Tensor class. The main object of mptensor. More...

#include <tensor.hpp>

Public Types
typedef C	value_type
	`double` or `complex` More...

typedef Matrix< C >	matrix_type
	type of Matrix class More...

typedef Matrix< C >::comm_type	comm_type
	type of communicator. More...

Public Member Functions
const Shape &	shape () const
	Shape of tensor. More...

size_t	rank () const
	Rank of tensor. More...

size_t	ndim () const
	Rank of tensor. More...

size_t	local_size () const
	Size of local storage. More...

size_t	get_upper_rank () const
	Upper rank for matrix representation. More...

const Axes &	get_axes_map () const
	Map of axes for lazy evaluation of transpose. More...

const Matrix< C > &	get_matrix () const
	distributed Matrix More...

Matrix< C > &	get_matrix ()
	distributed Matrix More...

const comm_type &	get_comm () const
	Communicator. More...

int	get_comm_size () const
	Size of communicator. More...

int	get_comm_rank () const
	Rank of process. More...

Index	global_index (size_t i) const
	Convert local index to global index. More...

void	global_index_fast (size_t i, Index &idx) const
	Convert local index to global index fast. More...

void	local_position (const Index &idx, int &comm_rank, size_t &local_idx) const
	Calculate rank which has the given global index and its local index. More...

const C &	operator[] (size_t local_idx) const
	Const array subscript operator. More...

C &	operator[] (size_t local_idx)
	Array subscript operator. More...

bool	get_value (const Index &idx, C &val) const
	Get an element. More...

void	set_value (const Index &idx, C val)
	Set an element. More...

void	print_info (std::ostream &out, const std::string &tag="") const
	Output information of tensor. More...

void	print_info_mpi (std::ostream &, const std::string &tag="") const
	Output information of tensor. More...

void	save (const std::string &filename) const
	Save a tensor to files. More...

void	load (const std::string &filename)
	Load a tensor from files. More...

Tensor< Matrix, C > &	transpose (const Axes &axes)
	Transposition of tensor with lazy evaluation. More...

template<typename D >
Tensor< Matrix, C > &	multiply_vector (const std::vector< D > &vec, size_t n_axes)
	Element-wise vector multiplication. More...

template<typename D0 , typename D1 >
Tensor< Matrix, C > &	multiply_vector (const std::vector< D0 > &vec0, size_t n_axes0, const std::vector< D1 > &vec1, size_t n_axes1)
	Element-wise vector multiplication. More...

template<typename D0 , typename D1 , typename D2 >
Tensor< Matrix, C > &	multiply_vector (const std::vector< D0 > &vec0, size_t n_axes0, const std::vector< D1 > &vec1, size_t n_axes1, const std::vector< D2 > &vec2, size_t n_axes2)
	Element-wise vector multiplication. More...

template<typename D0 , typename D1 , typename D2 , typename D3 >
Tensor< Matrix, C > &	multiply_vector (const std::vector< D0 > &vec0, size_t n_axes0, const std::vector< D1 > &vec1, size_t n_axes1, const std::vector< D2 > &vec2, size_t n_axes2, const std::vector< D3 > &vec3, size_t n_axes3)
	Element-wise vector multiplication. More...

Tensor< Matrix, C > &	set_slice (const Tensor &a, size_t n_axes, size_t i_begin, size_t i_end)
	Inverse of slice(). More...

Tensor< Matrix, C > &	set_slice (const Tensor &a, const Index &index_begin, const Index &index_end)
	Inverse of slice(). More...

Tensor< lapack::Matrix, C >	gather ()
	Gather all elements into a non-distributed tensor. More...

std::vector< C >	flatten ()
	Return a copy of the flattened vector. More...

Tensor< Matrix, C > &	operator+= (const Tensor &rhs)
	Addition assignment. More...

Tensor< Matrix, C > &	operator-= (const Tensor &rhs)
	Subtraction assignment. More...

Tensor< Matrix, C > &	operator*= (C rhs)
	Scalar-multiplication assignment. More...

Tensor< Matrix, C > &	operator/= (C rhs)
	Scalar-division assignment. More...

Tensor< Matrix, C > &	operator= (C rhs)
	Initialize all elements by rhs. More...

template<typename UnaryOperation >
Tensor< Matrix, C > &	map (UnaryOperation op)
	Apply a unary operation to each element. More...

void	prep_global_to_local () const
	Preprocess for fast conversion from global index to local one. More...

void	prep_local_to_global () const
	Preprocess for fast conversion from local index to global one. More...

void	make_l2g_map () const
	Preprocess for fast conversion from local index to global one. More...

void	global_index_l2g_map (size_t lindex, size_t gindex[]) const
	Convert local index to global index using l2g_map. More...

void	global_index_l2g_map_transpose (size_t lindex, const size_t axes_trans[], size_t index_new[]) const
	Convert local index to global index of transposed tensor using l2g_map. More...

void	local_position_fast (size_t g_row, size_t g_col, int &comm_rank, size_t &local_idx) const


	Tensor ()
	Default constructor of tensor. More...

	Tensor (const Shape &)
	Constructor of tensor. More...

	Tensor (const comm_type &)
	Constructor of tensor. More...

	Tensor (const comm_type &, const Shape &)
	Constructor of tensor. More...

	Tensor (const comm_type &, const Shape &, size_t upper_rank)
	Constructor of tensor. More...

	Tensor (const comm_type &, const Tensor< lapack::Matrix, C > &)
	Constructor of tensor from non-distributed tensor. More...

	Tensor (const comm_type &, const std::vector< C > &)
	Constructor of tensor from non-distributed vector. More...

Detailed Description

template<template< typename > class Matrix, typename C>
class mptensor::Tensor< Matrix, C >

Tensor class. The main object of mptensor.

Member Typedef Documentation

◆ comm_type

template<template< typename > class Matrix, typename C >

typedef Matrix<C>::comm_type mptensor::Tensor< Matrix, C >::comm_type

type of communicator.

MPI_Comm or int.

◆ matrix_type

template<template< typename > class Matrix, typename C >

typedef Matrix<C> mptensor::Tensor< Matrix, C >::matrix_type

type of Matrix class

◆ value_type

template<template< typename > class Matrix, typename C >

typedef C mptensor::Tensor< Matrix, C >::value_type

double or complex

Member Function Documentation

◆ flatten()

template<template< typename > class Matrix, typename C >

std::vector< C > mptensor::Tensor< Matrix, C >::flatten

Return a copy of the flattened vector.

Returns: A flattened vector, which is global (not distriuted).

Attention: A flattened vector may require huge memory.

◆ gather()

template<template< typename > class Matrix, typename C >

Tensor< lapack::Matrix, C > mptensor::Tensor< Matrix, C >::gather

Gather all elements into a non-distributed tensor.

Returns: A non-distributed global tensor.

Attention: A non-distributed global tensor may require huge memory.

◆ get_axes_map()

template<template< typename > class Matrix, typename C >

const Axes & mptensor::Tensor< Matrix, C >::get_axes_map

inline

Map of axes for lazy evaluation of transpose.

axes_map stores an index mapping from a before-transposed tensor to an after-transposed tensor.

Let V a 3-leg tensor with shape=[10, 20, 30] and axes_map=[0, 1, 2]. When we transpose V as T = V.transpose(Axes(1, 2, 0));, T has shape=[20, 30, 10] and axes_map=[2, 0, 1]. Thus, axes_map satisfies axes_map[iV] = iT.

◆ get_comm()

template<template< typename > class Matrix, typename C >

const Tensor< Matrix, C >::comm_type & mptensor::Tensor< Matrix, C >::get_comm

inline

Communicator.

◆ get_comm_rank()

template<template< typename > class Matrix, typename C >

int mptensor::Tensor< Matrix, C >::get_comm_rank

inline

Rank of process.

◆ get_comm_size()

template<template< typename > class Matrix, typename C >

int mptensor::Tensor< Matrix, C >::get_comm_size

inline

Size of communicator.

◆ get_matrix() [1/2]

template<template< typename > class Matrix, typename C >

Matrix< C > & mptensor::Tensor< Matrix, C >::get_matrix

inline

distributed Matrix

◆ get_matrix() [2/2]

template<template< typename > class Matrix, typename C >

const Matrix< C > & mptensor::Tensor< Matrix, C >::get_matrix

inline

distributed Matrix

◆ get_upper_rank()

template<template< typename > class Matrix, typename C >

size_t mptensor::Tensor< Matrix, C >::get_upper_rank

inline

Upper rank for matrix representation.

◆ get_value()

template<template< typename > class Matrix, typename C >

bool mptensor::Tensor< Matrix, C >::get_value	(	const Index &	idx,
		C &	val
	)		const

Get an element.

Parameters

[in]	idx	Global index.
[out]	val	Value of the element.

Returns: True if my process has the element specified by the global index.

◆ global_index()

template<template< typename > class Matrix, typename C >

Index mptensor::Tensor< Matrix, C >::global_index ( size_t lindex ) const

Convert local index to global index.

Parameters

[in] lindex Local index

Returns: Global index

◆ global_index_fast()

template<template< typename > class Matrix, typename C >

void mptensor::Tensor< Matrix, C >::global_index_fast	(	size_t	lindex,
		Index &	gindex
	)		const

Convert local index to global index fast.

Parameters

[in]	lindex	Local index
[out]	gindex	Global index.

Warning: The size of gindex should be larger than the rank of tensor.

◆ global_index_l2g_map()

template<template< typename > class Matrix, typename C >

void mptensor::Tensor< Matrix, C >::global_index_l2g_map	(	size_t	lindex,
		size_t	gindex[]
	)		const

inline

Convert local index to global index using l2g_map.

Parameters

[in]	lindex	Local index
[out]	gindex	Global index.

Warning: The size of gindex should be larger than the rank of tensor.

◆ global_index_l2g_map_transpose()

template<template< typename > class Matrix, typename C >

void mptensor::Tensor< Matrix, C >::global_index_l2g_map_transpose	(	size_t	lindex,
		const size_t	axes_trans[],
		size_t	index_new[]
	)		const

inline

Convert local index to global index of transposed tensor using l2g_map.

Parameters

[in]	lindex	Local index.
[in]	axes_trans	axes mapping (see below).
[out]	index_new	Global index of transposed tensor.

axes_trans[i] = axes_inv[axes_map[i]]

Here axes_inv is inverse of axes in transpose().

Warning: The size of axes_trans and index_new should be larger than the rank of tensor.

◆ load()

template<template< typename > class Matrix, typename C >

void mptensor::Tensor< Matrix, C >::load ( const std::string & filename )

Load a tensor from files.

Rank-0 process reads an ASCII file with shape information whose name is given by filename . Every process restores tensor elements from a binary file filename.[rank_no].bin and an ASCII file filename.[rank_no].idx .

Parameters

filename Name of the base file.

Note: [rank_no] in the name of binary files has at least 4 digit, (ex. filename.0001.bin).

◆ local_position()

template<template< typename > class Matrix, typename C >

void mptensor::Tensor< Matrix, C >::local_position	(	const Index &	index,
		int &	comm_rank,
		size_t &	local_idx
	)		const

Calculate rank which has the given global index and its local index.

Parameters

[in]	index	Global index.
[out]	comm_rank	Rank which has the element at the global index.
[out]	local_idx	Local index in comm_rank.

◆ local_position_fast()

template<template< typename > class Matrix, typename C >

void mptensor::Tensor< Matrix, C >::local_position_fast	(	size_t	g_row,
		size_t	g_col,
		int &	comm_rank,
		size_t &	local_idx
	)		const

inline

◆ local_size()

template<template< typename > class Matrix, typename C >

size_t mptensor::Tensor< Matrix, C >::local_size

inline

Size of local storage.

◆ make_l2g_map()

template<template< typename > class Matrix, typename C >

void mptensor::Tensor< Matrix, C >::make_l2g_map

inline

Preprocess for fast conversion from local index to global one.

◆ map()

template<template< typename > class Matrix, typename C >

template<typename UnaryOperation >

Tensor< Matrix, C > & mptensor::Tensor< Matrix, C >::map ( UnaryOperation op )

Apply a unary operation to each element.

Parameters

op	Unary operation.

Returns: Result.

◆ multiply_vector() [1/4]

template<template< typename > class Matrix, typename C >

template<typename D >

Tensor< Matrix, C > & mptensor::Tensor< Matrix, C >::multiply_vector	(	const std::vector< D > &	vec,
		size_t	n_axes
	)

Element-wise vector multiplication.

For example, T.multiply_vector(v,1) is equivalent to \( T_{ijk} := v_j T_{ijk}. \)

Parameters

vec	Vector
n_axes	Axes to multiply the vector

Attention: The size of vec should be larger than the bond dimension of n_axes.

◆ multiply_vector() [2/4]

template<template< typename > class Matrix, typename C >

template<typename D0 , typename D1 >

Tensor< Matrix, C > & mptensor::Tensor< Matrix, C >::multiply_vector	(	const std::vector< D0 > &	vec0,
		size_t	n_axes0,
		const std::vector< D1 > &	vec1,
		size_t	n_axes1
	)

Element-wise vector multiplication.

For example, T.multiply_vector(v,1,w,0) is equivalent to \( T_{ijk} := v_j w_i T_{ijk}. \)

Parameters

vec0	Vector
n_axes0	Axes to multiply the vector `vec0`.
vec1	Vector
n_axes1	Axes to multiply the vector `vec1`.

Attention: The size of vecX should be larger than the bond dimension of n_axesX.

◆ multiply_vector() [3/4]

template<template< typename > class Matrix, typename C >

template<typename D0 , typename D1 , typename D2 >

Tensor< Matrix, C > & mptensor::Tensor< Matrix, C >::multiply_vector	(	const std::vector< D0 > &	vec0,
		size_t	n_axes0,
		const std::vector< D1 > &	vec1,
		size_t	n_axes1,
		const std::vector< D2 > &	vec2,
		size_t	n_axes2
	)

Element-wise vector multiplication.

For example, T.multiply_vector(v,1,w,0,x,2) is equivalent to \( T_{ijkl} := v_j w_i x_k T_{ijkl}. \)

Parameters

vec0	Vector
n_axes0	Axes to multiply the vector `vec0`.
vec1	Vector
n_axes1	Axes to multiply the vector `vec1`.
vec2	Vector
n_axes2	Axes to multiply the vector `vec2`.

Attention: The size of vecX should be larger than the bond dimension of n_axesX.

◆ multiply_vector() [4/4]

template<template< typename > class Matrix, typename C >

template<typename D0 , typename D1 , typename D2 , typename D3 >

Tensor< Matrix, C > & mptensor::Tensor< Matrix, C >::multiply_vector	(	const std::vector< D0 > &	vec0,
		size_t	n_axes0,
		const std::vector< D1 > &	vec1,
		size_t	n_axes1,
		const std::vector< D2 > &	vec2,
		size_t	n_axes2,
		const std::vector< D3 > &	vec3,
		size_t	n_axes3
	)

Element-wise vector multiplication.

For example, T.multiply_vector(v,1,w,0,x,2,y,4) is equivalent to \( T_{ijklm} := v_j w_i x_k y_m T_{ijklm}. \)

Parameters

vec0	Vector
n_axes0	Axes to multiply the vector `vec0`.
vec1	Vector
n_axes1	Axes to multiply the vector `vec1`.
vec2	Vector
n_axes2	Axes to multiply the vector `vec2`.
vec3	Vector
n_axes3	Axes to multiply the vector `vec3`.

Attention: The size of vecX should be larger than the bond dimension of n_axesX.

◆ ndim()

template<template< typename > class Matrix, typename C >

size_t mptensor::Tensor< Matrix, C >::ndim

inline

Rank of tensor.

Note: Same as rank(). This function is for numpy compatibility with numpy.

◆ operator*=()

template<template< typename > class Matrix, typename C >

Tensor< Matrix, C > & mptensor::Tensor< Matrix, C >::operator*= ( C rhs )

Scalar-multiplication assignment.

◆ operator+=()

template<template< typename > class Matrix, typename C >

Tensor< Matrix, C > & mptensor::Tensor< Matrix, C >::operator+= ( const Tensor< Matrix, C > & rhs )

Addition assignment.

◆ operator-=()

template<template< typename > class Matrix, typename C >

Tensor< Matrix, C > & mptensor::Tensor< Matrix, C >::operator-= ( const Tensor< Matrix, C > & rhs )

Subtraction assignment.

◆ operator/=()

template<template< typename > class Matrix, typename C >

Tensor< Matrix, C > & mptensor::Tensor< Matrix, C >::operator/= ( C rhs )

Scalar-division assignment.

◆ operator=()

template<template< typename > class Matrix, typename C >

Tensor< Matrix, C > & mptensor::Tensor< Matrix, C >::operator= ( C rhs )

Initialize all elements by rhs.

◆ operator[]() [1/2]

template<template< typename > class Matrix, typename C >

C & mptensor::Tensor< Matrix, C >::operator[] ( size_t local_idx )

inline

Array subscript operator.

Attention: This function does not check validity of local index.

◆ operator[]() [2/2]

template<template< typename > class Matrix, typename C >

const C & mptensor::Tensor< Matrix, C >::operator[] ( size_t local_idx ) const

inline

Const array subscript operator.

Attention: This function does not check validity of local index.

◆ prep_global_to_local()

template<template< typename > class Matrix, typename C >

void mptensor::Tensor< Matrix, C >::prep_global_to_local

inline

Preprocess for fast conversion from global index to local one.

◆ prep_local_to_global()

template<template< typename > class Matrix, typename C >

void mptensor::Tensor< Matrix, C >::prep_local_to_global

inline

Preprocess for fast conversion from local index to global one.

◆ print_info()

template<template< typename > class Matrix, typename C >

void mptensor::Tensor< Matrix, C >::print_info	(	std::ostream &	out,
		const std::string &	tag = `""`
	)		const

Output information of tensor.

Every process outputs information to output stream.

Parameters

out	Output stream.
tag	(optional) A tag which is inserted at the head of the line.

◆ print_info_mpi()

template<template< typename > class Matrix, typename C >

void mptensor::Tensor< Matrix, C >::print_info_mpi	(	std::ostream &	out,
		const std::string &	tag = `""`
	)		const

Output information of tensor.

All processes output information of a tensor one by one.

Note: Since this function uses MPI_Barrier, all the processes should call this function at the same time.

Parameters

out	Output stream.
tag	(optional) A tag which is inserted at the head of each line.

◆ rank()

template<template< typename > class Matrix, typename C >

size_t mptensor::Tensor< Matrix, C >::rank

inline

Rank of tensor.

◆ save()

template<template< typename > class Matrix, typename C >

void mptensor::Tensor< Matrix, C >::save ( const std::string & filename ) const

Save a tensor to files.

Rank-0 process creates an ASCII file with shape information whose name is given by filename . Every process saves tensor elements to a binary file filename.[rank_no].bin and an ASCII file filename.[rank_no].idx .

Parameters

filename Name of the base file.

Note: rank_no in the name of binary files has at least 4 digit, (ex. filename.0001.bin).

◆ set_slice() [1/2]

template<template< typename > class Matrix, typename C >

Tensor< Matrix, C > & mptensor::Tensor< Matrix, C >::set_slice	(	const Tensor< Matrix, C > &	a,
		const Index &	index_begin,
		const Index &	index_end
	)

Inverse of slice().

If index_begin[r]==index_end[r], this rank is not sliced. T.set_slice( slice(T,i,j), i,j) does nothing. For example, T.set_slice(A,Index(1,0,3),Index(4,0,6)); is equal to T[1:4,:,3:6]=A[:,:,:] in Python.

Parameters

[in]	a	A sliced tensor to be set.
[in]	index_begin	Start indices.
[in]	index_end	End indices.

◆ set_slice() [2/2]

template<template< typename > class Matrix, typename C >

Tensor< Matrix, C > & mptensor::Tensor< Matrix, C >::set_slice	(	const Tensor< Matrix, C > &	a,
		size_t	n_axes,
		size_t	i_begin,
		size_t	i_end
	)

Inverse of slice().

T.set_slice( slice(T,r,i,j), r,i,j) does nothing. For example, T.set_slice(A,1,4,10); is equal to T[:,4:10,:]=A[:,:,:] in Python.

Parameters

[in]	a	A sliced tensor to be set.
[in]	n_axes	sliced Axes.
[in]	i_begin	Start index of slice.
[in]	i_end	End index of slice.

◆ set_value()

template<template< typename > class Matrix, typename C >

void mptensor::Tensor< Matrix, C >::set_value	(	const Index &	idx,
		C	val
	)

Set an element.

If my process does not have the element, this function does nothing.

Parameters

[in]	idx	Global index.
[in]	val	Value of the element.

◆ shape()

template<template< typename > class Matrix, typename C >

const Shape & mptensor::Tensor< Matrix, C >::shape

inline

Shape of tensor.

◆ transpose()

template<template< typename > class Matrix, typename C >

Tensor< Matrix, C > & mptensor::Tensor< Matrix, C >::transpose ( const Axes & axes )

Transposition of tensor with lazy evaluation.

When axes=[1,2,0], \( T_{ijk} \) is transformed into \( T_{jki} \).

Parameters

[in] axes Order of axes.

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

/home/runner/work/mptensor/mptensor/include/mptensor/tensor.hpp
/home/runner/work/mptensor/mptensor/include/mptensor/file_io/load.hpp
/home/runner/work/mptensor/mptensor/include/mptensor/file_io/save.hpp
/home/runner/work/mptensor/mptensor/include/mptensor/tensor_impl.hpp

Public Types

Public Member Functions

Detailed Description

template<template< typename > class Matrix, typename C> class mptensor::Tensor< Matrix, C >

Member Typedef Documentation

◆ comm_type

◆ matrix_type

◆ value_type

Member Function Documentation

◆ flatten()

◆ gather()

◆ get_axes_map()

◆ get_comm()

◆ get_comm_rank()

◆ get_comm_size()

◆ get_matrix() [1/2]

◆ get_matrix() [2/2]

◆ get_upper_rank()

◆ get_value()

◆ global_index()

◆ global_index_fast()

◆ global_index_l2g_map()

◆ global_index_l2g_map_transpose()

◆ load()

◆ local_position()

◆ local_position_fast()

◆ local_size()

◆ make_l2g_map()

◆ map()

◆ multiply_vector() [1/4]

◆ multiply_vector() [2/4]

◆ multiply_vector() [3/4]

◆ multiply_vector() [4/4]

◆ ndim()

◆ operator*=()

◆ operator+=()

◆ operator-=()

◆ operator/=()

◆ operator=()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ prep_global_to_local()

◆ prep_local_to_global()

◆ print_info()

◆ print_info_mpi()

◆ rank()

◆ save()

◆ set_slice() [1/2]

◆ set_slice() [2/2]

◆ set_value()

◆ shape()

◆ transpose()

template<template< typename > class Matrix, typename C>
class mptensor::Tensor< Matrix, C >