mptensor Namespace Reference

Namespaces
namespace	debug
	Namespace for debugging.
namespace	io_helper
namespace	lapack
	Namespace for the non-distributed Matrix class with LAPACK.
namespace	matrix_interface
	Nameclass for Matrix inteface.
namespace	mpi
namespace	mpi_wrapper
	Wrappers of MPI library.
namespace	random_tensor
namespace	scalapack
	Namespace for the distributed Matrix class with ScaLAPACK, PBLAS, and BLACS.

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

Typedefs
typedef std::complex< double >	complex
using	DTensor = Tensor< scalapack::Matrix, double >
using	ZTensor = Tensor< scalapack::Matrix, complex >
typedef Index	Axes
typedef Index	Shape

Functions
template<typename C >
constexpr size_t	value_type_tag ()
template<>
constexpr size_t	value_type_tag< double > ()
template<>
constexpr size_t	value_type_tag< complex > ()
template<typename C >
constexpr char *	value_type_name ()
template<>
constexpr char *	value_type_name< double > ()
template<>
constexpr char *	value_type_name< complex > ()
Index	range (const size_t start, const size_t stop)
	Create an increasing sequence. it is similar to range() in python.
Index	range (const size_t stop)
bool	is_no_transpose (const Axes &axes, const Axes &axes_map, size_t rank)
template<template< typename > class Matrix, typename C >
int	rsvd (const Tensor< Matrix, C > &a, const Axes &axes_row, const Axes &axes_col, Tensor< Matrix, C > &u, std::vector< double > &s, Tensor< Matrix, C > &vt, const size_t target_rank, const size_t oversamp)
	Singular value decomposition by randomized algorithm.
template<template< typename > class Matrix, typename C >
int	rsvd (const Tensor< Matrix, C > &a, const Axes &axes_row, const Axes &axes_col, Tensor< Matrix, C > &u, std::vector< double > &s, Tensor< Matrix, C > &vt, const size_t target_rank)
	RSVD with oversamp = target_rank.
template<template< typename > class Matrix, typename C , typename Func1 , typename Func2 >
int	rsvd (Func1 &multiply_row, Func2 &multiply_col, const Shape &shape_row, const Shape &shape_col, Tensor< Matrix, C > &u, std::vector< double > &s, Tensor< Matrix, C > &vt, const size_t target_rank, const size_t oversamp)
	Singular value decomposition by randomized algorithm.
template<template< typename > class Matrix, typename C , typename Func1 , typename Func2 >
int	rsvd (Func1 &multiply_row, Func2 &multiply_col, const Shape &shape_row, const Shape &shape_col, Tensor< Matrix, C > &u, std::vector< double > &s, Tensor< Matrix, C > &vt, const size_t target_rank)
	RSVD with oversamp = target_rank.
void	set_seed (unsigned int seed)
	Set seed for random number generator.
template<template< typename > class Matrix, typename C >
Tensor< Matrix, C >	transpose (Tensor< Matrix, C > T, const Axes &axes)
	Transposition of tensor with lazy evaluation.
template<template< typename > class Matrix, typename C >
Tensor< Matrix, C >	transpose (const Tensor< Matrix, C > &T, const Axes &axes, size_t urank_new)
	Transposition of tensor without lazy evaluation.
template<template< typename > class Matrix, typename C >
Tensor< Matrix, C >	reshape (const Tensor< Matrix, C > &T, const Shape &shape_new)
	Change the shape of tensor.
template<template< typename > class Matrix, typename C >
Tensor< Matrix, C >	slice (const Tensor< Matrix, C > &T, size_t n_axes, size_t i_begin, size_t i_end)
	Slice a tensor.
template<template< typename > class Matrix, typename C >
Tensor< Matrix, C >	slice (const Tensor< Matrix, C > &T, const Index &index_begin, const Index &index_end)
	Slice a tensor.
template<template< typename > class Matrix, typename C >
Tensor< Matrix, C >	extend (const Tensor< Matrix, C > &T, const Shape &shape_new)
	Extend the size of a tensor.
template<template< typename > class Matrix, typename C >
C	trace (const Tensor< Matrix, C > &M)
	Trace of matrix (rank-2 tensor)
template<template< typename > class Matrix, typename C >
C	trace (const Tensor< Matrix, C > &T, const Axes &axes_1, const Axes &axes_2)
	Full trace of tensor.
template<template< typename > class Matrix, typename C >
C	trace (const Tensor< Matrix, C > &A, const Tensor< Matrix, C > &B, const Axes &axes_a, const Axes &axes_b)
	Full contraction of two tensors.
template<template< typename > class Matrix, typename C >
Tensor< Matrix, C >	contract (const Tensor< Matrix, C > &T, const Axes &axes_1, const Axes &axes_2)
	Partial trace of tensor.
template<template< typename > class Matrix, typename C >
Tensor< Matrix, C >	tensordot (const Tensor< Matrix, C > &a, const Tensor< Matrix, C > &b, const Axes &axes_a, const Axes &axes_b)
	Compute tensor dot product.
template<template< typename > class Matrix, typename C >
Tensor< Matrix, C >	kron (const Tensor< Matrix, C > &a, const Tensor< Matrix, C > &b)
	Compute the Kronecker product.
template<template< typename > class Matrix, typename C >
int	svd (const Tensor< Matrix, C > &a, std::vector< double > &s)
	Singular value decomposition for rank-2 tensor (matrix)
template<template< typename > class Matrix, typename C >
int	svd (const Tensor< Matrix, C > &a, Tensor< Matrix, C > &u, std::vector< double > &s, Tensor< Matrix, C > &vt)
	Singular value decomposition for rank-2 tensor (matrix)
template<template< typename > class Matrix, typename C >
int	svd (const Tensor< Matrix, C > &a, const Axes &axes_row, const Axes &axes_col, std::vector< double > &s)
	Singular value decomposition for tensor.
template<template< typename > class Matrix, typename C >
int	svd (const Tensor< Matrix, C > &a, const Axes &axes_row, const Axes &axes_col, Tensor< Matrix, C > &u, std::vector< double > &s, Tensor< Matrix, C > &vt)
	Singular value decomposition for tensor.
template<template< typename > class Matrix, typename C >
int	psvd (const Tensor< Matrix, C > &a, std::vector< double > &s, const size_t target_rank)
	Partial SVD for rank-2 tensor (matrix)
template<template< typename > class Matrix, typename C >
int	psvd (const Tensor< Matrix, C > &a, Tensor< Matrix, C > &u, std::vector< double > &s, Tensor< Matrix, C > &vt, const size_t target_rank)
	Partial SVD for rank-2 tensor (matrix)
template<template< typename > class Matrix, typename C >
int	psvd (const Tensor< Matrix, C > &a, const Axes &axes_row, const Axes &axes_col, std::vector< double > &s, const size_t target_rank)
	Partial SVD for tensor.
template<template< typename > class Matrix, typename C >
int	psvd (const Tensor< Matrix, C > &a, const Axes &axes_row, const Axes &axes_col, Tensor< Matrix, C > &u, std::vector< double > &s, Tensor< Matrix, C > &vt, const size_t target_rank)
	Partial SVD for tensor.
template<template< typename > class Matrix, typename C >
int	qr (const Tensor< Matrix, C > &a, Tensor< Matrix, C > &q, Tensor< Matrix, C > &r)
	QR decomposition of matrix (rank-2 tensor)
template<template< typename > class Matrix, typename C >
int	qr (const Tensor< Matrix, C > &a, const Axes &axes_row, const Axes &axes_col, Tensor< Matrix, C > &q, Tensor< Matrix, C > &r)
	QR decomposition of tensor.
template<template< typename > class Matrix, typename C >
int	eigh (const Tensor< Matrix, C > &a, std::vector< double > &eigval, Tensor< Matrix, C > &eigvec)
template<template< typename > class Matrix, typename C >
int	eigh (const Tensor< Matrix, C > &a, std::vector< double > &eigval)
template<template< typename > class Matrix, typename C >
int	eigh (const Tensor< Matrix, C > &a, const Axes &axes_row, const Axes &axes_col, std::vector< double > &eigval, Tensor< Matrix, C > &eigvec)
template<template< typename > class Matrix, typename C >
int	eigh (const Tensor< Matrix, C > &a, const Axes &axes_row, const Axes &axes_col, std::vector< double > &w)
	Compute the eigenvalues of a complex Hermitian or real symmetric tensor.
template<template< typename > class Matrix, typename C >
int	eigh (const Tensor< Matrix, C > &a, const Axes &axes_row_a, const Axes &axes_col_a, const Tensor< Matrix, C > &b, const Axes &axes_row_b, const Axes &axes_col_b, std::vector< double > &eigval, Tensor< Matrix, C > &eigvec)
template<template< typename > class Matrix, typename C >
int	eig (const Tensor< Matrix, C > &a, std::vector< complex > &w, Tensor< Matrix, complex > &z)
	Compute the eigenvalues and eigenvectors of a general matrix (rank-2 tensor)
template<template< typename > class Matrix, typename C >
int	eig (const Tensor< Matrix, C > &a, std::vector< complex > &w)
	Compute only the eigenvalues of a general matrix (rank-2 tensor)
template<template< typename > class Matrix, typename C >
int	eig (const Tensor< Matrix, C > &a, const Axes &axes_row, const Axes &axes_col, std::vector< complex > &w, Tensor< Matrix, complex > &z)
	Compute the eigenvalues and eigenvectors of a general tensor.
template<template< typename > class Matrix, typename C >
int	eig (const Tensor< Matrix, C > &a, const Axes &axes_row, const Axes &axes_col, std::vector< complex > &w)
	Compute the eigenvalues of a general tensor.
template<template< typename > class Matrix, typename C >
int	solve (const Tensor< Matrix, C > &a, const std::vector< C > &b, std::vector< C > &x)
	Solve linear equation \( A\vec{x}=\vec{b}\).
template<template< typename > class Matrix, typename C >
int	solve (const Tensor< Matrix, C > &a, const Tensor< Matrix, C > &b, Tensor< Matrix, C > &x)
	Solve linear equation \( AX=B\).
template<template< typename > class Matrix, typename C >
int	solve (const Tensor< Matrix, C > &a, const Tensor< Matrix, C > &b, Tensor< Matrix, C > &x, const Axes &axes_row_a, const Axes &axes_col_a, const Axes &axes_row_b, const Axes &axes_col_b)
	Solve linear equation \( AX=B\).
template<template< typename > class Matrix, typename C >
Tensor< Matrix, C >	operator+ (Tensor< Matrix, C > rhs)
	Unary plus.
template<template< typename > class Matrix, typename C >
Tensor< Matrix, C >	operator- (Tensor< Matrix, C > rhs)
	Unary minus.
template<template< typename > class Matrix, typename C >
Tensor< Matrix, C >	operator+ (Tensor< Matrix, C > lhs, const Tensor< Matrix, C > &rhs)
	Addition.
template<template< typename > class Matrix, typename C >
Tensor< Matrix, C >	operator- (Tensor< Matrix, C > lhs, const Tensor< Matrix, C > &rhs)
	Subtraction.
template<template< typename > class Matrix, typename C , typename D >
Tensor< Matrix, C >	operator* (Tensor< Matrix, C > lhs, D rhs)
	Tensor-scalar multiplication.
template<template< typename > class Matrix, typename C , typename D >
Tensor< Matrix, C >	operator/ (Tensor< Matrix, C > lhs, D rhs)
	Scalar division.
template<template< typename > class Matrix, typename C , typename D >
Tensor< Matrix, C >	operator* (D lhs, Tensor< Matrix, C > rhs)
	Scalar-tensor multiplication.
template<template< typename > class Matrix, typename C >
Tensor< Matrix, C >	sqrt (Tensor< Matrix, C > t)
	Take square-root of each element.
template<template< typename > class Matrix, typename C >
Tensor< Matrix, C >	conj (Tensor< Matrix, C > t)
	Take conjugate of each element.
template<template< typename > class Matrix, typename C >
double	max (const Tensor< Matrix, C > &t)
	Return the maximum element. For complex, same as max_abs().
template<template< typename > class Matrix, typename C >
double	min (const Tensor< Matrix, C > &t)
	Return the minimum element. For complex, same as min_abs().
template<template< typename > class Matrix, typename C >
double	max_abs (const Tensor< Matrix, C > &t)
	Return maximum of the absolute value of an element.
template<template< typename > class Matrix, typename C >
double	min_abs (const Tensor< Matrix, C > &t)
	Return minimum of the absolute value of an element.
template<template< typename > class Matrix, typename C >
std::ostream &	operator<< (std::ostream &out, const Tensor< Matrix, C > &t)
	Output elements of tensor in numpy style.

Typedef Documentation

Axes

typedef Index mptensor::Axes

DTensor

using mptensor::DTensor = typedef Tensor<scalapack::Matrix, double>

Shape

typedef Index mptensor::Shape

ZTensor

using mptensor::ZTensor = typedef Tensor<scalapack::Matrix, complex>

Function Documentation

is_no_transpose()

bool mptensor::is_no_transpose	(	const Axes &	axes,
		const Axes &	axes_map,
		size_t	rank
	)

operator+()

Index mptensor::operator+ ( const Index &  , const Index &    )

related

operator<<()

std::ostream & mptensor::operator<< ( std::ostream &  os, const Index &  idx  )

related

range() [1/2]

Index mptensor::range	(	const size_t	start,
		const size_t	stop
	)

Create an increasing sequence. it is similar to range() in python.

range() [2/2]

Index mptensor::range ( const size_t  stop )

inline

value_type_name()

template<typename C >

constexpr char * mptensor::value_type_name ( )

constexpr

value_type_name< complex >()

template<>

constexpr char * mptensor::value_type_name< complex > ( )

constexpr

value_type_name< double >()

template<>

constexpr char * mptensor::value_type_name< double > ( )

constexpr

value_type_tag()

template<typename C >

constexpr size_t mptensor::value_type_tag ( )

constexpr

value_type_tag< complex >()

template<>

constexpr size_t mptensor::value_type_tag< complex > ( )

constexpr

value_type_tag< double >()

template<>

constexpr size_t mptensor::value_type_tag< double > ( )

constexpr