Randomized algorithm

template<template< typename > class Matrix, typename C >
int	mptensor::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. More...
template<template< typename > class Matrix, typename C >
int	mptensor::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. More...
template<template< typename > class Matrix, typename C , typename Func1 , typename Func2 >
int	mptensor::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. More...
template<template< typename > class Matrix, typename C , typename Func1 , typename Func2 >
int	mptensor::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. More...
void	mptensor::set_seed (unsigned int seed)
	Set seed for random number generator. More...

Detailed Description

Function to decompose a tensor by randomized algorithms.

Function Documentation

rsvd() [1/4]

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

int mptensor::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.

rsvd() [2/4]

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

int mptensor::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.

For example,

rsvd(A, Axes(0,3), Axes(1,2), U, S, VT, k, p)

calculates the following decomposition.

\[ A_{abcd} \simeq \sum_{i=0}^{k-1} U_{adi} S_i (V^\dagger)_{ibc}, \]

where \( k \) is the target rank.

Parameters

[in]	a	A tensor to be decomposed.
[in]	axes_row	Axes for left singular vectors.
[in]	axes_col	Axes for right singular vectors.
[out]	u	Tensor \( U \) corresponds to left signular vectors.
[out]	s	Singluar values.
[out]	vt	Tensor \( V^\dagger \) corresponds to right singular vectors.
[in]	target_rank	The number of singular values to be calculated
[in]	oversamp	Oversampling parameter for randomized algorithm

Returns

Information from linear-algebra library.

rsvd() [3/4]

template<template< typename > class Matrix, typename C , typename Func1 , typename Func2 >

int mptensor::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.

rsvd() [4/4]

template<template< typename > class Matrix, typename C , typename Func1 , typename Func2 >

int mptensor::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.

Parameters

[in]	multiply_row	A function object which takes a Tensor with Shape(shape_col+[target_rank+oversamp]) and returns a Tensor with Shape(shape_row+[target_rank+oversamp]).
[in]	multiply_col	A function object which takes a Tensor with Shape([target_rank+oversamp]+shape_row) and returns a Tensor with Shape([target_rank+oversamp]+shape_col).
[in]	shape_row	Shape of row indices.
[in]	shape_col	Shape of column indices.
[out]	u	Tensor \( U \) corresponds to left singular vectors. Its shape is Shape(shape_row+[target_rank]).
[out]	s	Singular values.
[out]	vt	Tensor \( V^\dagger \) corresponds to right singular vectors. Its shape is Shape([target_rank]+shape_col).
[in]	target_rank	The number of singular values to be calculated
[in]	oversamp	Oversampling parameter for randomized algorithm

Returns

Information from linear-algebra library.

set_seed()

void mptensor::set_seed ( unsigned int  seed )

inline

Set seed for random number generator.

Parameters

[in]

seed

Value of seed.

Warning

Set different seed values for each MPI process.