#include <RandomizedMatrixDecomposition.h>

Classes
struct	Y_former
	functor for forming Y = matrix * randomvector More...

Public Types
typedef TensorTypeData< T >::scalar_type	scalar_type

Public Member Functions
	RandomizedMatrixDecomposition ()=default
	RandomizedMatrixDecomposition (const RandomizedMatrixDecomposition &other)=default
	RandomizedMatrixDecomposition (const RMDFactory &factory)
	RandomizedMatrixDecomposition (const Tensor< T > &matrix, const double thresh)
Tensor< T >	compute_range (const Tensor< T > &columnspace, const Tensor< T > &rowspace, const double &eps)
	compute the range of the matrix given in decomposed form
Tensor< T >	compute_range (const Tensor< T > &tensor, const double &eps, std::array< long, 2 > matrixdim={0, 0})
	compute the range of the matrix
bool	exceeds_maxrank () const
	check if the computed rank is too large
Tensor< T >	get_range () const
void	set_maxrank (const long max_rank)

Static Public Member Functions
static scalar_type	check_range (const Tensor< T > &matrix, const Tensor< T > &range)
	return the error of the range Q
static Tensor< T >	make_SVD_decaying_matrix (const Tensor< T > &matrix, const int n=1)
	helper function
static Tensor< T >	resize_to_matrix (const Tensor< T > &matrix, std::array< long, 2 > vectordim={0, 0})
	resize Tensor to a matrix

Private Member Functions
Tensor< T >	do_compute_range (const Y_former &Y, const double &eps) const
	perform the actual computation of the range

Private Attributes
long	maxrank =LONG_MAX
	maximum rank to abort the decomposition
long	oversampling =10
	oversampling parameter
Tensor< T >	range =Tensor<T>(0l,0l)
	the range that spans the input matrix

Member Typedef Documentation

◆ scalar_type

template<typename T>

typedef TensorTypeData<T>::scalar_type madness::RandomizedMatrixDecomposition< T >::scalar_type

Constructor & Destructor Documentation

◆ RandomizedMatrixDecomposition() [1/4]

template<typename T>

madness::RandomizedMatrixDecomposition< T >::RandomizedMatrixDecomposition ( )

default

Referenced by RandomizedMatrixDecomposition().

◆ RandomizedMatrixDecomposition() [2/4]

template<typename T>

madness::RandomizedMatrixDecomposition< T >::RandomizedMatrixDecomposition ( const RandomizedMatrixDecomposition< T > & other )

default

References RandomizedMatrixDecomposition().

◆ RandomizedMatrixDecomposition() [3/4]

template<typename T>

madness::RandomizedMatrixDecomposition< T >::RandomizedMatrixDecomposition ( const RMDFactory & factory )

inline

References maxrank, and oversampling.

◆ RandomizedMatrixDecomposition() [4/4]

template<typename T>

madness::RandomizedMatrixDecomposition< T >::RandomizedMatrixDecomposition	(	const Tensor< T > &	matrix,
		const double	thresh )

inline

References compute_range(), madness::FunctionDefaults< NDIM >::thresh, and range.

Member Function Documentation

◆ check_range()

template<typename T>

scalar_type madness::RandomizedMatrixDecomposition< T >::check_range	(	const Tensor< T > &	matrix,
		const Tensor< T > &	range )

inlinestatic

return the error of the range Q

explicitly compute the error measure || A - Q Q^T A ||

References madness::conj(), madness::inner(), range, and residual().

Referenced by test_stuff().

◆ compute_range() [1/2]

template<typename T>

Tensor< T > madness::RandomizedMatrixDecomposition< T >::compute_range	(	const Tensor< T > &	columnspace,
		const Tensor< T > &	rowspace,
		const double &	eps )

compute the range of the matrix given in decomposed form

see above; Matrix is given by A(i,j)=columnspace(r,i) * rowspace(r,j)

Parameters

[in]	columnspace	columnspace of the input tensor/matrix A
[in]	rowspace	rowspace of the input tensor/matrix A
[in]	eps	the accuracy of the representation

Returns: range the range of the input tensor

References madness::BaseTensor::dim(), do_compute_range(), MADNESS_ASSERT, maxrank, madness::BaseTensor::ndim(), Q(), range, and madness::BaseTensor::size().

◆ compute_range() [2/2]

template<typename T>

Tensor< T > madness::RandomizedMatrixDecomposition< T >::compute_range	(	const Tensor< T > &	tensor,
		const double &	eps,
		std::array< long, 2 >	matrixdim = {0,0} )

compute the range of the matrix

compute the range of the matrix, following Alg 4.2 of Halko, Martinsson, Tropp, 2011

follows Halko, Martinsson, Tropp (2011), Alg. 4.2 the final range will satisfy for the input tensor A: || A - Q Q^T A || < eps method will change member variables "range" and "maxrank"

Parameters

[in]	tensor	the input tensor/matrix A (see matrixdim if not a matrix)
[in]	eps	the accuracy of the representation
[in]	matrixdim	how to reshape the tensor if it is not a matrix

Returns: range the range of the input tensor

References do_compute_range(), maxrank, madness::Tensor< T >::normf(), range, and resize_to_matrix().

Referenced by RandomizedMatrixDecomposition(), madness::SVDTensor< T >::compute_randomized_svd(), madness::SVDTensor< T >::orthonormalize_random(), and test_stuff().

◆ do_compute_range()

template<typename T>

Tensor< T > madness::RandomizedMatrixDecomposition< T >::do_compute_range	(	const Y_former &	Y,
		const double &	eps ) const

private

perform the actual computation of the range

References madness::_(), madness::conj(), madness::BaseTensor::dim(), madness::Tensor< T >::fillrandom(), madness::inner(), madness::RandomizedMatrixDecomposition< T >::Y_former::m(), MADNESS_EXCEPTION, maxrank, madness::RandomizedMatrixDecomposition< T >::Y_former::maxrank(), madness::RandomizedMatrixDecomposition< T >::Y_former::n(), madness::Tensor< T >::normf(), oversampling, madness::constants::pi, Q(), madness::qr(), and R.

Referenced by compute_range(), and compute_range().

◆ exceeds_maxrank()

template<typename T>

bool madness::RandomizedMatrixDecomposition< T >::exceeds_maxrank ( ) const

inline

check if the computed rank is too large

References maxrank, and range.

Referenced by madness::SVDTensor< T >::compute_randomized_svd(), and test_stuff().

◆ get_range()

template<typename T>

Tensor< T > madness::RandomizedMatrixDecomposition< T >::get_range ( ) const

inline

References range.

Referenced by test_stuff().

◆ make_SVD_decaying_matrix()

template<typename T>

Tensor< T > madness::RandomizedMatrixDecomposition< T >::make_SVD_decaying_matrix	(	const Tensor< T > &	matrix,
		const int	n = 1 )

inlinestatic

helper function

References madness::_(), madness::inner(), and madness::svd().

Referenced by test_stuff().

◆ resize_to_matrix()

template<typename T>

Tensor< T > madness::RandomizedMatrixDecomposition< T >::resize_to_matrix	(	const Tensor< T > &	matrix,
		std::array< long, 2 >	vectordim = {0,0} )

inlinestatic

resize Tensor to a matrix

Referenced by compute_range(), madness::SVDTensor< T >::compute_svd(), and madness::SVDTensor< T >::compute_svd_from_range().

◆ set_maxrank()

template<typename T>

void madness::RandomizedMatrixDecomposition< T >::set_maxrank ( const long max_rank )

inline

References maxrank.

Member Data Documentation

◆ maxrank

template<typename T>

long madness::RandomizedMatrixDecomposition< T >::maxrank =LONG_MAX

private

maximum rank to abort the decomposition

Referenced by RandomizedMatrixDecomposition(), compute_range(), compute_range(), do_compute_range(), exceeds_maxrank(), and set_maxrank().

◆ oversampling

template<typename T>

long madness::RandomizedMatrixDecomposition< T >::oversampling =10

private

oversampling parameter

Referenced by RandomizedMatrixDecomposition(), and do_compute_range().

◆ range

template<typename T>

Tensor<T> madness::RandomizedMatrixDecomposition< T >::range =Tensor<T>(0l,0l)

private

the range that spans the input matrix

Referenced by RandomizedMatrixDecomposition(), check_range(), compute_range(), compute_range(), exceeds_maxrank(), and get_range().

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

Classes

Public Types

Public Member Functions

Static Public Member Functions

Private Member Functions

Private Attributes

Member Typedef Documentation

◆ scalar_type

Constructor & Destructor Documentation

◆ RandomizedMatrixDecomposition() [1/4]

◆ RandomizedMatrixDecomposition() [2/4]

◆ RandomizedMatrixDecomposition() [3/4]

◆ RandomizedMatrixDecomposition() [4/4]

Member Function Documentation

◆ check_range()

◆ compute_range() [1/2]

◆ compute_range() [2/2]

◆ do_compute_range()

◆ exceeds_maxrank()

◆ get_range()

◆ make_SVD_decaying_matrix()

◆ resize_to_matrix()

◆ set_maxrank()

Member Data Documentation

◆ maxrank

◆ oversampling

◆ range