tensor.hpp File Reference

Tensor class. More...

#include <algorithm>
#include <cassert>
#include <iostream>
#include <string>
#include <vector>
#include "complex.hpp"
#include "index.hpp"
#include "matrix.hpp"
#include "tensor_impl.hpp"
#include "rsvd.hpp"
#include "file_io/save.hpp"
#include "file_io/load.hpp"

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Classes
class	mptensor::Tensor< Matrix, C >
	Tensor class. The main object of mptensor. More...

Namespaces
namespace	mptensor

Typedefs
typedef Index	mptensor::Axes
typedef Index	mptensor::Shape

Functions
template<template< typename > class Matrix, typename C >
Tensor< Matrix, C >	mptensor::transpose (Tensor< Matrix, C > T, const Axes &axes)
	Transposition of tensor with lazy evaluation.
template<template< typename > class Matrix, typename C >
Tensor< Matrix, C >	mptensor::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 >	mptensor::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 >	mptensor::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 >	mptensor::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 >	mptensor::extend (const Tensor< Matrix, C > &T, const Shape &shape_new)
	Extend the size of a tensor.
template<template< typename > class Matrix, typename C >
C	mptensor::trace (const Tensor< Matrix, C > &M)
	Trace of matrix (rank-2 tensor)
template<template< typename > class Matrix, typename C >
C	mptensor::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	mptensor::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 >	mptensor::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 >	mptensor::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 >	mptensor::kron (const Tensor< Matrix, C > &a, const Tensor< Matrix, C > &b)
	Compute the Kronecker product.
template<template< typename > class Matrix, typename C >
int	mptensor::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	mptensor::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	mptensor::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	mptensor::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	mptensor::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	mptensor::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	mptensor::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	mptensor::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	mptensor::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	mptensor::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	mptensor::eigh (const Tensor< Matrix, C > &a, std::vector< double > &eigval, Tensor< Matrix, C > &eigvec)
template<template< typename > class Matrix, typename C >
int	mptensor::eigh (const Tensor< Matrix, C > &a, std::vector< double > &eigval)
template<template< typename > class Matrix, typename C >
int	mptensor::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	mptensor::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	mptensor::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	mptensor::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	mptensor::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	mptensor::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	mptensor::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	mptensor::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	mptensor::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	mptensor::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 >	mptensor::operator+ (Tensor< Matrix, C > rhs)
	Unary plus.
template<template< typename > class Matrix, typename C >
Tensor< Matrix, C >	mptensor::operator- (Tensor< Matrix, C > rhs)
	Unary minus.
template<template< typename > class Matrix, typename C >
Tensor< Matrix, C >	mptensor::operator+ (Tensor< Matrix, C > lhs, const Tensor< Matrix, C > &rhs)
	Addition.
template<template< typename > class Matrix, typename C >
Tensor< Matrix, C >	mptensor::operator- (Tensor< Matrix, C > lhs, const Tensor< Matrix, C > &rhs)
	Subtraction.
template<template< typename > class Matrix, typename C , typename D >
Tensor< Matrix, C >	mptensor::operator* (Tensor< Matrix, C > lhs, D rhs)
	Tensor-scalar multiplication.
template<template< typename > class Matrix, typename C , typename D >
Tensor< Matrix, C >	mptensor::operator/ (Tensor< Matrix, C > lhs, D rhs)
	Scalar division.
template<template< typename > class Matrix, typename C , typename D >
Tensor< Matrix, C >	mptensor::operator* (D lhs, Tensor< Matrix, C > rhs)
	Scalar-tensor multiplication.
template<template< typename > class Matrix, typename C >
Tensor< Matrix, C >	mptensor::sqrt (Tensor< Matrix, C > t)
	Take square-root of each element.
template<template< typename > class Matrix, typename C >
Tensor< Matrix, C >	mptensor::conj (Tensor< Matrix, C > t)
	Take conjugate of each element.
template<template< typename > class Matrix, typename C >
double	mptensor::max (const Tensor< Matrix, C > &t)
	Return the maximum element. For complex, same as max_abs().
template<template< typename > class Matrix, typename C >
double	mptensor::min (const Tensor< Matrix, C > &t)
	Return the minimum element. For complex, same as min_abs().
template<template< typename > class Matrix, typename C >
double	mptensor::max_abs (const Tensor< Matrix, C > &t)
	Return maximum of the absolute value of an element.
template<template< typename > class Matrix, typename C >
double	mptensor::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 &	mptensor::operator<< (std::ostream &out, const Tensor< Matrix, C > &t)
	Output elements of tensor in numpy style.

Detailed Description

Tensor class.

Author

Satoshi Morita morit.nosp@m.a@is.nosp@m.sp.u-.nosp@m.toky.nosp@m.o.ac..nosp@m.jp

Date

Jan 14 2015