◆ TTNetwork() [6/7]

template<bool isOperator>

xerus::TTNetwork< isOperator >::TTNetwork	(	const Tensor &	_tensor,
		const double	_eps = `EPSILON`,
		const size_t	_maxRank = `std::numeric_limits<size_t>::max()`
	)

explicit

Constructs a TTNetwork from the given Tensor.

The higher order SVD algorithm is used to decompose the given Tensor into the TT format.

Parameters

_tensor	The Tensor to decompose.
_eps	the accuracy to be used in the decomposition.
_maxRank	the maximal allowed rank (applies to all positions).

Definition at line 50 of file ttNetwork.cpp.

◆ TTNetwork() [7/7]

template<bool isOperator>

xerus::TTNetwork< isOperator >::TTNetwork	(	const Tensor &	_tensor,
		const double	_eps,
		const RankTuple &	_maxRanks
	)

explicit

Constructs a TTNetwork from the given Tensor.

The higher order SVD algorithm is used to decompose the given Tensor into the TT format.

Parameters

_tensor	The Tensor to decompose.
_eps	the accuracy to be used in the decomposition.
_maxRanks	maximal ranks to be used

Definition at line 112 of file ttNetwork.cpp.

Member Function Documentation

◆ assume_core_position()

template<bool isOperator>

void xerus::TTNetwork< isOperator >::assume_core_position ( const size_t _pos )

stores _pos as the current core position without verifying of ensuring that this is the case

this is particularly useful after constructing an own TT tensor with set_component calls as these will assume that all orthogonalities are destroyed

Definition at line 735 of file ttNetwork.cpp.

◆ canonicalize_left()

template<bool isOperator>

void xerus::TTNetwork< isOperator >::canonicalize_left ( )

Move the core to the left.

Basically calls move_core() with _position = 0

Definition at line 632 of file ttNetwork.cpp.

◆ canonicalize_right()

template<bool isOperator>

void xerus::TTNetwork< isOperator >::canonicalize_right ( )

Move the core to the left.

Basically calls move_core() with _position = degree()-1

Definition at line 638 of file ttNetwork.cpp.

◆ chop()

template<bool isOperator>

std::pair< TensorNetwork, TensorNetwork > xerus::TTNetwork< isOperator >::chop ( const size_t _position ) const

Splits the TTNetwork into two parts by removing the node.

Parameters

_position index of the component to be removed, thereby also defining the position of the split.

Returns: a std::pair containing the two remaining parts as TensorNetworks.

Definition at line 515 of file ttNetwork.cpp.

◆ component()

template<bool isOperator>

Tensor & xerus::TTNetwork< isOperator >::component ( const size_t _idx )

Complete access to a specific component of the TT decomposition.

Note: This function will not update rank and external dimension informations if it is used to set a component.

This function gives complete access to the components, only intended for internal use.

Parameters

_idx	index of the component to access.

Returns: a reference to the requested component.

Definition at line 457 of file ttNetwork.cpp.

◆ construct_train_from_full()

template<bool isOperator>

static void xerus::TTNetwork< isOperator >::construct_train_from_full	(	TensorNetwork &	_out,
		const Tensor &	_A,
		const double	_eps
	)

staticprotected

Constructs a TTNetwork in _out by decomposing the given Tensor _A.

◆ contract_unconnected_subnetworks()

template<bool isOperator>

void xerus::TTNetwork< isOperator >::contract_unconnected_subnetworks ( )

overridevirtual

Contracts all nodes that are not connected to any external links.

Reimplemented from xerus::TensorNetwork.

Definition at line 748 of file ttNetwork.cpp.

◆ degrees_of_freedom() [1/2]

template<bool isOperator>

size_t xerus::TTNetwork< isOperator >::degrees_of_freedom	(	const std::vector< size_t > &	_dimensions,
		const std::vector< size_t > &	_ranks
	)

static

calculates the number of degrees of freedom of the manifold of fixed tt-rank _ranks with the given _dimensions

Definition at line 406 of file ttNetwork.cpp.

◆ degrees_of_freedom() [2/2]

template<bool isOperator>

size_t xerus::TTNetwork< isOperator >::degrees_of_freedom ( )

calculates the number of degrees of freedom of the manifold of fixed tt-rank that the given TTTensor is part of

Definition at line 426 of file ttNetwork.cpp.

◆ dirac() [1/2]

template<bool isOperator>

TTNetwork< isOperator > xerus::TTNetwork< isOperator >::dirac	(	std::vector< size_t >	_dimensions,
		const std::vector< size_t > &	_position
	)

static

: Returns a TTNetwork with a single entry equals oen and all other zero.

Parameters

_dimensions	the dimensions of the new tensor.
_position	The position of the one

Definition at line 257 of file ttNetwork.cpp.

◆ dirac() [2/2]

template<bool isOperator>

TTNetwork< isOperator > xerus::TTNetwork< isOperator >::dirac	(	std::vector< size_t >	_dimensions,
		const size_t	_position
	)

static

: Returns a Tensor with a single entry equals oen and all other zero.

Parameters

_dimensions	the dimensions of the new tensor.
_position	The position of the one

Definition at line 281 of file ttNetwork.cpp.

◆ exceeds_maximal_ranks()

template<bool isOperator>

bool xerus::TTNetwork< isOperator >::exceeds_maximal_ranks ( ) const

protected

Tests whether any rank exceeds the theoretic maximal value it should have.

Does not check for the actual minimal rank for this tensor. But if any rank exceeds the theoretic maximum it is guaranteed not to be the minimal rank.

Returns: TRUE if any rank exceeds its theoretic maximum.

Definition at line 349 of file ttNetwork.cpp.

◆ fix_mode()

template<bool isOperator>

void xerus::TTNetwork< isOperator >::fix_mode	(	const size_t	_mode,
		const size_t	_slatePosition
	)

overridevirtual

Fixes a specific mode to a specific value, effectively reducing the order by one.

Parameters

_mode	the mode in which the slate shall be fixed, e.g. 0 to fix the first mode.
_slatePosition	the position in the corresponding mode that shall be used.

Reimplemented from xerus::TensorNetwork.

Definition at line 432 of file ttNetwork.cpp.

◆ frob_norm()

template<bool isOperator>

value_t xerus::TTNetwork< isOperator >::frob_norm ( ) const

overridevirtual

Calculates the frobenious norm of the TensorNetwork.

Returns: the frobenious norm of the TensorNetwork.

Reimplemented from xerus::TensorNetwork.

Definition at line 782 of file ttNetwork.cpp.

◆ get_component()

template<bool isOperator>

const Tensor & xerus::TTNetwork< isOperator >::get_component ( const size_t _idx ) const

Read access to a specific component of the TT decomposition.

This function should be used to access the components, instead of direct access via nodes[...], because the implementation does not store the first component in nodes[0] but rather as nodes[1] etc. nodes[0] is an order one node with dimension one only used to allow the first component to be an order three tensor.

Parameters

_idx	index of the component to access.

Returns: a const reference to the requested component.

Definition at line 464 of file ttNetwork.cpp.

◆ get_copy()

template<bool isOperator>

TensorNetwork * xerus::TTNetwork< isOperator >::get_copy ( ) const

overridevirtual

Returns a new copy of the network.

Reimplemented from xerus::TensorNetwork.

Definition at line 743 of file ttNetwork.cpp.

◆ identity() [1/2]

template<>

TTNetwork< true > xerus::TTNetwork< true >::identity ( const std::vector< size_t > & _dimensions )

Definition at line 195 of file ttNetwork.cpp.

◆ identity() [2/2]

template<bool isOperator>

template<bool B = isOperator, typename std::enable_if< B, int >::type = 0>

static TTNetwork XERUS_warn_unused xerus::TTNetwork< isOperator >::identity ( const std::vector< size_t > & _dimensions )

static

: Construct a TTOperator with the given dimensions representing the identity.

Only applicable for TTOperators, i.e. not for TTtensors

Parameters

_dimensions the dimensions of the new TTOperator.

◆ kronecker()

template<bool isOperator>

TTNetwork< isOperator > xerus::TTNetwork< isOperator >::kronecker ( const std::vector< size_t > & _dimensions )

static

: Returns a TTNetwork representation of the kronecker delta.

That is each entry is one if all indices are equal and zero otherwise. Note iff d=2 this coincides with identity.

Parameters

_dimensions the dimensions of the new tensor.

Definition at line 224 of file ttNetwork.cpp.

◆ move_core()

template<bool isOperator>

void xerus::TTNetwork< isOperator >::move_core	(	const size_t	_position,
		const bool	_keepRank = `false`
	)

Move the core to a new position.

The core is moved to _position and the nodes between the old and the new position are orthogonalized accordingly. If the TTNetwork is not yet canonicalized it will be with _position as new corePosition.

Parameters

_position	the new core position.
_keepRank	by default a rank revealing QR decomposition is used to move the core and the ranks are reduced accordingly. If _keepRank is set the rank is not reduced, this is need e.g. in the ALS.

Definition at line 582 of file ttNetwork.cpp.

◆ num_ranks()

template<bool isOperator>

size_t xerus::TTNetwork< isOperator >::num_ranks ( ) const

protected

Return the number of ranks, i.e. 0 for degree zero and degree()/N-1 otherwise.

Definition at line 363 of file ttNetwork.cpp.

◆ ones()

template<bool isOperator>

TTNetwork< isOperator > xerus::TTNetwork< isOperator >::ones ( const std::vector< size_t > & _dimensions )

static

: Returns a the (rank one) TT-Tensor with all entries equal to one.

Parameters

_dimensions the dimensions of the new tensor.

Definition at line 170 of file ttNetwork.cpp.

◆ operator*=()

template<bool isOperator>

void xerus::TTNetwork< isOperator >::operator*= ( const value_t _factor )

overridevirtual

Calculates the entrywise multiplication of this TensorNetwork with a constant _factor.

Internally this only results in a change in the global factor.

Parameters

_factor the factor.

Reimplemented from xerus::TensorNetwork.

Definition at line 860 of file ttNetwork.cpp.

◆ operator+=()

template<bool isOperator>

TTNetwork< isOperator > & xerus::TTNetwork< isOperator >::operator+= ( const TTNetwork< isOperator > & _other )

Adds a given TTNetwork to this one.

To be well-defined it is required that the dimensions of this and _other coincide. The rank of the result are in general the entrywise sum of the ranks of this and _other.

Parameters

_other the TTNetwork to add.

Returns: reference to this TTNetwork.

Definition at line 797 of file ttNetwork.cpp.

◆ operator-=()

template<bool isOperator>

TTNetwork< isOperator > & xerus::TTNetwork< isOperator >::operator-= ( const TTNetwork< isOperator > & _other )

Subtracts the _other TTNetwork entrywise from this one.

To be well-defined it is required that the dimensions of this and _other coincide. The rank of the result are in general the entrywise sum of the ranks of this and _other.

Parameters

_other the Tensor to be subtracted to this one.

Returns: a reference to this TTNetwork.

Definition at line 851 of file ttNetwork.cpp.

◆ operator/=()

template<bool isOperator>

void xerus::TTNetwork< isOperator >::operator/= ( const value_t _divisor )

overridevirtual

Calculates the entrywise divison of this TensorNetwork by a constant _divisor.

Internally this only results in a change in the global factor.

Parameters

_divisor the divisor.

Reimplemented from xerus::TensorNetwork.

Definition at line 872 of file ttNetwork.cpp.

◆ operator=() [1/2]

template<bool isOperator>

TTNetwork& xerus::TTNetwork< isOperator >::operator= ( const TTNetwork< isOperator > & _other )

default

TTNetworks are default assignable.

◆ operator=() [2/2]

template<bool isOperator>

TTNetwork& xerus::TTNetwork< isOperator >::operator= ( TTNetwork< isOperator > && _other )

default

TTNetworks are default move-assignable.

◆ random() [1/3]

template<bool isOperator>

template<class distribution = std::normal_distribution<value_t>, class generator = std::mt19937_64>

static TTNetwork XERUS_warn_unused xerus::TTNetwork< isOperator >::random	(	std::vector< size_t >	_dimensions,
		const std::vector< size_t > &	_ranks,
		distribution &	_dist = `xerus::misc::defaultNormalDistribution`,
		generator &	_rnd = `xerus::misc::randomEngine`
	)

inlinestatic

Transforms a given TensorNetwork to a TTNetwork.

This is not yet implemented different from casting to Tensor and then using a HOSVD.

Parameters

_network	The network to transform.
_eps	the accuracy to be used in the transformation. Random constructs a TTNetwork with the given dimensions and ranks.

The entries of the componend tensors are sampled independendly using the provided random generator and distribution.

Parameters

_dimensions	the dimensions of the to be created TTNetwork.
_ranks	the ranks of the to be created TTNetwork.
_rnd	the random engine to be passed to the constructor of the component tensors.
_dist	the random distribution to be passed to the constructor of the component tensors.

Definition at line 129 of file ttNetwork.h.

◆ random() [2/3]

template<bool isOperator>

template<class distribution = std::normal_distribution<value_t>, class generator = std::mt19937_64>

static TTNetwork XERUS_warn_unused xerus::TTNetwork< isOperator >::random	(	const std::vector< size_t > &	_dimensions,
		const size_t	_rank,
		distribution &	_dist = `xerus::misc::defaultNormalDistribution`,
		generator &	_rnd = `xerus::misc::randomEngine`
	)

inlinestatic

Random constructs a TTNetwork with the given dimensions and ranks limited by the given rank.

The entries of the componend tensors are sampled independendly using the provided random generator and distribution.

Parameters

_dimensions	the dimensions of the to be created TTNetwork.
_rank	the maximal allowed rank.
_rnd	the random engine to be passed to the constructor of the component tensors.
_dist	the random distribution to be passed to the constructor of the component tensors.

Definition at line 167 of file ttNetwork.h.

◆ random() [3/3]

template<bool isOperator>

template<class distribution = std::normal_distribution<value_t>, class generator = std::mt19937_64>

static TTNetwork XERUS_warn_unused xerus::TTNetwork< isOperator >::random	(	const std::vector< size_t > &	_dimensions,
		const std::vector< size_t > &	_ranks,
		const std::function< void(Tensor &)> &	_modifySingularValues,
		distribution &	_dist = `xerus::misc::defaultNormalDistribution`,
		generator &	_rnd = `xerus::misc::randomEngine`
	)

inlinestatic

Random constructs a TTNetwork with the given dimensions and ranks.

The entries of the componend tensors are sampled independendly using the provided random generator and distribution. the singular values of all matricisations M(1..n,n+1..N) are fixed according to the given function a posteriori The callback function is assumed to take a reference to a diagonal tensor and modify it to represent the desired singular values.

Definition at line 179 of file ttNetwork.h.

◆ rank()

template<bool isOperator>

size_t xerus::TTNetwork< isOperator >::rank ( const size_t _i ) const

Gets the rank of a specific egde of the TTNetwork.

Parameters

_i	Position of the edge in question.

Returns: The current rank of edge _i.

Definition at line 728 of file ttNetwork.cpp.

◆ ranks()

template<bool isOperator>

std::vector< size_t > xerus::TTNetwork< isOperator >::ranks ( ) const

Gets the ranks of the TTNetwork.

Returns: A vector containing the current ranks.

Definition at line 717 of file ttNetwork.cpp.

◆ reduce_to_maximal_ranks()

template<bool isOperator>

std::vector< size_t > xerus::TTNetwork< isOperator >::reduce_to_maximal_ranks	(	std::vector< size_t >	_ranks,
		const std::vector< size_t > &	_dimensions
	)

static

Reduces the given ranks to the maximal possible.

If a given rank is already smaller or equal it is left unchanged.

Parameters

_ranks	the inital ranks to be reduced.
_dimensions	the dimensions used to calculate the maximal ranks.

Returns: the reduced ranks.

Definition at line 370 of file ttNetwork.cpp.

◆ require_correct_format()

template<bool isOperator>

void xerus::TTNetwork< isOperator >::require_correct_format ( ) const

overridevirtual

Tests whether the network resembles that of a TTTensor and checks consistency with the underlying tensor objects.

Note that this will NOT check for orthogonality of canonicalized TTNetworks.

Reimplemented from xerus::TensorNetwork.

Definition at line 290 of file ttNetwork.cpp.

◆ resize_mode()

template<bool isOperator>

void xerus::TTNetwork< isOperator >::resize_mode	(	const size_t	_mode,
		const size_t	_newDim,
		const size_t	_cutPos = `~0ul`
	)

overridevirtual

Resizes a specific mode of the TensorNetwork.

Parameters

_mode	the mode to resize.
_newDim	the new value that resized mode shall have.
_cutPos	the position within the selected mode in front of which slates are inserted or removed. By default the current dimension, i.e new slates are added after the last current one and removed starting from the last one.

Reimplemented from xerus::TensorNetwork.

Definition at line 438 of file ttNetwork.cpp.

◆ round() [1/4]

template<bool isOperator>

void xerus::TTNetwork< isOperator >::round	(	const std::vector< size_t > &	_maxRanks,
		const double	_eps = `EPSILON`
	)

Reduce all ranks up to a given accuracy and maximal number.

Parameters

_maxRanks	maximal allowed ranks. All current ranks that are larger than the given ones are reduced by truncation.
_eps	the accuracy to use for truncation in the individual SVDs.

Definition at line 644 of file ttNetwork.cpp.

◆ round() [2/4]

template<bool isOperator>

void xerus::TTNetwork< isOperator >::round ( const size_t _maxRank )

Reduce all ranks to the given number.

Parameters

_maxRank maximal allowed rank. All current ranks that are larger than this are reduced by truncation.

Definition at line 669 of file ttNetwork.cpp.

◆ round() [3/4]

template<bool isOperator>

void xerus::TTNetwork< isOperator >::round ( const int _maxRank )

Reduce all ranks to the given number.

Parameters

_maxRank maximal allowed rank. All current ranks that are larger than this are reduced by truncation.

Definition at line 675 of file ttNetwork.cpp.

◆ round() [4/4]

template<bool isOperator>

void xerus::TTNetwork< isOperator >::round ( const value_t _eps )

Reduce all ranks up to a given accuracy.

Parameters

_eps	the accuracy to use for truncation in the individual SVDs.

Definition at line 682 of file ttNetwork.cpp.

◆ set_component()

template<bool isOperator>

void xerus::TTNetwork< isOperator >::set_component	(	const size_t	_idx,
		Tensor	_T
	)

Sets a specific component of the TT decomposition.

This function also takes care of adjusting the corresponding link dimensions and external dimensions if needed. However this might still leave the TTNetwork in an invalid if the rank is changed. In this case it is the callers responsibility to also update the other component tensors consistently to account for that rank change.

Parameters

_idx	index of the component to set.
_T	Tensor to use as the new component tensor.

Definition at line 471 of file ttNetwork.cpp.

◆ soft_threshold() [1/2]

template<bool isOperator>

void xerus::TTNetwork< isOperator >::soft_threshold	(	const double	_tau,
		const bool	_preventZero = `false`
	)

Applies the soft threshholding operation to all ranks.

Parameters

_tau	the soft threshholding parameter to be applied. I.e. all singular values are reduced to max(0, Lambda_ui - _tau).

Definition at line 711 of file ttNetwork.cpp.

◆ soft_threshold() [2/2]

template<bool isOperator>

void xerus::TTNetwork< isOperator >::soft_threshold	(	const std::vector< double > &	_taus,
		const bool	_preventZero = `false`
	)

Applies soft threshholding operations to all ranks.

Parameters

_taus the soft threshholding parameters to be applied. I.e. all singular values of the j-th matrification are reduced to max(0, Lambda_ui - _tau[j]).

Definition at line 688 of file ttNetwork.cpp.

◆ specialized_contraction()

template<bool isOperator>

virtual bool xerus::TTNetwork< isOperator >::specialized_contraction	(	std::unique_ptr< internal::IndexedTensorMoveable< TensorNetwork >> &	_out,
		internal::IndexedTensorReadOnly< TensorNetwork > &&	_me,
		internal::IndexedTensorReadOnly< TensorNetwork > &&	_other
	)		const

inlineoverridevirtual

(Internal) Calculates the contraction between _me and _other and stores the result in _out. Requires that *this is the tensorObjectReadOnly of _me.

Reimplemented from xerus::TensorNetwork.

Definition at line 506 of file ttNetwork.h.

◆ specialized_contraction_f() [1/3]

template<bool isOperator>

static bool xerus::TTNetwork< isOperator >::specialized_contraction_f	(	std::unique_ptr< internal::IndexedTensorMoveable< TensorNetwork >> &	_out,
		internal::IndexedTensorReadOnly< TensorNetwork > &&	_me,
		internal::IndexedTensorReadOnly< TensorNetwork > &&	_other
	)

static

◆ specialized_contraction_f() [2/3]

template<>

bool xerus::TTNetwork< false >::specialized_contraction_f	(	std::unique_ptr< internal::IndexedTensorMoveable< TensorNetwork >> &	,
		internal::IndexedTensorReadOnly< TensorNetwork > &&	,
		internal::IndexedTensorReadOnly< TensorNetwork > &&
	)

Definition at line 883 of file ttNetwork.cpp.

◆ specialized_contraction_f() [3/3]

template<>

bool xerus::TTNetwork< true >::specialized_contraction_f	(	std::unique_ptr< internal::IndexedTensorMoveable< TensorNetwork >> &	_out,
		internal::IndexedTensorReadOnly< TensorNetwork > &&	_me,
		internal::IndexedTensorReadOnly< TensorNetwork > &&	_other
	)

Definition at line 889 of file ttNetwork.cpp.

◆ specialized_evaluation()

template<bool isOperator>

void xerus::TTNetwork< isOperator >::specialized_evaluation	(	internal::IndexedTensorWritable< TensorNetwork > &&	_me,
		internal::IndexedTensorReadOnly< TensorNetwork > &&	_other
	)

overridevirtual

(Internal) Evaluates _other into _me. Requires that *this is the tensorObjectReadOnly of _me.

Reimplemented from xerus::TensorNetwork.

Definition at line 1064 of file ttNetwork.cpp.

◆ specialized_sum()

template<bool isOperator>

virtual bool xerus::TTNetwork< isOperator >::specialized_sum	(	std::unique_ptr< internal::IndexedTensorMoveable< TensorNetwork >> &	_out,
		internal::IndexedTensorReadOnly< TensorNetwork > &&	_me,
		internal::IndexedTensorReadOnly< TensorNetwork > &&	_other
	)		const

inlineoverridevirtual

(Internal) Calculates the sum between _me and _other and stores the result in _out. Requires that *this is the tensorObjectReadOnly of _me.

Reimplemented from xerus::TensorNetwork.

Definition at line 510 of file ttNetwork.h.

◆ specialized_sum_f()

template<bool isOperator>

bool xerus::TTNetwork< isOperator >::specialized_sum_f	(	std::unique_ptr< internal::IndexedTensorMoveable< TensorNetwork >> &	_out,
		internal::IndexedTensorReadOnly< TensorNetwork > &&	_me,
		internal::IndexedTensorReadOnly< TensorNetwork > &&	_other
	)

static

Definition at line 982 of file ttNetwork.cpp.

◆ transpose()

template<bool isOperator>

template<bool B = isOperator, typename std::enable_if< B, int >::type = 0>

void xerus::TTNetwork< isOperator >::transpose ( )

inline

Transpose the TTOperator.

Swaps all external indices to create the transposed operator.

Definition at line 443 of file ttNetwork.h.

◆ use_dense_representations()

template<bool isOperator>

void xerus::TTNetwork< isOperator >::use_dense_representations ( )

Converts all components to use dense representations.

Note: This might be required because not all functionality of TTNetworks is available with sparse component tensors.

Definition at line 450 of file ttNetwork.cpp.

Member Data Documentation

◆ canonicalized

template<bool isOperator>

bool xerus::TTNetwork< isOperator >::canonicalized

Flag indicating whether the TTNetwork is canonicalized.

Definition at line 51 of file ttNetwork.h.

◆ corePosition

template<bool isOperator>

size_t xerus::TTNetwork< isOperator >::corePosition

The position of the core.

If canonicalized is TRUE, corePosition gives the position of the core tensor. All components with smaller index are then left-orthogonalized and all components with larger index right-orthogonalized.

Definition at line 58 of file ttNetwork.h.

◆ N

template<bool isOperator>

constexpr const size_t xerus::TTNetwork< isOperator >::N = isOperator?2:1

static

The number of external links in each node, i.e. one for TTTensors and two for TTOperators.

Definition at line 48 of file ttNetwork.h.

The documentation for this class was generated from the following files:

/home/gitlab-runner/builds/9071116c/0/xerus/xerus/include/xerus/performanceData.h
/home/gitlab-runner/builds/9071116c/0/xerus/xerus/include/xerus/ttNetwork.h
/home/gitlab-runner/builds/9071116c/0/xerus/xerus/src/xerus/ttNetwork.cpp

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Protected Member Functions

Static Protected Member Functions

Additional Inherited Members

Detailed Description

template<bool isOperator> class xerus::TTNetwork< isOperator >

Constructor & Destructor Documentation

◆ TTNetwork() [1/7]

◆ TTNetwork() [2/7]

◆ TTNetwork() [3/7]

◆ TTNetwork() [4/7]

◆ TTNetwork() [5/7]

◆ TTNetwork() [6/7]

◆ TTNetwork() [7/7]

Member Function Documentation

◆ assume_core_position()

◆ canonicalize_left()

◆ canonicalize_right()

◆ chop()

◆ component()

◆ construct_train_from_full()

◆ contract_unconnected_subnetworks()

◆ degrees_of_freedom() [1/2]

◆ degrees_of_freedom() [2/2]

◆ dirac() [1/2]

◆ dirac() [2/2]

◆ exceeds_maximal_ranks()

◆ fix_mode()

◆ frob_norm()

◆ get_component()

◆ get_copy()

◆ identity() [1/2]

◆ identity() [2/2]

◆ kronecker()

◆ move_core()

◆ num_ranks()

◆ ones()

◆ operator*=()

◆ operator+=()

◆ operator-=()

◆ operator/=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ random() [1/3]

◆ random() [2/3]

◆ random() [3/3]

◆ rank()

◆ ranks()

◆ reduce_to_maximal_ranks()

◆ require_correct_format()

◆ resize_mode()

◆ round() [1/4]

◆ round() [2/4]

◆ round() [3/4]

◆ round() [4/4]

◆ set_component()

◆ soft_threshold() [1/2]

◆ soft_threshold() [2/2]

◆ specialized_contraction()

◆ specialized_contraction_f() [1/3]

◆ specialized_contraction_f() [2/3]

◆ specialized_contraction_f() [3/3]

◆ specialized_evaluation()

◆ specialized_sum()

◆ specialized_sum_f()

◆ transpose()

◆ use_dense_representations()

Member Data Documentation

◆ canonicalized

◆ corePosition

◆ N

template<bool isOperator>
class xerus::TTNetwork< isOperator >