Detailed Description

template<size_t Nlegs, typename Symmetry, typename MatrixType>
struct Multipede< Nlegs, Symmetry, MatrixType >

General tensor with quantum number blocks.

Template Parameters

Nlegs	: Amount of tensor legs, must be >=2. A two-legged tensor is coded separately as Biped.
Symmetry	: A class providing all relevant functions and infos that are determined by the Symmetry. Click here for more information.
MatrixType	: `MatrixXd` or `MatrixXcd`

Note: special typedefs not caught by Doxygen:
Tripod<Symmetry,MatrixType> (Nlegs=3, e.g. the transfer matrix in $\left<\Psi|H|\Psi\right>$ )
Quadruped<Symmetry,MatrixType> (Nlegs=4, e.g. the transfer matrix in $\left<\Psi|H^2|\Psi\right>$ ).

Definition at line 32 of file Multipede.h.

#include <Multipede.h>

Public Types
typedef Symmetry::qType	qType

typedef MatrixType::Scalar	Scalar

Public Member Functions
	Multipede ()

	Multipede (const Biped< Symmetry, MatrixType > &B, qType Q=Symmetry::qvacuum())

constexpr size_t	rank () const

Multipede< Nlegs, Symmetry, MatrixType > &	operator= (const Multipede< Nlegs, Symmetry, MatrixType > &Vin)


double	memory (MEMUNIT memunit=GB) const

double	overhead (MEMUNIT memunit=MB) const

string	dict_info () const

string	print (const bool &SHOW_MATRICES=false, const size_t &precision=3) const


void	clear ()

void	setZero ()

void	setVacuum ()

void	setTarget (std::array< qType, Nlegs > Q)

void	setTarget (vector< std::array< qType, Nlegs > > Q)

void	setIdentity (size_t Drows, size_t Dcols, size_t amax=1, size_t bmax=1)

void	setIdentity (size_t amax, size_t bmax, const Qbasis< Symmetry > &base, const qarray< Symmetry::Nq > &Q=Symmetry::qvacuum())

void	addScale (const Scalar &factor, const Multipede< Nlegs, Symmetry, MatrixType > &Mrhs)


void	save (string filename, bool PRINT=false) const

void	load (string filename, bool PRINT=false)


qType	in (size_t q) const

qType	out (size_t q) const

qType	mid (size_t q) const

qType	bot (size_t q) const

qType	top (size_t q) const


void	push_back (std::array< qType, Nlegs > quple, const boost::multi_array< MatrixType, LEGLIMIT > &M)

void	push_back (std::initializer_list< qType > qlist, const boost::multi_array< MatrixType, LEGLIMIT > &M)

void	insert (std::pair< qType, size_t > ab, const Multipede< Nlegs, Symmetry, MatrixType > &Trhs)


template<typename OtherMatrixType >
Multipede< Nlegs, Symmetry, OtherMatrixType >	cast () const

Scalar	compare (const Multipede< Nlegs, Symmetry, MatrixType > &Mrhs) const

Biped< Symmetry, MatrixType >	BipedSliceQmid (qType qslice=Symmetry::qvacuum()) const

size_t	dim = 0

vector< std::array< qType, Nlegs > >	index

vector< boost::multi_array< MatrixType, LEGLIMIT > >	block

unordered_map< std::array< qType, Nlegs >, size_t >	dict

std::size_t	size () const

Member Typedef Documentation

◆ qType

template<size_t Nlegs, typename Symmetry , typename MatrixType >

typedef Symmetry::qType Multipede< Nlegs, Symmetry, MatrixType >::qType

Definition at line 34 of file Multipede.h.

◆ Scalar

template<size_t Nlegs, typename Symmetry , typename MatrixType >

typedef MatrixType::Scalar Multipede< Nlegs, Symmetry, MatrixType >::Scalar

Definition at line 35 of file Multipede.h.

Constructor & Destructor Documentation

◆ Multipede() [1/2]

template<size_t Nlegs, typename Symmetry , typename MatrixType >

Multipede< Nlegs, Symmetry, MatrixType >::Multipede ( )

inline

Definition at line 37 of file Multipede.h.

◆ Multipede() [2/2]

template<size_t Nlegs, typename Symmetry , typename MatrixType >

Multipede< Nlegs, Symmetry, MatrixType >::Multipede	(	const Biped< Symmetry, MatrixType > &	B,
		qType	Q = `Symmetry::qvacuum()`
	)

inlineexplicit

Converts a Biped to a Tripod, adding a trivial middle leg equal to the vacuum. Made explicit to prohibit automatic conversion between Biped and Multipede.

Definition at line 43 of file Multipede.h.

Member Function Documentation

◆ addScale()

template<size_t Nlegs, typename Symmetry , typename MatrixType >

void Multipede< Nlegs, Symmetry, MatrixType >::addScale	(	const Scalar &	factor,
		const Multipede< Nlegs, Symmetry, MatrixType > &	Mrhs
	)

Deletes the contents of index, block, dict.

Definition at line 257 of file Multipede.h.

◆ BipedSliceQmid()

template<size_t Nlegs, typename Symmetry , typename MatrixType >

Biped< Symmetry, MatrixType > Multipede< Nlegs, Symmetry, MatrixType >::BipedSliceQmid ( qType qslice = Symmetry::qvacuum() ) const

Takes Biped-slice from a Tripod over the middle quantum number qslice.

Definition at line 716 of file Multipede.h.

◆ bot()

template<size_t Nlegs, typename Symmetry , typename MatrixType >

qType Multipede< Nlegs, Symmetry, MatrixType >::bot ( size_t q ) const

inline

Convenience function to return a quantum number of the block q to preserve the sanity of the programmer. For the naming convention see Multipede::index.

Definition at line 156 of file Multipede.h.

◆ cast()

template<size_t Nlegs, typename Symmetry , typename MatrixType >

template<typename OtherMatrixType >

Multipede< Nlegs, Symmetry, OtherMatrixType > Multipede< Nlegs, Symmetry, MatrixType >::cast ( ) const

inline

Casts tensors to OtherMatrixType, i.e. usually from real to complex.

Definition at line 180 of file Multipede.h.

◆ clear()

template<size_t Nlegs, typename Symmetry , typename MatrixType >

void Multipede< Nlegs, Symmetry, MatrixType >::clear

Deletes the contents of index, block, dict.

Definition at line 408 of file Multipede.h.

◆ compare()

template<size_t Nlegs, typename Symmetry , typename MatrixType >

MatrixType::Scalar Multipede< Nlegs, Symmetry, MatrixType >::compare ( const Multipede< Nlegs, Symmetry, MatrixType > & Mrhs ) const

Shifts qin and qout by Q, qmid is unchanged Shifts qmid and qout by Q, qin is unchanged

Definition at line 698 of file Multipede.h.

◆ dict_info()

template<size_t Nlegs, typename Symmetry , typename MatrixType >

string Multipede< Nlegs, Symmetry, MatrixType >::dict_info

Prints Multipede<Nlegs,Symmetry,MatrixType>::dict into a string.

Definition at line 359 of file Multipede.h.

◆ in()

template<size_t Nlegs, typename Symmetry , typename MatrixType >

qType Multipede< Nlegs, Symmetry, MatrixType >::in ( size_t q ) const

inline

Convenience function to return a quantum number of the block q to preserve the sanity of the programmer. For the naming convention see Multipede::index.

Definition at line 152 of file Multipede.h.

◆ insert()

template<size_t Nlegs, typename Symmetry , typename MatrixType >

void Multipede< Nlegs, Symmetry, MatrixType >::insert	(	std::pair< qType, size_t >	ab,
		const Multipede< Nlegs, Symmetry, MatrixType > &	Trhs
	)

Adds a new block to the tensor specified by the incoming quantum numbers quple.

Warning: Does not check whether the block for these quantum numbers already exists.

Definition at line 555 of file Multipede.h.

◆ load()

template<size_t Nlegs, typename Symmetry , typename MatrixType >

void Multipede< Nlegs, Symmetry, MatrixType >::load	(	string	filename,
		bool	PRINT = `false`
	)

Definition at line 797 of file Multipede.h.

◆ memory()

template<size_t Nlegs, typename Symmetry , typename MatrixType >

double Multipede< Nlegs, Symmetry, MatrixType >::memory ( MEMUNIT memunit = GB ) const

Calculates the (theoretically) allocated memory (note: by default in GB).

Definition at line 374 of file Multipede.h.

◆ mid()

template<size_t Nlegs, typename Symmetry , typename MatrixType >

qType Multipede< Nlegs, Symmetry, MatrixType >::mid ( size_t q ) const

inline

Convenience function to return a quantum number of the block q to preserve the sanity of the programmer. For the naming convention see Multipede::index.

Definition at line 154 of file Multipede.h.

◆ operator=()

template<size_t Nlegs, typename Symmetry , typename MatrixType >

Multipede< Nlegs, Symmetry, MatrixType > & Multipede< Nlegs, Symmetry, MatrixType >::operator= ( const Multipede< Nlegs, Symmetry, MatrixType > & Vin )

inline

Definition at line 216 of file Multipede.h.

◆ out()

template<size_t Nlegs, typename Symmetry , typename MatrixType >

qType Multipede< Nlegs, Symmetry, MatrixType >::out ( size_t q ) const

inline

Convenience function to return a quantum number of the block q to preserve the sanity of the programmer. For the naming convention see Multipede::index.

Definition at line 153 of file Multipede.h.

◆ overhead()

template<size_t Nlegs, typename Symmetry , typename MatrixType >

double Multipede< Nlegs, Symmetry, MatrixType >::overhead ( MEMUNIT memunit = MB ) const

Calculates the (theoretical) additional memory associated with the subspace blocks (note: by default in MB).

Definition at line 387 of file Multipede.h.

◆ print()

template<size_t Nlegs, typename Symmetry , typename MatrixType >

std::string Multipede< Nlegs, Symmetry, MatrixType >::print	(	const bool &	SHOW_MATRICES = `false`,
		const size_t &	precision = `3`
	)		const

Calculates the (theoretically) allocated memory (note: by default in GB).

Definition at line 593 of file Multipede.h.

◆ push_back() [1/2]

template<size_t Nlegs, typename Symmetry , typename MatrixType >

void Multipede< Nlegs, Symmetry, MatrixType >::push_back	(	std::array< qType, Nlegs >	quple,
		const boost::multi_array< MatrixType, LEGLIMIT > &	M
	)

Adds a new block to the tensor specified by the incoming quantum numbers quple.

Warning: Does not check whether the block for these quantum numbers already exists.

Definition at line 438 of file Multipede.h.

◆ push_back() [2/2]

template<size_t Nlegs, typename Symmetry , typename MatrixType >

void Multipede< Nlegs, Symmetry, MatrixType >::push_back	(	std::initializer_list< qType >	qlist,
		const boost::multi_array< MatrixType, LEGLIMIT > &	M
	)

Adds a new block to the tensor specified by the initializer list qlist (must be of size Nlegs). For the ordering convention see Multipede::index.

Warning: Does not check whether the block for these quantum numbers already exists.

Definition at line 452 of file Multipede.h.

◆ rank()

template<size_t Nlegs, typename Symmetry , typename MatrixType >

constexpr size_t Multipede< Nlegs, Symmetry, MatrixType >::rank ( ) const

inlineconstexpr

Const reference to the number of legs Nlegs

Definition at line 59 of file Multipede.h.

◆ save()

template<size_t Nlegs, typename Symmetry , typename MatrixType >

void Multipede< Nlegs, Symmetry, MatrixType >::save	(	string	filename,
		bool	PRINT = `false`
	)		const

Definition at line 734 of file Multipede.h.

◆ setIdentity() [1/2]

template<size_t Nlegs, typename Symmetry , typename MatrixType >

void Multipede< Nlegs, Symmetry, MatrixType >::setIdentity	(	size_t	amax,
		size_t	bmax,
		const Qbasis< Symmetry > &	base,
		const qarray< Symmetry::Nq > &	Q = `Symmetry::qvacuum()`
	)

Deletes the contents of index, block, dict.

Definition at line 529 of file Multipede.h.

◆ setIdentity() [2/2]

template<size_t Nlegs, typename Symmetry , typename MatrixType >

void Multipede< Nlegs, Symmetry, MatrixType >::setIdentity	(	size_t	Drows,
		size_t	Dcols,
		size_t	amax = `1`,
		size_t	bmax = `1`
	)

Deletes the contents of index, block, dict.

Definition at line 508 of file Multipede.h.

◆ setTarget() [1/2]

template<size_t Nlegs, typename Symmetry , typename MatrixType >

void Multipede< Nlegs, Symmetry, MatrixType >::setTarget ( std::array< qType, Nlegs > Q )

Creates a single block of size 1x1 containing 1 and the corresponding quantum numbers according to the input Q. Needed for the transfer matrix from the last site in matrix element calculations.

Definition at line 479 of file Multipede.h.

◆ setTarget() [2/2]

template<size_t Nlegs, typename Symmetry , typename MatrixType >

void Multipede< Nlegs, Symmetry, MatrixType >::setTarget ( vector< std::array< qType, Nlegs > > Q )

Deletes the contents of index, block, dict.

Definition at line 492 of file Multipede.h.

◆ setVacuum()

template<size_t Nlegs, typename Symmetry , typename MatrixType >

void Multipede< Nlegs, Symmetry, MatrixType >::setVacuum

Creates a single block of size 1x1 containing 1 and the corresponding quantum numbers to the vacuum (all of them). Needed in for the transfer matrix to the first site in matrix element calculations.

Definition at line 462 of file Multipede.h.

◆ setZero()

template<size_t Nlegs, typename Symmetry , typename MatrixType >

void Multipede< Nlegs, Symmetry, MatrixType >::setZero

Sets all matrices in Multipede<Nlegs,Symmetry,MatrixType>::block to zero, preserving the rows and columns.

Definition at line 397 of file Multipede.h.

◆ size()

template<size_t Nlegs, typename Symmetry , typename MatrixType >

std::size_t Multipede< Nlegs, Symmetry, MatrixType >::size ( ) const

inline

Convenience access to the amount of blocks. Equal to either of the following: index.size(), block.size()

Definition at line 67 of file Multipede.h.

◆ top()

template<size_t Nlegs, typename Symmetry , typename MatrixType >

qType Multipede< Nlegs, Symmetry, MatrixType >::top ( size_t q ) const

inline

Convenience function to return a quantum number of the block q to preserve the sanity of the programmer. For the naming convention see Multipede::index.

Definition at line 157 of file Multipede.h.

Member Data Documentation

◆ block

template<size_t Nlegs, typename Symmetry , typename MatrixType >

vector<boost::multi_array<MatrixType,LEGLIMIT> > Multipede< Nlegs, Symmetry, MatrixType >::block

Vector of quantum number blocks. The matrix block[q] is characterized by the quantum number array index[q]. Since the handling of template-sized arrays is no fun at all, the implementation is done in the following way: block[q] is always a boost multi_array of dimension LEGLIMIT which is set = 2. Tripods need only one dimension (two are already absorbed into MatrixType), therefore the rest needs to be set to 1 and the access goes by T.block[q][a][0]. LEGLIMIT can be increased and some code adjustment can be made (filling in dummy "[0]") if bigger tensors are required.

Definition at line 88 of file Multipede.h.

◆ dict

template<size_t Nlegs, typename Symmetry , typename MatrixType >

unordered_map<std::array<qType,Nlegs>,size_t> Multipede< Nlegs, Symmetry, MatrixType >::dict

Dictionary allowing one to find the index of block for a given array of Nlegs quantum numbers in $O(1)$ operations without looping over the blocks. For the ordering convention see Multipede::index.

Definition at line 95 of file Multipede.h.

◆ dim

template<size_t Nlegs, typename Symmetry , typename MatrixType >

size_t Multipede< Nlegs, Symmetry, MatrixType >::dim = 0

Convenience access to the amount of blocks. Equal to either of the following: index.size(), block.size()

Definition at line 66 of file Multipede.h.

◆ index

template<size_t Nlegs, typename Symmetry , typename MatrixType >

vector<std::array<qType,Nlegs> > Multipede< Nlegs, Symmetry, MatrixType >::index

Vector of all incoming quantum numbers. The entries are arrays of size Nlegs. The sorting is according to the following convention:

incoming 2. outgoing 3. middle (Nlegs=3)

incoming 2. outgoing 3. bottom 4. top (Nlegs=4) The middle, bottom and top quantum numbers are always outgoing for the left transfer matrix and incoming for the right transfer matrix in matrix element calculations.

Definition at line 77 of file Multipede.h.

The documentation for this struct was generated from the following file:

Multipede.h

Detailed Description

Public Types

Public Member Functions

Member Typedef Documentation

◆ qType

◆ Scalar

Constructor & Destructor Documentation

◆ Multipede() [1/2]

◆ Multipede() [2/2]

Member Function Documentation

◆ addScale()

◆ BipedSliceQmid()

◆ bot()

◆ cast()

◆ clear()

◆ compare()

◆ dict_info()

◆ in()

◆ insert()

◆ load()

◆ memory()

◆ mid()

◆ operator=()

◆ out()

◆ overhead()

◆ print()

◆ push_back() [1/2]

◆ push_back() [2/2]

◆ rank()

◆ save()

◆ setIdentity() [1/2]

◆ setIdentity() [2/2]

◆ setTarget() [1/2]

◆ setTarget() [2/2]

◆ setVacuum()

◆ setZero()

◆ size()

◆ top()

Member Data Documentation

◆ block

◆ dict

◆ dim

◆ index