LowRankFunction represents a hi-dimensional (NDIM) function as a sum of products of low-dimensional (LDIM) functions. More...

#include <lowrankfunction.h>

Collaboration diagram for madness::LowRankFunction< T, NDIM, LDIM >:

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Public Member Functions
	LowRankFunction (const LowRankFunction &other)
	shallow copy ctor

	LowRankFunction (std::vector< Function< T, LDIM > > g, std::vector< Function< T, LDIM > > h, double tol, std::string orthomethod)

	LowRankFunction (World &world)

double	check_orthonormality (const std::vector< Function< T, LDIM > > &v) const

double	check_orthonormality (const Tensor< T > &ovlp) const

std::vector< Function< T, LDIM > >	get_functions (const particle< LDIM > &p) const

std::vector< Function< T, LDIM > >	get_g () const

std::vector< Function< T, LDIM > >	get_h () const

double	l2error (const LRFunctorBase< T, NDIM > &lrfunctor1) const
	compute the l2 error \|functor - \sum_i g_ih_i\|_2

TensorTypeData< T >::scalar_type	norm2 () const
	l2 norm

T	operator() (const Vector< double, NDIM > &r) const
	function evaluation

template<typename Q >
LowRankFunction	operator* (const Q a) const
	scale by a scalar

LowRankFunction	operator* (const T a) const
	out-of-place scale by a scalar (no type conversion)

LowRankFunction &	operator*= (const T a)
	in-place scale by a scalar (no type conversion)

LowRankFunction	operator+ (const LowRankFunction &b) const
	addition

LowRankFunction &	operator+= (const LowRankFunction &b)
	in-place addition

LowRankFunction	operator- (const LowRankFunction &b) const
	subtraction

LowRankFunction &	operator-= (const LowRankFunction &b)
	in-place subtraction

LowRankFunction &	operator= (const LowRankFunction &f)

void	optimize (const LRFunctorBase< T, NDIM > &lrfunctor1, const long nopt=1)
	optimize the lrf using the lrfunctor

std::vector< Function< T, LDIM > >	orthonormalize (const std::vector< Function< T, LDIM > > &g) const
	orthonormalize the argument vector

long	rank () const

Function< T, NDIM >	reconstruct () const

void	remove_linear_depdencies (double thresh=-1.0)
	remove linear dependencies without orthonormalization

void	reorthonormalize (double thresh=-1.0)
	after external operations g might not be orthonormal and/or optimal – reorthonormalize

double	size () const
	return the size in GByte

Public Attributes
bool	do_print =false

std::vector< Function< T, LDIM > >	g

std::vector< Function< T, LDIM > >	h

std::string	orthomethod ="canonical"

const particle< LDIM >	p1 =particle<LDIM>::particle1()

const particle< LDIM >	p2 =particle<LDIM>::particle2()

double	rank_revealing_tol =1.e-8

World &	world

Friends
LowRankFunction	copy (const LowRankFunction &other)
	deep copy

LowRankFunction	operator* (const T a, const LowRankFunction &other)
	multiplication with a scalar

Detailed Description

template<typename T, std::size_t NDIM, std::size_t LDIM = NDIM/2>
class madness::LowRankFunction< T, NDIM, LDIM >

LowRankFunction represents a hi-dimensional (NDIM) function as a sum of products of low-dimensional (LDIM) functions.

f(1,2) = \sum_i g_i(1) h_i(2) a LowRankFunction can be created from a hi-dim function directly, or from a composite like f(1,2) phi(1) psi(2), where f(1,2) is a two-particle function (e.g. a Slater function)

Constructor & Destructor Documentation

◆ LowRankFunction() [1/3]

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

madness::LowRankFunction< T, NDIM, LDIM >::LowRankFunction ( World & world )

inline

◆ LowRankFunction() [2/3]

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

madness::LowRankFunction< T, NDIM, LDIM >::LowRankFunction	(	std::vector< Function< T, LDIM > >	g,
		std::vector< Function< T, LDIM > >	h,
		double	tol,
		std::string	orthomethod
	)

inline

◆ LowRankFunction() [3/3]

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

madness::LowRankFunction< T, NDIM, LDIM >::LowRankFunction ( const LowRankFunction< T, NDIM, LDIM > & other )

inline

shallow copy ctor

Member Function Documentation

◆ check_orthonormality() [1/2]

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

double madness::LowRankFunction< T, NDIM, LDIM >::check_orthonormality ( const std::vector< Function< T, LDIM > > & v ) const

inline

References madness::LowRankFunction< T, NDIM, LDIM >::check_orthonormality(), madness::matrix_inner(), v, and madness::LowRankFunction< T, NDIM, LDIM >::world.

Referenced by madness::LowRankFunction< T, NDIM, LDIM >::check_orthonormality(), and madness::LowRankFunction< T, NDIM, LDIM >::l2error().

◆ check_orthonormality() [2/2]

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

double madness::LowRankFunction< T, NDIM, LDIM >::check_orthonormality ( const Tensor< T > & ovlp ) const

inline

References madness::Tensor< T >::absmax(), madness::BaseTensor::dim(), madness::LowRankFunction< T, NDIM, LDIM >::do_print, madness::timer::do_print, madness::Tensor< T >::normf(), madness::print(), madness::World::rank(), madness::BaseTensor::size(), madness::timer::tag(), and madness::LowRankFunction< T, NDIM, LDIM >::world.

◆ get_functions()

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

std::vector< Function< T, LDIM > > madness::LowRankFunction< T, NDIM, LDIM >::get_functions ( const particle< LDIM > & p ) const

inline

References madness::LowRankFunction< T, NDIM, LDIM >::g, madness::LowRankFunction< T, NDIM, LDIM >::h, MADNESS_CHECK, and p().

◆ get_g()

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

std::vector< Function< T, LDIM > > madness::LowRankFunction< T, NDIM, LDIM >::get_g ( ) const

inline

References madness::LowRankFunction< T, NDIM, LDIM >::g.

Referenced by madness::CCPairFunction< T, NDIM >::op_dec_to_dec(), and madness::CCPairFunction< T, NDIM >::remove_linearly_dependent_terms().

◆ get_h()

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

std::vector< Function< T, LDIM > > madness::LowRankFunction< T, NDIM, LDIM >::get_h ( ) const

inline

References madness::LowRankFunction< T, NDIM, LDIM >::h.

Referenced by madness::CCPairFunction< T, NDIM >::op_dec_to_dec(), and madness::CCPairFunction< T, NDIM >::remove_linearly_dependent_terms().

◆ l2error()

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

double madness::LowRankFunction< T, NDIM, LDIM >::l2error ( const LRFunctorBase< T, NDIM > & lrfunctor1 ) const

inline

compute the l2 error |functor - \sum_i g_ih_i|_2

\int (f(1,2) - gh(1,2))^2 = \int f(1,2)^2 - 2\int f(1,2) gh(1,2) + \int gh(1,2)^2 since we are subtracting large numbers the numerics are sensitive, and NaN may be returned..

References madness::arg(), madness::LowRankFunction< T, NDIM, LDIM >::check_orthonormality(), madness::LowRankFunction< T, NDIM, LDIM >::do_print, madness::timer::do_print, madness::error(), madness::LowRankFunction< T, NDIM, LDIM >::g, madness::LowRankFunction< T, NDIM, LDIM >::h, madness::inner(), madness::matrix_inner(), madness::LRFunctorBase< T, NDIM, LDIM >::norm2(), madness::LowRankFunction< T, NDIM, LDIM >::p1, madness::LowRankFunction< T, NDIM, LDIM >::p2, madness::print(), madness::World::rank(), madness::timer::tag(), and madness::LowRankFunction< T, NDIM, LDIM >::world.

◆ norm2()

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

TensorTypeData< T >::scalar_type madness::LowRankFunction< T, NDIM, LDIM >::norm2 ( ) const

inline

l2 norm

References madness::LowRankFunction< T, NDIM, LDIM >::g, madness::LowRankFunction< T, NDIM, LDIM >::h, madness::matrix_inner(), and madness::LowRankFunction< T, NDIM, LDIM >::world.

◆ operator()()

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

T madness::LowRankFunction< T, NDIM, LDIM >::operator() ( const Vector< double, NDIM > & r ) const

inline

function evaluation

References madness::LowRankFunction< T, NDIM, LDIM >::g, madness::LowRankFunction< T, NDIM, LDIM >::h, and madness::LowRankFunction< T, NDIM, LDIM >::rank().

◆ operator*() [1/2]

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

template<typename Q >

LowRankFunction madness::LowRankFunction< T, NDIM, LDIM >::operator* ( const Q a ) const

inline

scale by a scalar

References a, madness::LowRankFunction< T, NDIM, LDIM >::g, madness::LowRankFunction< T, NDIM, LDIM >::h, NDIM, madness::LowRankFunction< T, NDIM, LDIM >::orthomethod, Q(), and madness::LowRankFunction< T, NDIM, LDIM >::rank_revealing_tol.

◆ operator*() [2/2]

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

LowRankFunction madness::LowRankFunction< T, NDIM, LDIM >::operator* ( const T a ) const

inline

out-of-place scale by a scalar (no type conversion)

References a, madness::LowRankFunction< T, NDIM, LDIM >::g, madness::LowRankFunction< T, NDIM, LDIM >::h, madness::LowRankFunction< T, NDIM, LDIM >::orthomethod, and madness::LowRankFunction< T, NDIM, LDIM >::rank_revealing_tol.

◆ operator*=()

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

LowRankFunction & madness::LowRankFunction< T, NDIM, LDIM >::operator*= ( const T a )

inline

in-place scale by a scalar (no type conversion)

References a, and madness::LowRankFunction< T, NDIM, LDIM >::g.

◆ operator+()

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

LowRankFunction madness::LowRankFunction< T, NDIM, LDIM >::operator+ ( const LowRankFunction< T, NDIM, LDIM > & b ) const

inline

addition

References b, and madness::LowRankFunction< T, NDIM, LDIM >::copy.

◆ operator+=()

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

LowRankFunction & madness::LowRankFunction< T, NDIM, LDIM >::operator+= ( const LowRankFunction< T, NDIM, LDIM > & b )

inline

in-place addition

References madness::append(), b, madness::LowRankFunction< T, NDIM, LDIM >::copy, madness::LowRankFunction< T, NDIM, LDIM >::g, and madness::LowRankFunction< T, NDIM, LDIM >::h.

◆ operator-()

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

LowRankFunction madness::LowRankFunction< T, NDIM, LDIM >::operator- ( const LowRankFunction< T, NDIM, LDIM > & b ) const

inline

subtraction

References b, and madness::LowRankFunction< T, NDIM, LDIM >::copy.

◆ operator-=()

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

LowRankFunction & madness::LowRankFunction< T, NDIM, LDIM >::operator-= ( const LowRankFunction< T, NDIM, LDIM > & b )

inline

in-place subtraction

References madness::append(), b, madness::LowRankFunction< T, NDIM, LDIM >::copy, madness::LowRankFunction< T, NDIM, LDIM >::g, and madness::LowRankFunction< T, NDIM, LDIM >::h.

◆ operator=()

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

LowRankFunction & madness::LowRankFunction< T, NDIM, LDIM >::operator= ( const LowRankFunction< T, NDIM, LDIM > & f )

inline

References madness::f, madness::LowRankFunction< T, NDIM, LDIM >::g, and madness::LowRankFunction< T, NDIM, LDIM >::h.

◆ optimize()

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

void madness::LowRankFunction< T, NDIM, LDIM >::optimize	(	const LRFunctorBase< T, NDIM > &	lrfunctor1,
		const long	nopt = `1`
	)

inline

optimize the lrf using the lrfunctor

Parameters

[in] nopt number of iterations (wrt to Alg. 4.3 in Halko)

References madness::LowRankFunction< T, NDIM, LDIM >::do_print, madness::timer::do_print, madness::LowRankFunction< T, NDIM, LDIM >::g, madness::LowRankFunction< T, NDIM, LDIM >::h, madness::inner(), madness::LowRankFunction< T, NDIM, LDIM >::orthonormalize(), madness::LowRankFunction< T, NDIM, LDIM >::p1, madness::LowRankFunction< T, NDIM, LDIM >::p2, madness::timer::tag(), madness::truncate(), and madness::LowRankFunction< T, NDIM, LDIM >::world.

Referenced by madness::CCPairFunction< T, NDIM >::op_dec_to_dec().

◆ orthonormalize()

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

std::vector< Function< T, LDIM > > madness::LowRankFunction< T, NDIM, LDIM >::orthonormalize ( const std::vector< Function< T, LDIM > > & g ) const

inline

orthonormalize the argument vector

References madness::LowRankFunction< T, NDIM, LDIM >::g, madness::FunctionDefaults< NDIM >::get_thresh(), MADNESS_EXCEPTION, madness::matrix_inner(), madness::LowRankFunction< T, NDIM, LDIM >::orthomethod, madness::orthonormalize_canonical(), madness::orthonormalize_rrcd(), madness::print(), madness::LowRankFunction< T, NDIM, LDIM >::rank_revealing_tol, madness::truncate(), and madness::LowRankFunction< T, NDIM, LDIM >::world.

Referenced by madness::LowRankFunction< T, NDIM, LDIM >::optimize().

◆ rank()

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

long madness::LowRankFunction< T, NDIM, LDIM >::rank ( ) const

inline

References madness::LowRankFunction< T, NDIM, LDIM >::g.

Referenced by madness::LowRankFunction< T, NDIM, LDIM >::operator()().

◆ reconstruct()

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

Function< T, NDIM > madness::LowRankFunction< T, NDIM, LDIM >::reconstruct ( ) const

inline

References madness::LowRankFunction< T, NDIM, LDIM >::g, madness::LowRankFunction< T, NDIM, LDIM >::h, and madness::hartree_product().

◆ remove_linear_depdencies()

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

void madness::LowRankFunction< T, NDIM, LDIM >::remove_linear_depdencies ( double thresh = -1.0 )

inline

remove linear dependencies without orthonormalization

◆ reorthonormalize()

template<typename T , std::size_t NDIM, std::size_t LDIM = NDIM/2>

void madness::LowRankFunction< T, NDIM, LDIM >::reorthonormalize ( double thresh = -1.0 )

inline

after external operations g might not be orthonormal and/or optimal – reorthonormalize

orthonormalization similar to Bischoff, Harrison, Valeev, JCP 137 104103 (2012), Sec II C 3 f =\sum_i g_i h_i = g X- (X+)^T (Y+)^T Y- h = g X- U S V^T Y- h = g (X- U) (S V^T Y-) h requires 2 matrix_inner and 2 transforms. g and h are optimal, but contain all cusps etc..

Parameters

[in] thresh SVD threshold

References madness::_(), madness::LowRankFunction< T, NDIM, LDIM >::copy, madness::LowRankFunction< T, NDIM, LDIM >::g, madness::LowRankFunction< T, NDIM, LDIM >::h, madness::inner(), MADNESS_CHECK_THROW, madness::matrix_inner(), madness::LowRankFunction< T, NDIM, LDIM >::rank_revealing_tol, madness::svd(), madness::syev(), thresh, madness::transform(), madness::truncate(), and madness::LowRankFunction< T, NDIM, LDIM >::world.