The main namespace of xerus. More...

Namespaces
	blasWrapper
	In this namespace the minimal wrappers for the BLAS and LAPACK functions are collected.

	internal
	Namespace for function and classes designated only for internal use.

	misc
	Collection of classes and functions that provide elementary functionality that is not special to xerus as a tensor library.

Classes
class	ADFVariant
	Wrapper class for all ADF variants. More...

class	ALSVariant
	Wrapper class for all ALS variants (dmrg etc.) More...

class	CQ
	Helper class to allow an intuitive syntax for an rank revealing orthogonal factorisation. More...

class	GeometricCGVariant
	Wrapper class for all geometric (ie. Riemannian) CG variants. More...

struct	HOSVDRetraction
	retraction that performs a HOSVD to project back onto the Manifold More...

class	Index
	Class used to represent indices that can be used to write tensor calculations in index notation. More...

class	InternalSolver

class	MeasurmentComparator

class	PerformanceData
	Storage class for the performance data collected during an algorithm (typically iteration count, time and residual) More...

class	QC
	Helper class to allow an intuitive syntax for an rank revealing orthogonal factorisation. More...

class	QR
	Helper class to allow an intuitive syntax for QR factorisations. More...

class	RankOneMeasurementSet

class	RQ
	Helper class to allow an intuitive syntax for RQ factorisations. More...

class	SinglePointMeasurementSet
	Class used to represent a single point measurments. More...

class	SteepestDescentVariant
	Wrapper class for all steepest descent variants. More...

class	SVD
	Helper class to allow an intuitive syntax for SVD factorisations. More...

class	Tensor
	Class that handles simple (non-decomposed) tensors in a dense or sparse representation. More...

class	TensorFactorisation
	Abstract super class for all tensor factorisations. More...

class	TensorNetwork
	Very general class used to represent arbitary tensor networks. More...

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

class	TTTangentVector
	class to compactly represent tangent vectors of the manifold of constant TT-rank More...

class	UQMeasurementSet

Typedefs
typedef uint8_t	byte
	unsigned int type of exactly 8 bit More...

typedef int16_t	int16

typedef int32_t	int32

typedef int64_t	int64

typedef int8_t	int8

typedef TTNetwork< true >	TTOperator

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

using	TTRetractionII = std::function< void(TTTensor &, const TTTensor &)>

typedef TTNetwork< false >	TTTensor

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

typedef unsigned int	uint

typedef uint16_t	uint16

typedef uint32_t	uint32

typedef uint64_t	uint64

typedef uint8_t	uint8

typedef unsigned long	ulong

typedef unsigned short	ushort

typedef double	value_t
	The type of values to be used by xerus. More...

Functions
const ADFVariant	ADF (0, 1e-8, 0.999)

const ALSVariant	ALS (1, 0, ALSVariant::lapack_solver, false)

const ALSVariant	ALS_SPD (1, 0, ALSVariant::lapack_solver, true)

void	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	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...

bool	approx_entrywise_equal (const xerus::Tensor &_a, const xerus::Tensor &_b, const xerus::value_t _eps=EPSILON)
	Checks whether two Tensors are approximately entrywise equal. More...

bool	approx_entrywise_equal (const xerus::Tensor &_tensor, const std::vector< value_t > &_values, const xerus::value_t _eps=EPSILON)
	Compares the given Tensor entriewise to the given data. More...

bool	approx_equal (const TensorNetwork &_a, const TensorNetwork &_b, const value_t _eps=EPSILON)
	Checks whether two TensorNetworks are approximately equal. More...

bool	approx_equal (const TensorNetwork &_a, const Tensor &_b, const value_t _eps=EPSILON)
	Convinience wrapper, casts the the given TensorNetwork _a to Tensor and calls the Tensor function. More...

bool	approx_equal (const Tensor &_a, const TensorNetwork &_b, const value_t _eps=EPSILON)
	Convinience wrapper, casts the the given TensorNetwork _b to Tensor and calls the Tensor function. More...

bool	approx_equal (const xerus::Tensor &_a, const xerus::Tensor &_b, const xerus::value_t _eps=EPSILON)
	Checks whether two tensors are approximately equal. More...

const ALSVariant	ASD (1, 0, ALSVariant::ASD_solver, false)

const ALSVariant	ASD_SPD (1, 0, ALSVariant::ASD_solver, true)

template<class MeasurmentSet >
void	calc_measurment_norm (double *_norms, const MeasurmentSet &_measurments)

template<>
void	calc_measurment_norm< RankOneMeasurementSet > (double *_norms, const RankOneMeasurementSet &_measurments)

template<>
void	calc_measurment_norm< SinglePointMeasurementSet > (double *_norms, const SinglePointMeasurementSet &_measurments)

void	calculate_cq (Tensor &_C, Tensor &_Q, Tensor _input, const size_t _splitPos)
	Low-Level CQ calculation of a given Tensor _input = _C _Q. More...

XERUS_force_inline std::tuple< size_t, size_t, size_t >	calculate_factorization_sizes (const Tensor &_input, const size_t _splitPos)

void	calculate_qc (Tensor &_Q, Tensor &_C, Tensor _input, const size_t _splitPos)
	Low-Level QC calculation of a given Tensor _input = _Q _C. More...

void	calculate_qr (Tensor &_Q, Tensor &_R, Tensor _input, const size_t _splitPos)
	Low-Level QR calculation of a given Tensor _input = _Q _R. More...

void	calculate_rq (Tensor &_R, Tensor &_Q, Tensor _input, const size_t _splitPos)
	Low-Level RQ calculation of a given Tensor _input = _R _Q. More...

void	calculate_svd (Tensor &_U, Tensor &_S, Tensor &_Vt, Tensor _input, const size_t _splitPos, const size_t _maxRank, const value_t _eps)
	Low-Level SVD calculation of a given Tensor _input = _U _S _Vt. More...

void	contract (Tensor &_result, const Tensor &_lhs, const bool _lhsTrans, const Tensor &_rhs, const bool _rhsTrans, const size_t _numModes)
	Low-level contraction between Tensors. More...

Tensor	contract (const Tensor &_lhs, const bool _lhsTrans, const Tensor &_rhs, const bool _rhsTrans, const size_t _numModes)

XERUS_force_inline void	contract (Tensor &_result, const Tensor &_lhs, const Tensor &_rhs, const size_t _numModes)
	Low-level contraction between Tensors. More...

XERUS_force_inline Tensor	contract (const Tensor &_lhs, const Tensor &_rhs, const size_t _numModes)

void	decomposition_als (TTTensor &_x, const Tensor &_b, const double _eps=EPSILON, const size_t _maxIterations=1000)

const ALSVariant	DMRG (2, 0, ALSVariant::lapack_solver, false)

const ALSVariant	DMRG_SPD (2, 0, ALSVariant::lapack_solver, true)

template<bool isOperator>
TTNetwork< isOperator >	dyadic_product (const TTNetwork< isOperator > &_lhs, const TTNetwork< isOperator > &_rhs)
	Computes the dyadic product of _lhs and _rhs. More...

template<bool isOperator>
TTNetwork< isOperator >	dyadic_product (const std::vector< TTNetwork< isOperator >> &_tensors)
	Computes the dyadic product of all given TTNetworks. More...

template TTNetwork< true >	dyadic_product (const TTNetwork< true > &_lhs, const TTNetwork< true > &_rhs)

template TTNetwork< false >	dyadic_product (const TTNetwork< false > &_lhs, const TTNetwork< false > &_rhs)

template TTNetwork< true >	dyadic_product (const std::vector< TTNetwork< true >> &_tensors)

template TTNetwork< false >	dyadic_product (const std::vector< TTNetwork< false >> &_tensors)

template<bool isOperator>
TTNetwork< isOperator >	entrywise_product (const TTNetwork< isOperator > &_A, const TTNetwork< isOperator > &_B)
	Calculates the componentwise product of two tensors given in the TT format. More...

Tensor	entrywise_product (const Tensor &_A, const Tensor &_B)
	calculates the entrywise product of two Tensors More...

template TTNetwork< false >	entrywise_product (const TTNetwork< false > &_A, const TTNetwork< false > &_B)

template TTNetwork< true >	entrywise_product (const TTNetwork< true > &_A, const TTNetwork< true > &_B)

template<bool isOperator>
size_t	find_largest_entry (const TTNetwork< isOperator > &_T, double _accuracy, value_t _lowerBound=0.0)
	Finds the position of the approximately largest entry. More...

template size_t	find_largest_entry (const TTNetwork< true > &, double, value_t)

template size_t	find_largest_entry (const TTNetwork< false > &, double, value_t)

static XERUS_force_inline value_t	frob_norm (const TensorNetwork &_network)
	Calculates the frobenious norm of the given TensorNetwork. More...

static XERUS_force_inline value_t	frob_norm (const Tensor &_tensor)
	Calculates the frobenius norm of the given tensor. More...

const GeometricCGVariant	GeometricCG (0, 1e-8, false, SubmanifoldRetractionI, ProjectiveVectorTransport)

template<bool isOperator>
std::vector< std::vector< std::tuple< size_t, size_t, value_t > > >	get_grouped_entries (const Tensor &_component)

std::vector< size_t >	get_step_sizes (const Tensor::DimensionTuple &_dimensions)

void	HOSVDRetractionI (TTTensor &_U, const TTTangentVector &_change)
	retraction that performs a HOSVD to project back onto the Manifold More...

void	HOSVDRetractionII (TTTensor &_U, const TTTensor &_change)

double	IHT (TTTensor &_x, const SinglePointMeasurementSet &_measurments, PerformanceData &_perfData=NoPerfData)

void	increase_indices (const size_t _i, value_t *&_outPosition, const std::vector< size_t > &_stepSizes, const std::vector< size_t > &_baseDimensions)

void	line_search (TTTensor &_x, value_t &_alpha, const TTTangentVector &_direction, value_t _derivative, value_t &_residual, std::function< void(TTTensor &, const TTTangentVector &)> _retraction, std::function< value_t()> _calculate_residual, value_t _changeInAlpha=0.5)

void	matrix_matrix_product (double const _C, const size_t _leftDim, const size_t _rightDim, const double _alpha, const std::map< size_t, double > &_A, const bool _transposeA, const size_t _midDim, const double const _B, const bool _transposeB)

void	matrix_matrix_product (double const _C, const size_t _leftDim, const size_t _rightDim, const double _alpha, const double const _A, const bool _transposeA, const size_t _midDim, const std::map< size_t, double > &_B, const bool _transposeB)

void	matrix_matrix_product (std::map< size_t, double > &_C, const size_t _leftDim, const size_t _rightDim, const double _alpha, const std::map< size_t, double > &_A, const bool _transposeA, const size_t _midDim, const double *const _B, const bool _transposeB)

void	matrix_matrix_product (std::map< size_t, double > &_C, const size_t _leftDim, const size_t _rightDim, const double _alpha, const double *const _A, const bool _transposeA, const size_t _midDim, const std::map< size_t, double > &_B, const bool _transposeB)

void	matrix_matrix_product (double const _C, const size_t _leftDim, const size_t _rightDim, const double _alpha, const std::map< size_t, double > &_A, const bool _transposeA, const size_t _midDim, const double const _B)

void	matrix_matrix_product (std::map< size_t, double > &_C, const size_t, const size_t _rightDim, const double _alpha, const std::map< size_t, double > &_A, const size_t _midDim, const double *const _B)

PerformanceData	NoPerfData (false, false)

static XERUS_force_inline value_t	one_norm (const Tensor &_tensor)
	Calculates the 1-norm of the given tensor. More...

bool	operator!= (const Index &_a, const Index &_b)
	Two Indices are equal if their valueId coincides. Fixed indices are never equal. More...

TTTangentVector	operator* (value_t _alpha, const TTTangentVector &_rhs)

TensorNetwork	operator* (TensorNetwork &_lhs, value_t _factor)

TensorNetwork	operator* (value_t _factor, TensorNetwork &_rhs)

template<bool isOperator>
TTNetwork< isOperator >	operator* (TTNetwork< isOperator > _network, const value_t _factor)
	Calculates the entrywise multiplication of the given TTNetwork _network with a constant _factor. More...

template<bool isOperator>
TTNetwork< isOperator >	operator* (const value_t _factor, TTNetwork< isOperator > _network)
	Calculates the entrywise multiplication of the given TTNetwork _network with a constant _factor. More...

Tensor	operator* (const value_t _factor, Tensor _tensor)
	Calculates the entrywise multiplication of the Tensor _tensor with the constant _factor. More...

Tensor	operator* (Tensor _tensor, const value_t _factor)
	Calculates the entrywise multiplication of the Tensor _tensor with the constant _factor. More...

template TTNetwork< false >	operator* (TTNetwork< false > _network, const value_t _factor)

template TTNetwork< true >	operator* (TTNetwork< true > _network, const value_t _factor)

template TTNetwork< false >	operator* (const value_t _factor, TTNetwork< false > _network)

template TTNetwork< true >	operator* (const value_t _factor, TTNetwork< true > _network)

template<bool isOperator>
TTNetwork< isOperator >	operator+ (TTNetwork< isOperator > _lhs, const TTNetwork< isOperator > &_rhs)
	Calculates the entrywise sum of the given TTNetworks _lhs and _rhs. More...

Tensor	operator+ (Tensor _lhs, const Tensor &_rhs)
	Calculates the entrywise sum of _lhs and _rhs. More...

template TTNetwork< false >	operator+ (TTNetwork< false > _lhs, const TTNetwork< false > &_rhs)

template TTNetwork< true >	operator+ (TTNetwork< true > _lhs, const TTNetwork< true > &_rhs)

template<bool isOperator>
TTNetwork< isOperator >	operator- (TTNetwork< isOperator > _lhs, const TTNetwork< isOperator > &_rhs)
	Calculates the entrywise difference of the given TTNetworks _lhs and _rhs. More...

Tensor	operator- (Tensor _lhs, const Tensor &_rhs)
	Calculates the entrywise difference between _lhs and _rhs. More...

template TTNetwork< false >	operator- (TTNetwork< false > _lhs, const TTNetwork< false > &_rhs)

template TTNetwork< true >	operator- (TTNetwork< true > _lhs, const TTNetwork< true > &_rhs)

internal::IndexedTensorMoveable< Tensor >	operator/ (internal::IndexedTensorReadOnly< Tensor > &&_b, internal::IndexedTensorReadOnly< Tensor > &&_A)

TensorNetwork	operator/ (TensorNetwork &_lhs, value_t _factor)

template<bool isOperator>
TTNetwork< isOperator >	operator/ (TTNetwork< isOperator > _network, const value_t _divisor)
	Calculates the entrywise divison of this TTNetwork by a constant _divisor. More...

Tensor	operator/ (Tensor _tensor, const value_t _divisor)
	Calculates the entrywise divison of the Tensor _tensor with the constant _divisor. More...

template TTNetwork< false >	operator/ (TTNetwork< false > _network, const value_t _divisor)

template TTNetwork< true >	operator/ (TTNetwork< true > _network, const value_t _divisor)

bool	operator< (const Index &_a, const Index &_b)
	The Comparision operator is needed for indices to be orderable in std::set, the valueId is used. More...

std::ostream &	operator<< (std::ostream &_out, const xerus::Index &_idx)
	Allows to pretty print indices, giving the valueId and span. More...

std::ostream &	operator<< (std::ostream &_out, const TensorNetwork::Link &_rhs)

std::ostream &	operator<< (std::ostream &_out, const Tensor &_tensor)
	Prints the Tensor to the given outStream. More...

bool	operator== (const Index &_a, const Index &_b)
	Two Indices are equal if their valueId coincides. Fixed indices are never equal. More...

template<bool isOperator>
void	perform_component_product (Tensor &_newComponent, const Tensor &_componentA, const Tensor &_componentB)

template<class MeasurmentSet >
size_t	position_or_zero (const MeasurmentSet &_measurments, const size_t _meas, const size_t _corePosition)

template<>
size_t	position_or_zero< RankOneMeasurementSet > (const RankOneMeasurementSet &, const size_t, const size_t)

template<>
size_t	position_or_zero< SinglePointMeasurementSet > (const SinglePointMeasurementSet &_measurments, const size_t _meas, const size_t _corePosition)

XERUS_force_inline void	prepare_factorization_output (Tensor &_lhs, Tensor &_rhs, const Tensor &_input, const size_t _splitPos, const size_t _rank, Tensor::Representation _rep)

std::unique_ptr< Tensor >	prepare_split (size_t &_lhsSize, size_t &_rhsSize, size_t &_rank, size_t &_splitPos, std::vector< Index > &_lhsPreliminaryIndices, std::vector< Index > &_rhsPreliminaryIndices, internal::IndexedTensorReadOnly< Tensor > &&_base, internal::IndexedTensor< Tensor > &&_lhs, internal::IndexedTensor< Tensor > &&_rhs)

void	ProjectiveVectorTransport (const TTTensor &_newBase, TTTangentVector &_tangentVector)
	simple vector transport by projecting onto the new tangent plane More...

void	pseudo_inverse (Tensor &_inverse, const Tensor &_input, const size_t _splitPos)
	Low-Level calculation of the pseudo inverse of a given Tensor. More...

Tensor	pseudo_inverse (const Tensor &_input, const size_t _splitPos)

Tensor	randVar_to_position (const double _v, const size_t _polyDegree)

void	reshuffle (Tensor &_out, const Tensor &_base, const std::vector< size_t > &_shuffle)
	: Performs a simple reshuffle. Much less powerfull then a full evaluate, but more efficient. More...

Tensor	reshuffle (const Tensor &_base, const std::vector< size_t > &_shuffle)

XERUS_force_inline void	set_factorization_output (Tensor &_lhs, std::unique_ptr< value_t[]> &&_lhsData, Tensor &_rhs, std::unique_ptr< value_t[]> &&_rhsData, const Tensor &_input, const size_t _splitPos, const size_t _rank)

XERUS_force_inline void	set_factorization_output (Tensor &_lhs, std::map< size_t, value_t > &&_lhsData, Tensor &_rhs, std::map< size_t, value_t > &&_rhsData, const Tensor &_input, const size_t _splitPos, const size_t _rank)

void	solve (internal::IndexedTensorWritable< Tensor > &&_x, internal::IndexedTensorReadOnly< Tensor > &&_A, internal::IndexedTensorReadOnly< Tensor > &&_b)

void	solve (Tensor &_X, const Tensor &_A, const Tensor &_B, size_t _extraDegree=0)
	Solves the equation Ax = b for x. If the solution is not unique, the output need not be the minimal norm solution. More...

void	solve_least_squares (Tensor &_X, const Tensor &_A, const Tensor &_B, const size_t _extraDegree=0)
	Solves the least squares problem \|\|_A _X - _B\|\|_F. More...

const SteepestDescentVariant	SteepestDescent (0, 1e-8, false, SubmanifoldRetractionII)

void	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	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...

XERUS_force_inline void	transpose (double const __restrict _out, const double const __restrict _in, const size_t _leftDim, const size_t _rightDim)

XERUS_force_inline std::unique_ptr< double[]>	transpose (const double *const _A, const size_t _leftDim, const size_t _rightDim)

XERUS_force_inline void	transpose (std::map< size_t, double > &__restrict _out, const std::map< size_t, double > &__restrict _in, const size_t _leftDim, const size_t _rightDim)

XERUS_force_inline std::map< size_t, double >	transpose (const std::map< size_t, double > &_A, const size_t _leftDim, const size_t _rightDim)

template<bool isOperator>
void	transpose_if_operator (TTNetwork< isOperator > &_ttNetwork)

template<>
void	transpose_if_operator< false > (TTNetwork< false > &)

template<>
void	transpose_if_operator< true > (TTNetwork< true > &_ttNetwork)

void	uq_adf (TTTensor &_x, const std::vector< std::vector< double >> &_randomVariables, const std::vector< Tensor > &_solutions)

TTTensor	uq_adf (const UQMeasurementSet &_measurments, const TTTensor &_guess)

Tensor	uq_avg (const TTTensor &_x, const size_t _N, const size_t _numSpecial)

std::pair< std::vector< std::vector< double > >, std::vector< Tensor > >	uq_mc (const TTTensor &_x, const size_t _N, const size_t _numSpecial)

Variables
const ADFVariant	ADF
	Default variant of the ADF algorithm. More...

const ALSVariant	ALS
	default variant of the single-site ALS algorithm for non-symmetric operators using the lapack solver More...

const ALSVariant	ALS_SPD
	default variant of the single-site ALS algorithm for symmetric positive-definite operators using the lapack solver More...

const ALSVariant	ASD
	default variant of the alternating steepest descent for non-symmetric operators More...

const ALSVariant	ASD_SPD
	default variant of the alternating steepest descent for symmetric positive-definite operators More...

const ALSVariant	DMRG
	default variant of the two-site DMRG algorithm for non-symmetric operators using the lapack solver More...

const ALSVariant	DMRG_SPD
	default variant of the two-site DMRG algorithm for symmetric positive-definite operators using the lapack solver More...

constexpr const value_t	EPSILON = 8*std::numeric_limits<value_t>::epsilon()
	The default epsilon value in xerus. More...

const GeometricCGVariant	GeometricCG
	default variant of the steepest descent algorithm using the lapack solver More...

PerformanceData	NoPerfData

const SteepestDescentVariant	SteepestDescent
	default variant of the steepest descent algorithm using the lapack solver More...

const int	VERSION_COMMIT = XERUS_VERSION_COMMIT

const int	VERSION_MAJOR = XERUS_VERSION_MAJOR

const int	VERSION_MINOR = XERUS_VERSION_MINOR

const int	VERSION_REVISION = XERUS_VERSION_REVISION

Detailed Description

The main namespace of xerus.

With very few exceptions all classes, functions and variables declared by the xerus are placed in this namespace.

Typedef Documentation

◆ byte

typedef uint8_t xerus::byte

unsigned int type of exactly 8 bit

Definition at line 49 of file standard.h.

◆ int16

typedef int16_t xerus::int16

Definition at line 56 of file standard.h.

◆ int32

typedef int32_t xerus::int32

Definition at line 57 of file standard.h.

◆ int64

typedef int64_t xerus::int64

Definition at line 58 of file standard.h.

◆ int8

typedef int8_t xerus::int8

Definition at line 55 of file standard.h.

◆ TTOperator

typedef TTNetwork< true > xerus::TTOperator

Definition at line 40 of file performanceData.h.

◆ TTRetractionI

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

Definition at line 70 of file retractions.h.

◆ TTRetractionII

using xerus::TTRetractionII = typedef std::function<void(TTTensor &, const TTTensor &)>

Definition at line 71 of file retractions.h.

◆ TTTensor

typedef TTNetwork< false > xerus::TTTensor

Definition at line 37 of file performanceData.h.

◆ TTVectorTransport

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

Definition at line 72 of file retractions.h.

◆ uint

typedef unsigned int xerus::uint

Definition at line 51 of file standard.h.

◆ uint16

typedef uint16_t xerus::uint16

Definition at line 61 of file standard.h.

◆ uint32

typedef uint32_t xerus::uint32

Definition at line 62 of file standard.h.

◆ uint64

typedef uint64_t xerus::uint64

Definition at line 63 of file standard.h.

◆ uint8

typedef uint8_t xerus::uint8

Definition at line 60 of file standard.h.

◆ ulong

typedef unsigned long xerus::ulong

Definition at line 52 of file standard.h.

◆ ushort

typedef unsigned short xerus::ushort

Definition at line 50 of file standard.h.

◆ value_t

typedef double xerus::value_t

The type of values to be used by xerus.

In future versions this should be allowed to be float, double, or complex. In the current version however this is fixed to double.

Definition at line 43 of file basic.h.

Function Documentation

◆ ADF()

const ADFVariant xerus::ADF	(	0	,
		1e-	8,
		0.	999
	)

◆ ALS()

const ALSVariant xerus::ALS	(	1	,
		0	,
		ALSVariant::lapack_solver	,
		false
	)

◆ ALS_SPD()

const ALSVariant xerus::ALS_SPD	(	1	,
		0	,
		ALSVariant::lapack_solver	,
		true
	)

◆ ALSRetractionI()

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

Definition at line 69 of file retractions.cpp.

◆ ALSRetractionII()

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

Definition at line 62 of file retractions.cpp.

◆ approx_entrywise_equal() [1/2]

bool xerus::approx_entrywise_equal	(	const xerus::Tensor &	_a,
		const xerus::Tensor &	_b,
		const xerus::value_t	_eps = `EPSILON`
	)

Checks whether two Tensors are approximately entrywise equal.

Check whether |_a[i] - _b[i] |/(|_a[i] | + |_b[i] | < _eps is fullfilled for all i.

Parameters

_a	the first test candidate.
_b	the second test candidate
_eps	the maximal relative difference between the entries of _a and _b.

Returns: TRUE if _a and _b are determined to be approximately equal, FALSE otherwise.

Definition at line 1745 of file tensor.cpp.

◆ approx_entrywise_equal() [2/2]

bool xerus::approx_entrywise_equal	(	const xerus::Tensor &	_tensor,
		const std::vector< value_t > &	_values,
		const xerus::value_t	_eps = `EPSILON`
	)

Compares the given Tensor entriewise to the given data.

Parameters

_tensor	the tensor.
_values	the data to compare to, must be of the same size as the Tensor has entries (i.e. size).
_eps	(optional) epsilon used to determine whether an entry is equal to a data point.

Returns: TRUE if approx_equal() is true for all entries/data points, FALSE otherwise.

Definition at line 1765 of file tensor.cpp.

◆ approx_equal() [1/4]

bool xerus::approx_equal	(	const TensorNetwork &	_a,
		const TensorNetwork &	_b,
		const value_t	_eps = `EPSILON`
	)

Checks whether two TensorNetworks are approximately equal.

Check whether ||_a - _b ||/(||a ||/2 + ||_b ||/2) < _eps, i.e. whether the relative difference in the frobenius norm is sufficently small.

Parameters

_a	the first test candidate.
_b	the second test candidate
_eps	the maximal relative difference between _a and _b.

Returns: TRUE if _a and _b are determined to be approximately equal, FALSE otherwise.

Definition at line 1411 of file tensorNetwork.cpp.

◆ approx_equal() [2/4]

bool xerus::approx_equal	(	const TensorNetwork &	_a,
		const Tensor &	_b,
		const value_t	_eps = `EPSILON`
	)

Convinience wrapper, casts the the given TensorNetwork _a to Tensor and calls the Tensor function.

Definition at line 1418 of file tensorNetwork.cpp.

◆ approx_equal() [3/4]

bool xerus::approx_equal	(	const Tensor &	_a,
		const TensorNetwork &	_b,
		const value_t	_eps = `EPSILON`
	)

Convinience wrapper, casts the the given TensorNetwork _b to Tensor and calls the Tensor function.

Definition at line 1423 of file tensorNetwork.cpp.

◆ approx_equal() [4/4]

bool xerus::approx_equal	(	const xerus::Tensor &	_a,
		const xerus::Tensor &	_b,
		const xerus::value_t	_eps = `EPSILON`
	)

Checks whether two tensors are approximately equal.

Check whether ||_a - _b ||/(||a ||/2 + ||_b ||/2) < _eps, i.e. whether the relative difference in the frobenius norm is sufficently small.

Parameters

_a	the first test candidate.
_b	the second test candidate
_eps	the maximal relative difference between _a and _b.

Returns: TRUE if _a and _b are determined to be approximately equal, FALSE otherwise.

Definition at line 1738 of file tensor.cpp.

◆ ASD()

const ALSVariant xerus::ASD	(	1	,
		0	,
		ALSVariant::ASD_solver	,
		false
	)

◆ ASD_SPD()

const ALSVariant xerus::ASD_SPD	(	1	,
		0	,
		ALSVariant::ASD_solver	,
		true
	)

◆ calc_measurment_norm()

template<class MeasurmentSet >

void xerus::calc_measurment_norm	(	double *	_norms,
		const MeasurmentSet &	_measurments
	)

inline

◆ calc_measurment_norm< RankOneMeasurementSet >()

template<>

void xerus::calc_measurment_norm< RankOneMeasurementSet >	(	double *	_norms,
		const RankOneMeasurementSet &	_measurments
	)

inline

Definition at line 556 of file adf.cpp.

◆ calc_measurment_norm< SinglePointMeasurementSet >()

template<>

void xerus::calc_measurment_norm< SinglePointMeasurementSet >	(	double *	_norms,
		const SinglePointMeasurementSet &	_measurments
	)

inline

Definition at line 549 of file adf.cpp.

◆ calculate_cq()

void xerus::calculate_cq	(	Tensor &	_C,
		Tensor &	_Q,
		Tensor	_input,
		const size_t	_splitPos
	)

Low-Level CQ calculation of a given Tensor _input = _C _Q.

This is a rank revealing RQ decomposition with coloum pivoting. In contrast to an RQ the C is not nessecarily upper triangular.

Parameters

_C	Output Tensor for the resulting R.
_Q	Output Tensor for the resulting Q.
_input	input Tensor of which the CQ shall be calculated.
_splitPos	index position at defining the matrification for which the CQ is calculated.

Definition at line 1548 of file tensor.cpp.

◆ calculate_factorization_sizes()

XERUS_force_inline std::tuple<size_t, size_t, size_t> xerus::calculate_factorization_sizes	(	const Tensor &	_input,
		const size_t	_splitPos
	)

Definition at line 1361 of file tensor.cpp.

◆ calculate_qc()

void xerus::calculate_qc	(	Tensor &	_Q,
		Tensor &	_C,
		Tensor	_input,
		const size_t	_splitPos
	)

Low-Level QC calculation of a given Tensor _input = _Q _C.

This is a rank revealing QR decomposition with coloum pivoting. In contrast to an QR the C is not nessecarily upper triangular.

Parameters

_Q	Output Tensor for the resulting Q.
_C	Output Tensor for the resulting R.
_input	input Tensor of which the QC shall be calculated.
_splitPos	index position at defining the matrification for which the QC is calculated.

Definition at line 1528 of file tensor.cpp.

◆ calculate_qr()

void xerus::calculate_qr	(	Tensor &	_Q,
		Tensor &	_R,
		Tensor	_input,
		const size_t	_splitPos
	)

Low-Level QR calculation of a given Tensor _input = _Q _R.

Parameters

_Q	Output Tensor for the resulting Q.
_R	Output Tensor for the resulting R.
_input	input Tensor of which the QR shall be calculated.
_splitPos	index position at defining the matrification for which the QR is calculated.

Definition at line 1492 of file tensor.cpp.

◆ calculate_rq()

void xerus::calculate_rq	(	Tensor &	_R,
		Tensor &	_Q,
		Tensor	_input,
		const size_t	_splitPos
	)

Low-Level RQ calculation of a given Tensor _input = _R _Q.

Parameters

_R	Output Tensor for the resulting R.
_Q	Output Tensor for the resulting Q.
_input	input Tensor of which the RQ shall be calculated.
_splitPos	index position at defining the matrification for which the RQ is calculated.

Definition at line 1511 of file tensor.cpp.

◆ calculate_svd()

void xerus::calculate_svd	(	Tensor &	_U,
		Tensor &	_S,
		Tensor &	_Vt,
		Tensor	_input,
		const size_t	_splitPos,
		const size_t	_maxRank,
		const value_t	_eps
	)

Low-Level SVD calculation of a given Tensor _input = _U _S _Vt.

Parameters

_U	Output Tensor for the resulting U.
_S	Output Tensor for the resulting S.
_Vt	Output Tensor for the resulting Vt.
_input	input Tensor of which the SVD shall be calculated.
_splitPos	index position at defining the matrification for which the SVD is calculated.

Definition at line 1424 of file tensor.cpp.

◆ contract() [1/4]

void xerus::contract	(	Tensor &	_result,
		const Tensor &	_lhs,
		const bool	_lhsTrans,
		const Tensor &	_rhs,
		const bool	_rhsTrans,
		const size_t	_numModes
	)

Low-level contraction between Tensors.

Parameters

_result	Output for the result of the contraction.
_lhs	left hand side of the contraction.
_lhsTrans	Flags whether the LHS should be transposed (in the matrifications sense).
_rhs	right hand side of the contraction.
_rhsTrans	Flags whether the RHS should be transposed (in the matrifications sense).
_numModes	number of modes that shall be contracted.

Definition at line 1252 of file tensor.cpp.

◆ contract() [2/4]

Tensor xerus::contract	(	const Tensor &	_lhs,
		const bool	_lhsTrans,
		const Tensor &	_rhs,
		const bool	_rhsTrans,
		const size_t	_numModes
	)

Definition at line 1354 of file tensor.cpp.

◆ contract() [3/4]

XERUS_force_inline void xerus::contract	(	Tensor &	_result,
		const Tensor &	_lhs,
		const Tensor &	_rhs,
		const size_t	_numModes
	)

Low-level contraction between Tensors.

Parameters

_result	Output for the result of the contraction.
_lhs	left hand side of the contraction.
_rhs	right hand side of the contraction.
_numModes	number of indices that shall be contracted.

Definition at line 869 of file tensor.h.

◆ contract() [4/4]

XERUS_force_inline Tensor xerus::contract	(	const Tensor &	_lhs,
		const Tensor &	_rhs,
		const size_t	_numModes
	)

Definition at line 873 of file tensor.h.

◆ decomposition_als()

void xerus::decomposition_als	(	TTTensor &	_x,
		const Tensor &	_b,
		const double	_eps = `EPSILON`,
		const size_t	_maxIterations = `1000`
	)

Definition at line 36 of file decompositionAls.cpp.

◆ DMRG()

const ALSVariant xerus::DMRG	(	2	,
		0	,
		ALSVariant::lapack_solver	,
		false
	)

◆ DMRG_SPD()

const ALSVariant xerus::DMRG_SPD	(	2	,
		0	,
		ALSVariant::lapack_solver	,
		true
	)

◆ dyadic_product() [1/6]

template<bool isOperator>

TTNetwork< isOperator > xerus::dyadic_product	(	const TTNetwork< isOperator > &	_lhs,
		const TTNetwork< isOperator > &	_rhs
	)

Computes the dyadic product of _lhs and _rhs.

This function is currently needed to keep the resulting network in the TTNetwork class. Apart from that the result is the same as result(i^d1, j^d2) = _lhs(i^d1)*_rhs(j^d2).

Returns: the dyadic product as a TTNetwork.

Definition at line 1319 of file ttNetwork.cpp.

◆ dyadic_product() [2/6]

template<bool isOperator>

TTNetwork< isOperator > xerus::dyadic_product ( const std::vector< TTNetwork< isOperator >> & _tensors )

Computes the dyadic product of all given TTNetworks.

This is nothing but the repeated application of dyadic_product() for the given TTNetworks.

Returns: the dyadic product as a TTNetwork.

Definition at line 1435 of file ttNetwork.cpp.

◆ dyadic_product() [3/6]

template TTNetwork<true> xerus::dyadic_product	(	const TTNetwork< true > &	_lhs,
		const TTNetwork< true > &	_rhs
	)

◆ dyadic_product() [4/6]

template TTNetwork<false> xerus::dyadic_product	(	const TTNetwork< false > &	_lhs,
		const TTNetwork< false > &	_rhs
	)

◆ dyadic_product() [5/6]

template TTNetwork<true> xerus::dyadic_product ( const std::vector< TTNetwork< true >> & _tensors )

◆ dyadic_product() [6/6]

template TTNetwork<false> xerus::dyadic_product ( const std::vector< TTNetwork< false >> & _tensors )

◆ entrywise_product() [1/4]

template<bool isOperator>

TTNetwork< isOperator > xerus::entrywise_product	(	const TTNetwork< isOperator > &	_A,
		const TTNetwork< isOperator > &	_B
	)

Calculates the componentwise product of two tensors given in the TT format.

In general the resulting rank = rank(A)*rank(B). Retains the core position of _A

Definition at line 1275 of file ttNetwork.cpp.

◆ entrywise_product() [2/4]

Tensor xerus::entrywise_product	(	const Tensor &	_A,
		const Tensor &	_B
	)

calculates the entrywise product of two Tensors

Definition at line 1708 of file tensor.cpp.

◆ entrywise_product() [3/4]

template TTNetwork<false> xerus::entrywise_product	(	const TTNetwork< false > &	_A,
		const TTNetwork< false > &	_B
	)

◆ entrywise_product() [4/4]

template TTNetwork<true> xerus::entrywise_product	(	const TTNetwork< true > &	_A,
		const TTNetwork< true > &	_B
	)

◆ find_largest_entry() [1/3]

template<bool isOperator>

size_t xerus::find_largest_entry	(	const TTNetwork< isOperator > &	_T,
		double	_accuracy,
		value_t	_lowerBound = `0.0`
	)

Finds the position of the approximately largest entry.

Finds an entry that is at least of size _accuracy * X_max in absolute value, where X_max is the largest entry of the tensor. The smaller _accuracy, the faster the algorithm will work.

Parameters

_accuracy	factor that determains the maximal deviation of the returned entry from the true largest entry.
_lowerBound	a lower bound for the largest entry, i.e. there must be an entry in the tensor which is at least of this size (in absolute value). The algorithm may fail completely if this is not fullfilled, but will work using its own approximation if no value (i.e. 0.0) is given.

Returns: the position of the entry found.

Definition at line 6 of file largestEntry.cpp.

◆ find_largest_entry() [2/3]

template size_t xerus::find_largest_entry	(	const TTNetwork< true > &	,
		double	,
		value_t
	)

◆ find_largest_entry() [3/3]

template size_t xerus::find_largest_entry	(	const TTNetwork< false > &	,
		double	,
		value_t
	)

◆ frob_norm() [1/2]

static XERUS_force_inline value_t xerus::frob_norm ( const TensorNetwork & _network )

static

Calculates the frobenious norm of the given TensorNetwork.

Parameters

_network the TensorNetwork of which the frobenious norm shall be calculated.

Returns: the frobenious norm.

Definition at line 534 of file tensorNetwork.h.

◆ frob_norm() [2/2]

static XERUS_force_inline value_t xerus::frob_norm ( const Tensor & _tensor )

static

Calculates the frobenius norm of the given tensor.

Parameters

_tensor the Tensor of which the frobenious norm shall be calculated.

Returns: the frobenius norm .

Definition at line 931 of file tensor.h.

◆ GeometricCG()

const GeometricCGVariant xerus::GeometricCG	(	0	,
		1e-	8,
		false	,
		SubmanifoldRetractionI	,
		ProjectiveVectorTransport
	)

◆ get_grouped_entries()

template<bool isOperator>

std::vector<std::vector<std::tuple<size_t, size_t, value_t> > > xerus::get_grouped_entries ( const Tensor & _component )

Definition at line 496 of file ttNetwork.cpp.

◆ get_step_sizes()

std::vector<size_t> xerus::get_step_sizes ( const Tensor::DimensionTuple & _dimensions )

inline

Definition at line 958 of file tensor.cpp.

◆ HOSVDRetractionI()

void xerus::HOSVDRetractionI	(	TTTensor &	_U,
		const TTTangentVector &	_change
	)

retraction that performs a HOSVD to project back onto the Manifold

Definition at line 56 of file retractions.cpp.

◆ HOSVDRetractionII()

void xerus::HOSVDRetractionII	(	TTTensor &	_U,
		const TTTensor &	_change
	)

Definition at line 50 of file retractions.cpp.

◆ IHT()

double xerus::IHT	(	TTTensor &	_x,
		const SinglePointMeasurementSet &	_measurments,
		PerformanceData &	_perfData = `NoPerfData`
	)

Definition at line 29 of file iht.cpp.

◆ increase_indices()

void xerus::increase_indices	(	const size_t	_i,
		value_t *&	_outPosition,
		const std::vector< size_t > &	_stepSizes,
		const std::vector< size_t > &	_baseDimensions
	)

Definition at line 39 of file indexedTensor_tensor_evaluate.cpp.

◆ line_search()

void xerus::line_search	(	TTTensor &	_x,
		value_t &	_alpha,
		const TTTangentVector &	_direction,
		value_t	_derivative,
		value_t &	_residual,
		std::function< void(TTTensor &, const TTTangentVector &)>	_retraction,
		std::function< value_t()>	_calculate_residual,
		value_t	_changeInAlpha = `0.5`
	)

Definition at line 37 of file steepestDescent.cpp.

◆ matrix_matrix_product() [1/6]

void xerus::matrix_matrix_product	(	double *const	_C,
		const size_t	_leftDim,
		const size_t	_rightDim,
		const double	_alpha,
		const std::map< size_t, double > &	_A,
		const bool	_transposeA,
		const size_t	_midDim,
		const double *const	_B,
		const bool	_transposeB
	)

Definition at line 97 of file sparseTimesFullContraction.cpp.

◆ matrix_matrix_product() [2/6]

void xerus::matrix_matrix_product	(	double *const	_C,
		const size_t	_leftDim,
		const size_t	_rightDim,
		const double	_alpha,
		const double *const	_A,
		const bool	_transposeA,
		const size_t	_midDim,
		const std::map< size_t, double > &	_B,
		const bool	_transposeB
	)

Definition at line 114 of file sparseTimesFullContraction.cpp.

◆ matrix_matrix_product() [3/6]

void xerus::matrix_matrix_product	(	std::map< size_t, double > &	_C,
		const size_t	_leftDim,
		const size_t	_rightDim,
		const double	_alpha,
		const std::map< size_t, double > &	_A,
		const bool	_transposeA,
		const size_t	_midDim,
		const double *const	_B,
		const bool	_transposeB
	)

Definition at line 183 of file sparseTimesFullContraction.cpp.

◆ matrix_matrix_product() [4/6]

void xerus::matrix_matrix_product	(	std::map< size_t, double > &	_C,
		const size_t	_leftDim,
		const size_t	_rightDim,
		const double	_alpha,
		const double *const	_A,
		const bool	_transposeA,
		const size_t	_midDim,
		const std::map< size_t, double > &	_B,
		const bool	_transposeB
	)

Definition at line 210 of file sparseTimesFullContraction.cpp.

◆ matrix_matrix_product() [5/6]

void xerus::matrix_matrix_product	(	double *const	_C,
		const size_t	_leftDim,
		const size_t	_rightDim,
		const double	_alpha,
		const std::map< size_t, double > &	_A,
		const bool	_transposeA,
		const size_t	_midDim,
		const double *const	_B
	)

Definition at line 66 of file sparseTimesFullContraction.cpp.

◆ matrix_matrix_product() [6/6]

void xerus::matrix_matrix_product	(	std::map< size_t, double > &	_C,
		const size_t	,
		const size_t	_rightDim,
		const double	_alpha,
		const std::map< size_t, double > &	_A,
		const size_t	_midDim,
		const double *const	_B
	)

Definition at line 132 of file sparseTimesFullContraction.cpp.

◆ NoPerfData()

PerformanceData xerus::NoPerfData	(	false	,
		false
	)

◆ one_norm()

static XERUS_force_inline value_t xerus::one_norm ( const Tensor & _tensor )

static

Calculates the 1-norm of the given tensor.

Parameters

_tensor the Tensor of which the norm shall be calculated.

Returns: the 1-norm

Definition at line 938 of file tensor.h.

◆ operator!=()

bool xerus::operator!=	(	const Index &	_a,
		const Index &	_b
	)

Two Indices are equal if their valueId coincides. Fixed indices are never equal.

Definition at line 167 of file index.cpp.

◆ operator*() [1/11]

TTTangentVector xerus::operator*	(	value_t	_alpha,
		const TTTangentVector &	_rhs
	)

Definition at line 161 of file retractions.cpp.

◆ operator*() [2/11]

TensorNetwork xerus::operator*	(	TensorNetwork &	_lhs,
		value_t	_factor
	)

Definition at line 1392 of file tensorNetwork.cpp.

◆ operator*() [3/11]

TensorNetwork xerus::operator*	(	value_t	_factor,
		TensorNetwork &	_rhs
	)

Definition at line 1398 of file tensorNetwork.cpp.

◆ operator*() [4/11]

template<bool isOperator>

TTNetwork< isOperator > xerus::operator*	(	TTNetwork< isOperator >	_network,
		const value_t	_factor
	)

Calculates the entrywise multiplication of the given TTNetwork _network with a constant _factor.

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

Parameters

_network	the TTNetwork,
_factor	the factor,

Returns: the resulting scaled TTNetwork.

Definition at line 1175 of file ttNetwork.cpp.

◆ operator*() [5/11]

template<bool isOperator>

TTNetwork< isOperator > xerus::operator*	(	const value_t	_factor,
		TTNetwork< isOperator >	_network
	)

Calculates the entrywise multiplication of the given TTNetwork _network with a constant _factor.

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

Parameters

_factor	the factor,
_network	the TTNetwork,

Returns: the resulting scaled TTNetwork.

Definition at line 1182 of file ttNetwork.cpp.

◆ operator*() [6/11]

Tensor xerus::operator*	(	const value_t	_factor,
		Tensor	_tensor
	)

Calculates the entrywise multiplication of the Tensor _tensor with the constant _factor.

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

Parameters

_factor	the factor to be used.
_tensor	the Tensor that shall be scaled.

Returns: the resulting scaled Tensor.

Definition at line 1233 of file tensor.cpp.

◆ operator*() [7/11]

Tensor xerus::operator*	(	Tensor	_tensor,
		const value_t	_factor
	)

Calculates the entrywise multiplication of the Tensor _tensor with the constant _factor.

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

Parameters

_tensor	the Tensor that shall be scaled.
_factor	the factor to be used.

Returns: the resulting scaled Tensor.

Definition at line 1239 of file tensor.cpp.

◆ operator*() [8/11]

template TTNetwork<false> xerus::operator*	(	TTNetwork< false >	_network,
		const value_t	_factor
	)

◆ operator*() [9/11]

template TTNetwork<true> xerus::operator*	(	TTNetwork< true >	_network,
		const value_t	_factor
	)

◆ operator*() [10/11]

template TTNetwork<false> xerus::operator*	(	const value_t	_factor,
		TTNetwork< false >	_network
	)

◆ operator*() [11/11]

template TTNetwork<true> xerus::operator*	(	const value_t	_factor,
		TTNetwork< true >	_network
	)

◆ operator+() [1/4]

template<bool isOperator>

TTNetwork< isOperator > xerus::operator+	(	TTNetwork< isOperator >	_lhs,
		const TTNetwork< isOperator > &	_rhs
	)

Calculates the entrywise sum of the given TTNetworks _lhs and _rhs.

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

Parameters

_lhs	the first summand.
_rhs	the second summand.

Returns: the sum.

Definition at line 1161 of file ttNetwork.cpp.

◆ operator+() [2/4]

Tensor xerus::operator+	(	Tensor	_lhs,
		const Tensor &	_rhs
	)

Calculates the entrywise sum of _lhs and _rhs.

To be well-defined it is required that the dimensions of _lhs and _rhs coincide.

Parameters

_lhs	the first summand.
_rhs	the second summand.

Returns: the sum.

Definition at line 1221 of file tensor.cpp.

◆ operator+() [3/4]

template TTNetwork<false> xerus::operator+	(	TTNetwork< false >	_lhs,
		const TTNetwork< false > &	_rhs
	)

◆ operator+() [4/4]

template TTNetwork<true> xerus::operator+	(	TTNetwork< true >	_lhs,
		const TTNetwork< true > &	_rhs
	)

◆ operator-() [1/4]

template<bool isOperator>

TTNetwork< isOperator > xerus::operator-	(	TTNetwork< isOperator >	_lhs,
		const TTNetwork< isOperator > &	_rhs
	)

Calculates the entrywise difference of the given TTNetworks _lhs and _rhs.

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

Parameters

_lhs	the minuend.
_rhs	the subtrahend.

Returns: the difference.

Definition at line 1168 of file ttNetwork.cpp.

◆ operator-() [2/4]

Tensor xerus::operator-	(	Tensor	_lhs,
		const Tensor &	_rhs
	)

Calculates the entrywise difference between _lhs and _rhs.

To be well-defined it is required that the dimensions of _lhs and _rhs coincide.

Parameters

_lhs	the minuend.
_rhs	the subtrahend.

Returns: the difference.

Definition at line 1227 of file tensor.cpp.

◆ operator-() [3/4]

template TTNetwork<false> xerus::operator-	(	TTNetwork< false >	_lhs,
		const TTNetwork< false > &	_rhs
	)

◆ operator-() [4/4]

template TTNetwork<true> xerus::operator-	(	TTNetwork< true >	_lhs,
		const TTNetwork< true > &	_rhs
	)

◆ operator/() [1/6]

internal::IndexedTensorMoveable< Tensor > xerus::operator/	(	internal::IndexedTensorReadOnly< Tensor > &&	_b,
		internal::IndexedTensorReadOnly< Tensor > &&	_A
	)

Definition at line 34 of file indexedTensor_tensor_solve.cpp.

◆ operator/() [2/6]

TensorNetwork xerus::operator/	(	TensorNetwork &	_lhs,
		value_t	_factor
	)

Definition at line 1404 of file tensorNetwork.cpp.

◆ operator/() [3/6]

template<bool isOperator>

TTNetwork< isOperator > xerus::operator/	(	TTNetwork< isOperator >	_network,
		const value_t	_divisor
	)

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

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

Parameters

_divisor the divisor,

Returns: the resulting scaled TTNetwork.

Definition at line 1189 of file ttNetwork.cpp.

◆ operator/() [4/6]

Tensor xerus::operator/	(	Tensor	_tensor,
		const value_t	_divisor
	)

Calculates the entrywise divison of the Tensor _tensor with the constant _divisor.

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

Parameters

_tensor	the Tensor that shall be scaled.
_divisor	the factor to be used.

Returns: the resulting scaled Tensor.

Definition at line 1245 of file tensor.cpp.

◆ operator/() [5/6]

template TTNetwork<false> xerus::operator/	(	TTNetwork< false >	_network,
		const value_t	_divisor
	)

◆ operator/() [6/6]

template TTNetwork<true> xerus::operator/	(	TTNetwork< true >	_network,
		const value_t	_divisor
	)

◆ operator<()

bool xerus::operator<	(	const Index &	_a,
		const Index &	_b
	)

The Comparision operator is needed for indices to be orderable in std::set, the valueId is used.

Definition at line 171 of file index.cpp.

◆ operator<<() [1/3]

std::ostream & xerus::operator<<	(	std::ostream &	_out,
		const xerus::Index &	_idx
	)

Allows to pretty print indices, giving the valueId and span.

Definition at line 175 of file index.cpp.

◆ operator<<() [2/3]

std::ostream & xerus::operator<<	(	std::ostream &	_out,
		const TensorNetwork::Link &	_rhs
	)

Definition at line 35 of file link.cpp.

◆ operator<<() [3/3]

std::ostream & xerus::operator<<	(	std::ostream &	_out,
		const Tensor &	_tensor
	)

Prints the Tensor to the given outStream.

Parameters

_out	the outstream to be printed to.
_tensor	the tensor.

Returns: _out.

Definition at line 1773 of file tensor.cpp.

◆ operator==()

bool xerus::operator==	(	const Index &	_a,
		const Index &	_b
	)

Two Indices are equal if their valueId coincides. Fixed indices are never equal.

Definition at line 163 of file index.cpp.

◆ perform_component_product()

template<bool isOperator>

void xerus::perform_component_product	(	Tensor &	_newComponent,
		const Tensor &	_componentA,
		const Tensor &	_componentB
	)

Definition at line 1210 of file ttNetwork.cpp.

◆ position_or_zero()

template<class MeasurmentSet >

size_t xerus::position_or_zero	(	const MeasurmentSet &	_measurments,
		const size_t	_meas,
		const size_t	_corePosition
	)

inline

◆ position_or_zero< RankOneMeasurementSet >()

template<>

size_t xerus::position_or_zero< RankOneMeasurementSet >	(	const RankOneMeasurementSet &	,
		const size_t	,
		const size_t
	)

inline

Definition at line 407 of file adf.cpp.

◆ position_or_zero< SinglePointMeasurementSet >()

template<>

size_t xerus::position_or_zero< SinglePointMeasurementSet >	(	const SinglePointMeasurementSet &	_measurments,
		const size_t	_meas,
		const size_t	_corePosition
	)

inline

Definition at line 402 of file adf.cpp.

◆ prepare_factorization_output()

XERUS_force_inline void xerus::prepare_factorization_output	(	Tensor &	_lhs,
		Tensor &	_rhs,
		const Tensor &	_input,
		const size_t	_splitPos,
		const size_t	_rank,
		Tensor::Representation	_rep
	)

Definition at line 1371 of file tensor.cpp.

◆ prepare_split()

std::unique_ptr<Tensor> xerus::prepare_split	(	size_t &	_lhsSize,
		size_t &	_rhsSize,
		size_t &	_rank,
		size_t &	_splitPos,
		std::vector< Index > &	_lhsPreliminaryIndices,
		std::vector< Index > &	_rhsPreliminaryIndices,
		internal::IndexedTensorReadOnly< Tensor > &&	_base,
		internal::IndexedTensor< Tensor > &&	_lhs,
		internal::IndexedTensor< Tensor > &&	_rhs
	)

Definition at line 36 of file indexedTensor_tensor_factorisations.cpp.

◆ ProjectiveVectorTransport()

void xerus::ProjectiveVectorTransport	(	const TTTensor &	_newBase,
		TTTangentVector &	_tangentVector
	)

simple vector transport by projecting onto the new tangent plane

Definition at line 283 of file retractions.cpp.

◆ pseudo_inverse() [1/2]

void xerus::pseudo_inverse	(	Tensor &	_inverse,
		const Tensor &	_input,
		const size_t	_splitPos
	)

Low-Level calculation of the pseudo inverse of a given Tensor.

Currently doen by calculation of the SVD.

Parameters

_inverse	Output the pseudo inverse.
_input	input Tensor of which the CQ shall be calculated.
_splitPos	index position at defining the matrification for which the pseudo inverse is calculated.

Definition at line 1568 of file tensor.cpp.

◆ pseudo_inverse() [2/2]

Tensor xerus::pseudo_inverse	(	const Tensor &	_input,
		const size_t	_splitPos
	)

Definition at line 1576 of file tensor.cpp.

◆ randVar_to_position()

Tensor xerus::randVar_to_position	(	const double	_v,
		const size_t	_polyDegree
	)

Definition at line 40 of file uqAdf.cpp.

◆ reshuffle() [1/2]

void xerus::reshuffle	(	Tensor &	_out,
		const Tensor &	_base,
		const std::vector< size_t > &	_shuffle
	)

: Performs a simple reshuffle. Much less powerfull then a full evaluate, but more efficient.

_shuffle shall be a vector that gives for every old index, its new position.

Definition at line 55 of file indexedTensor_tensor_evaluate.cpp.

◆ reshuffle() [2/2]

Tensor xerus::reshuffle	(	const Tensor &	_base,
		const std::vector< size_t > &	_shuffle
	)

Definition at line 139 of file indexedTensor_tensor_evaluate.cpp.

◆ set_factorization_output() [1/2]

XERUS_force_inline void xerus::set_factorization_output	(	Tensor &	_lhs,
		std::unique_ptr< value_t[]> &&	_lhsData,
		Tensor &	_rhs,
		std::unique_ptr< value_t[]> &&	_rhsData,
		const Tensor &	_input,
		const size_t	_splitPos,
		const size_t	_rank
	)

Definition at line 1398 of file tensor.cpp.

◆ set_factorization_output() [2/2]

XERUS_force_inline void xerus::set_factorization_output	(	Tensor &	_lhs,
		std::map< size_t, value_t > &&	_lhsData,
		Tensor &	_rhs,
		std::map< size_t, value_t > &&	_rhsData,
		const Tensor &	_input,
		const size_t	_splitPos,
		const size_t	_rank
	)

Definition at line 1411 of file tensor.cpp.

◆ solve() [1/2]

void xerus::solve	(	internal::IndexedTensorWritable< Tensor > &&	_x,
		internal::IndexedTensorReadOnly< Tensor > &&	_A,
		internal::IndexedTensorReadOnly< Tensor > &&	_b
	)

◆ solve() [2/2]

void xerus::solve	(	Tensor &	_X,
		const Tensor &	_A,
		const Tensor &	_B,
		size_t	_extraDegree = `0`
	)

Solves the equation Ax = b for x. If the solution is not unique, the output need not be the minimal norm solution.

Parameters

_X	Output Tensor for the result
_A	input Operator A
_B	input right-hand-side b
_extraDegree	number of modes that _x and _B sharefor which the solution should be computed independently.

Definition at line 1654 of file tensor.cpp.

◆ solve_least_squares()

void xerus::solve_least_squares	(	Tensor &	_X,
		const Tensor &	_A,
		const Tensor &	_B,
		const size_t	_extraDegree = `0`
	)

Solves the least squares problem ||_A _X - _B||_F.

Parameters

_X	Output Tensor for the resulting X.
_A	input Tensor A.
_B	input Tensor b.
_extraDegree	number of modes that _X and _B share and for which the least squares problem is independently solved.

Definition at line 1583 of file tensor.cpp.

◆ SteepestDescent()

const SteepestDescentVariant xerus::SteepestDescent	(	0	,
		1e-	8,
		false	,
		SubmanifoldRetractionII
	)

◆ SubmanifoldRetractionI()

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

Definition at line 269 of file retractions.cpp.

◆ SubmanifoldRetractionII()

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

Definition at line 264 of file retractions.cpp.

◆ transpose() [1/4]

XERUS_force_inline void xerus::transpose	(	double *const __restrict	_out,
		const double *const __restrict	_in,
		const size_t	_leftDim,
		const size_t	_rightDim
	)

Definition at line 35 of file sparseTimesFullContraction.cpp.

◆ transpose() [2/4]

XERUS_force_inline std::unique_ptr<double[]> xerus::transpose	(	const double *const	_A,
		const size_t	_leftDim,
		const size_t	_rightDim
	)

Definition at line 43 of file sparseTimesFullContraction.cpp.

◆ transpose() [3/4]

XERUS_force_inline void xerus::transpose	(	std::map< size_t, double > &__restrict	_out,
		const std::map< size_t, double > &__restrict	_in,
		const size_t	_leftDim,
		const size_t	_rightDim
	)

Definition at line 50 of file sparseTimesFullContraction.cpp.

◆ transpose() [4/4]

XERUS_force_inline std::map<size_t, double> xerus::transpose	(	const std::map< size_t, double > &	_A,
		const size_t	_leftDim,
		const size_t	_rightDim
	)

Definition at line 58 of file sparseTimesFullContraction.cpp.

◆ transpose_if_operator()

template<bool isOperator>

void xerus::transpose_if_operator ( TTNetwork< isOperator > & _ttNetwork )

◆ transpose_if_operator< false >()

template<>

void xerus::transpose_if_operator< false > ( TTNetwork< false > & )

Definition at line 974 of file ttNetwork.cpp.

◆ transpose_if_operator< true >()

template<>

void xerus::transpose_if_operator< true > ( TTNetwork< true > & _ttNetwork )

Definition at line 977 of file ttNetwork.cpp.

◆ uq_adf() [1/2]

void xerus::uq_adf	(	TTTensor &	_x,
		const std::vector< std::vector< double >> &	_randomVariables,
		const std::vector< Tensor > &	_solutions
	)

Definition at line 327 of file uqAdf.cpp.

◆ uq_adf() [2/2]

TTTensor xerus::uq_adf	(	const UQMeasurementSet &	_measurments,
		const TTTensor &	_guess
	)

Definition at line 334 of file uqAdf.cpp.

◆ uq_avg()

Tensor xerus::uq_avg	(	const TTTensor &	_x,
		const size_t	_N,
		const size_t	_numSpecial
	)

Definition at line 451 of file uqAdf.cpp.

◆ uq_mc()

std::pair< std::vector< std::vector< double > >, std::vector< Tensor > > xerus::uq_mc	(	const TTTensor &	_x,
		const size_t	_N,
		const size_t	_numSpecial
	)

Definition at line 425 of file uqAdf.cpp.

Variable Documentation

◆ ADF

const ADFVariant xerus::ADF(0, 1e-8, 0.999)

Default variant of the ADF algorithm.

◆ ALS

const ALSVariant xerus::ALS(1, 0, ALSVariant::lapack_solver, false)

default variant of the single-site ALS algorithm for non-symmetric operators using the lapack solver

◆ ALS_SPD

const ALSVariant xerus::ALS_SPD(1, 0, ALSVariant::lapack_solver, true)

default variant of the single-site ALS algorithm for symmetric positive-definite operators using the lapack solver

◆ ASD

const ALSVariant xerus::ASD(1, 0, ALSVariant::ASD_solver, false)

default variant of the alternating steepest descent for non-symmetric operators

◆ ASD_SPD

const ALSVariant xerus::ASD_SPD(1, 0, ALSVariant::ASD_solver, true)

default variant of the alternating steepest descent for symmetric positive-definite operators

◆ DMRG

const ALSVariant xerus::DMRG(2, 0, ALSVariant::lapack_solver, false)

default variant of the two-site DMRG algorithm for non-symmetric operators using the lapack solver

◆ DMRG_SPD

const ALSVariant xerus::DMRG_SPD(2, 0, ALSVariant::lapack_solver, true)

default variant of the two-site DMRG algorithm for symmetric positive-definite operators using the lapack solver

◆ EPSILON

constexpr const value_t xerus::EPSILON = 8*std::numeric_limits<value_t>::epsilon()

The default epsilon value in xerus.

This value is used as a default value by all xerus routines that work up to a certain accuracy, e.g. the singluar value decompostion or the ALS algorithm.

Definition at line 50 of file basic.h.

◆ GeometricCG

const GeometricCGVariant xerus::GeometricCG(0, 1e-8, false, SubmanifoldRetractionI, ProjectiveVectorTransport)

default variant of the steepest descent algorithm using the lapack solver

◆ NoPerfData

PerformanceData xerus::NoPerfData(false, false)

◆ SteepestDescent

const SteepestDescentVariant xerus::SteepestDescent(0, 1e-8, false, SubmanifoldRetractionII)

default variant of the steepest descent algorithm using the lapack solver

◆ VERSION_COMMIT

const int xerus::VERSION_COMMIT = XERUS_VERSION_COMMIT

Definition at line 31 of file standard.cpp.

◆ VERSION_MAJOR

const int xerus::VERSION_MAJOR = XERUS_VERSION_MAJOR

The version of the compiled xerus library

Definition at line 28 of file standard.cpp.

◆ VERSION_MINOR

const int xerus::VERSION_MINOR = XERUS_VERSION_MINOR

Definition at line 29 of file standard.cpp.

◆ VERSION_REVISION

const int xerus::VERSION_REVISION = XERUS_VERSION_REVISION

Definition at line 30 of file standard.cpp.

Namespaces

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ byte

◆ int16

◆ int32

◆ int64

◆ int8

◆ TTOperator

◆ TTRetractionI

◆ TTRetractionII

◆ TTTensor

◆ TTVectorTransport

◆ uint

◆ uint16

◆ uint32

◆ uint64

◆ uint8

◆ ulong

◆ ushort

◆ value_t

Function Documentation

◆ ADF()

◆ ALS()

◆ ALS_SPD()

◆ ALSRetractionI()

◆ ALSRetractionII()

◆ approx_entrywise_equal() [1/2]

◆ approx_entrywise_equal() [2/2]

◆ approx_equal() [1/4]

◆ approx_equal() [2/4]

◆ approx_equal() [3/4]

◆ approx_equal() [4/4]

◆ ASD()

◆ ASD_SPD()

◆ calc_measurment_norm()

◆ calc_measurment_norm< RankOneMeasurementSet >()

◆ calc_measurment_norm< SinglePointMeasurementSet >()

◆ calculate_cq()

◆ calculate_factorization_sizes()

◆ calculate_qc()

◆ calculate_qr()

◆ calculate_rq()

◆ calculate_svd()

◆ contract() [1/4]

◆ contract() [2/4]

◆ contract() [3/4]

◆ contract() [4/4]

◆ decomposition_als()

◆ DMRG()

◆ DMRG_SPD()

◆ dyadic_product() [1/6]

◆ dyadic_product() [2/6]

◆ dyadic_product() [3/6]

◆ dyadic_product() [4/6]

◆ dyadic_product() [5/6]

◆ dyadic_product() [6/6]

◆ entrywise_product() [1/4]

◆ entrywise_product() [2/4]

◆ entrywise_product() [3/4]

◆ entrywise_product() [4/4]

◆ find_largest_entry() [1/3]

◆ find_largest_entry() [2/3]

◆ find_largest_entry() [3/3]

◆ frob_norm() [1/2]

◆ frob_norm() [2/2]

◆ GeometricCG()

◆ get_grouped_entries()

◆ get_step_sizes()

◆ HOSVDRetractionI()

◆ HOSVDRetractionII()

◆ IHT()

◆ increase_indices()

◆ line_search()

◆ matrix_matrix_product() [1/6]

◆ matrix_matrix_product() [2/6]