Namespaces
namespace	dspace

Classes
class	DSpaceResetter
	Resets D space constructing full solutions as the new working set, removing instabilities from Q space, and clearing D space. More...

Functions
std::vector< std::pair< size_t, size_t > >	parameter_batches (const size_t nsol, const size_t nparam)

template<class R , class Q , class P >
void	construct_solution (const VecRef< R > &params, const std::vector< int > &roots, const subspace::Matrix< double > &solutions, const std::vector< std::reference_wrapper< P > > &pparams, const std::vector< std::reference_wrapper< Q > > &qparams, const std::vector< std::reference_wrapper< Q > > &dparams, size_t oP, size_t oQ, size_t oD, ArrayHandlers< R, Q, P > &handlers)

template<typename T >
std::vector< std::vector< T > >	construct_vectorP (const std::vector< int > &roots, const subspace::Matrix< T > &solutions, const size_t oP, const size_t nP)

template<class R >
void	normalise (const size_t n_roots, const VecRef< R > &params, const VecRef< R > &actions, array::ArrayHandler< R, R > &handler, Logger &logger)

template<class R , typename T >
void	update_errors (std::vector< T > &errors, const CVecRef< R > &residual, array::ArrayHandler< R, R > &handler)

template<typename T >
std::vector< int >	select_working_set (const size_t nw, const std::vector< T > &errors, const T threshold, const std::vector< T > &value_errors, const T value_threshold)

template<class R >
void	normalise (VecRef< R > &params, array::ArrayHandler< R, R > &handler, Logger &logger, double thresh=1.0e-14)

template<class R , class Q , class P , typename value_type >
auto	append_overlap_with_r (const subspace::Matrix< value_type > &overlap, const CVecRef< R > &params, const CVecRef< P > &pparams, const CVecRef< Q > &qparams, const CVecRef< Q > &dparams, ArrayHandlers< R, Q, P > &handlers, Logger &logger)
	Constructs overlap of the full subspace by appending overlap with new parameters to the overlap of previous subspace. More...

template<typename value_type >
auto	limit_qspace_size (const subspace::Dimensions &dims, const size_t max_size_qspace, const subspace::Matrix< value_type > &solutions, Logger &logger)
	Ensures that size Q space is within limit by proposing Q parameters for deletion. More...

template<class R , class Q , class P , typename value_type , typename value_type_abs >
auto	construct_dspace (const subspace::Matrix< value_type > &solutions, const subspace::IXSpace< R, Q, P > &xspace, const std::vector< int > &q_delete, const value_type_abs norm_thresh, const value_type_abs svd_thresh, array::ArrayHandler< Q, Q > &handler, Logger &logger)
	Constructs the new D space by projecting the solutions onto Qd+D subspace and ensuring they are well conditioned. More...

template<class R , class Q , class P , typename value_type , typename value_type_abs >
auto	modified_gram_schmidt (const VecRef< R > &rparams, const subspace::Matrix< value_type > &overlap, const subspace::Dimensions &dims, const CVecRef< P > &pparams, const CVecRef< Q > &qparams, const CVecRef< Q > &dparams, const value_type_abs norm_thresh, ArrayHandlers< R, Q, P > &handlers, Logger &logger)
	Orthogonalises R parameters against P+Q+D subspace (and themselves) More...

template<typename value_type , typename value_type_abs >
auto	redundant_parameters (const subspace::Matrix< value_type > &overlap, const size_t oR, const size_t nR, const value_type_abs svd_thresh, Logger &logger)
	Deduces a set of parameters that are redundant due to linear dependencies. More...

template<class R >
auto	get_new_working_set (const std::vector< int > &working_set, const CVecRef< R > &params, const CVecRef< R > &wparams)
	Returns new working set based on parameters included in wparams. More...

template<class R , class Q , class P , typename value_type_abs >
auto	propose_rspace (IterativeSolver< R, Q, P > &solver, const VecRef< R > &parameters, const VecRef< R > &residuals, subspace::IXSpace< R, Q, P > &xspace, subspace::ISubspaceSolver< R, Q, P > &subspace_solver, ArrayHandlers< R, Q, P > &handlers, Logger &logger, value_type_abs svd_thresh, value_type_abs res_norm_thresh, int max_size_qspace, molpro::profiler::Profiler &profiler)
	Proposes new parameters for the subspace from the preconditioned residuals. More...

template<class R , class Q , class P , typename value_type >
void	resize_qspace (subspace::IXSpace< R, Q, P > &xspace, const subspace::Matrix< value_type > &solutions, int m_max_Qsize_after_reset, Logger &logger)
	Removes Q parameters that have smallest contribution to any solution until Q space size is within limit. More...

template<class R , class Q >
auto	max_overlap_with_R (const CVecRef< R > &rparams, const CVecRef< Q > &qparams, array::ArrayHandler< R, Q > &handler, Logger &logger)
	Returns list of Q indices with maximum overlap to R parameters, sorted in descending order. More...

Function Documentation

◆ append_overlap_with_r()

template<class R , class Q , class P , typename value_type >

auto molpro::linalg::itsolv::detail::append_overlap_with_r	(	const subspace::Matrix< value_type > &	overlap,
		const CVecRef< R > &	params,
		const CVecRef< P > &	pparams,
		const CVecRef< Q > &	qparams,
		const CVecRef< Q > &	dparams,
		ArrayHandlers< R, Q, P > &	handlers,
		Logger &	logger
	)

Constructs overlap of the full subspace by appending overlap with new parameters to the overlap of previous subspace.

Parameters

ov	overlap of P+Q+D
params	new parameters
pparams	P space parameters
qparams	Q space parameters
dparams	D space parameters
handlers	array handlers
logger	logger

◆ construct_dspace()

template<class R , class Q , class P , typename value_type , typename value_type_abs >

auto molpro::linalg::itsolv::detail::construct_dspace	(	const subspace::Matrix< value_type > &	solutions,
		const subspace::IXSpace< R, Q, P > &	xspace,
		const std::vector< int > &	q_delete,
		const value_type_abs	norm_thresh,
		const value_type_abs	svd_thresh,
		array::ArrayHandler< Q, Q > &	handler,
		Logger &	logger
	)

Constructs the new D space by projecting the solutions onto Qd+D subspace and ensuring they are well conditioned.

Parameters

xspace	X space container
q_delete	Q parameters marked for deletion
norm_thresh	norm threshold for parameters to be considered null
svd_thresh	svd threshold for marking the null space
handler	array handler
logger	logger

Returns: D space parameters and actions

◆ construct_solution()

template<class R , class Q , class P >

void molpro::linalg::itsolv::detail::construct_solution	(	const VecRef< R > &	params,
		const std::vector< int > &	roots,
		const subspace::Matrix< double > &	solutions,
		const std::vector< std::reference_wrapper< P > > &	pparams,
		const std::vector< std::reference_wrapper< Q > > &	qparams,
		const std::vector< std::reference_wrapper< Q > > &	dparams,
		size_t	oP,
		size_t	oQ,
		size_t	oD,
		ArrayHandlers< R, Q, P > &	handlers
	)

◆ construct_vectorP()

template<typename T >

std::vector< std::vector< T > > molpro::linalg::itsolv::detail::construct_vectorP	(	const std::vector< int > &	roots,
		const subspace::Matrix< T > &	solutions,
		const size_t	oP,
		const size_t	nP
	)

◆ get_new_working_set()

template<class R >

auto molpro::linalg::itsolv::detail::get_new_working_set	(	const std::vector< int > &	working_set,
		const CVecRef< R > &	params,
		const CVecRef< R > &	wparams
	)

Returns new working set based on parameters included in wparams.

◆ limit_qspace_size()

template<typename value_type >

auto molpro::linalg::itsolv::detail::limit_qspace_size	(	const subspace::Dimensions &	dims,
		const size_t	max_size_qspace,
		const subspace::Matrix< value_type > &	solutions,
		Logger &	logger
	)

Ensures that size Q space is within limit by proposing Q parameters for deletion.

Parameters

dims	dimensions of current P+Q+D subspace
max_size_qspace	maximum size of Q space
solutions	solutions matrix
logger	logger

Returns: q parameters marked for deletions

◆ max_overlap_with_R()

template<class R , class Q >

auto molpro::linalg::itsolv::detail::max_overlap_with_R	(	const CVecRef< R > &	rparams,
		const CVecRef< Q > &	qparams,
		array::ArrayHandler< R, Q > &	handler,
		Logger &	logger
	)

Returns list of Q indices with maximum overlap to R parameters, sorted in descending order.

Parameters

rparams	R parameters
qparams	Q parameters to calculate maximum overlap of with R
handler	array handler
logger	logger

◆ modified_gram_schmidt()

template<class R , class Q , class P , typename value_type , typename value_type_abs >

auto molpro::linalg::itsolv::detail::modified_gram_schmidt	(	const VecRef< R > &	rparams,
		const subspace::Matrix< value_type > &	overlap,
		const subspace::Dimensions &	dims,
		const CVecRef< P > &	pparams,
		const CVecRef< Q > &	qparams,
		const CVecRef< Q > &	dparams,
		const value_type_abs	norm_thresh,
		ArrayHandlers< R, Q, P > &	handlers,
		Logger &	logger
	)

Orthogonalises R parameters against P+Q+D subspace (and themselves)

New vectors with norm less than threshold are considered null and are not normalised. Their indices in params are returned.

Parameters

rparams	R space parameters
overlap	overlap of P+Q+D subspace
dims	dimensions of P+Q+D subspace
pparams	P space parameters
qparams	Q space parameters
dparams	D space parameters
handlers	array handlers
norm_thresh	parameters with norm less than threshold are considered null and won't be orthogonalised against

Returns: indices of null parameters

◆ normalise() [1/2]

template<class R >

void molpro::linalg::itsolv::detail::normalise	(	const size_t	n_roots,
		const VecRef< R > &	params,
		const VecRef< R > &	actions,
		array::ArrayHandler< R, R > &	handler,
		Logger &	logger
	)

◆ normalise() [2/2]

template<class R >

void molpro::linalg::itsolv::detail::normalise	(	VecRef< R > &	params,
		array::ArrayHandler< R, R > &	handler,
		Logger &	logger,
		double	thresh = `1.0e-14`
	)

◆ parameter_batches()

std::vector< std::pair< size_t, size_t > > molpro::linalg::itsolv::detail::parameter_batches	(	const size_t	nsol,
		const size_t	nparam
	)

inline

◆ propose_rspace()

template<class R , class Q , class P , typename value_type_abs >

auto molpro::linalg::itsolv::detail::propose_rspace	(	IterativeSolver< R, Q, P > &	solver,
		const VecRef< R > &	parameters,
		const VecRef< R > &	residuals,
		subspace::IXSpace< R, Q, P > &	xspace,
		subspace::ISubspaceSolver< R, Q, P > &	subspace_solver,
		ArrayHandlers< R, Q, P > &	handlers,
		Logger &	logger,
		value_type_abs	svd_thresh,
		value_type_abs	res_norm_thresh,
		int	max_size_qspace,
		molpro::profiler::Profiler &	profiler
	)

Proposes new parameters for the subspace from the preconditioned residuals.

Outline

Basic procedure:

Gram-schmidt orthonormalise residuals amongst themselves
Gram-schmidt orthogonalise residuals against the old Q space and current solutions
Ensure that the resultant Q space is not linearly dependent by removing Q parameters with large overlap
Ensure that the size of Q space is within limit, by removing Q parameters with smallest contributions to current solutions
Reconstruct C space

Various possibilities:

Residuals are linearly dependent among themselves, worst case scenario there could be duplicates.
Residuals are linearly dependent with the old Q space, orthonormalisation against Q would result in almost null vectors.

Case 1 is handled at the start by normalising residuals and orthogonalising them among themselves. If it results in vectors with norm less then threshold than they are discarded and their action does not need to be evaluated.

Case 2 is handled during Gram-Schmidt procedure. Residuals are orthogonalised against the old Q space, if one of them has a small norm than an old q vector with largest overlap is deleted.

Parameters

parameters	output new parameters for the subspace.
residual	preconditioned residuals.

Returns: number of significant parameters to calculate the action for

◆ redundant_parameters()

template<typename value_type , typename value_type_abs >

auto molpro::linalg::itsolv::detail::redundant_parameters	(	const subspace::Matrix< value_type > &	overlap,
		const size_t	oR,
		const size_t	nR,
		const value_type_abs	svd_thresh,
		Logger &	logger
	)

Deduces a set of parameters that are redundant due to linear dependencies.

Only the last nR parameters are considered for removal. Linea dependencies are discovered by performing SVD of the overlap matrix.

Parameters

overlap	overlap matrix of the full subspace
oR	offset to the start of parameter block
nR	number of parameters to consider for removal
svd_thresh	singular value threshold for choosing the null space
logger	logger

Returns: indices of the last nR parameters that are considered redundant.

◆ resize_qspace()

template<class R , class Q , class P , typename value_type >

void molpro::linalg::itsolv::detail::resize_qspace	(	subspace::IXSpace< R, Q, P > &	xspace,
		const subspace::Matrix< value_type > &	solutions,
		int	m_max_Qsize_after_reset,
		Logger &	logger
	)

Removes Q parameters that have smallest contribution to any solution until Q space size is within limit.

◆ select_working_set()

template<typename T >

std::vector< int > molpro::linalg::itsolv::detail::select_working_set	(	const size_t	nw,
		const std::vector< T > &	errors,
		const T	threshold,
		const std::vector< T > &	value_errors,
		const T	value_threshold
	)

◆ update_errors()

template<class R , typename T >

void molpro::linalg::itsolv::detail::update_errors	(	std::vector< T > &	errors,
		const CVecRef< R > &	residual,
		array::ArrayHandler< R, R > &	handler
	)

Namespaces

Classes

Functions

Function Documentation

◆ append_overlap_with_r()

◆ construct_dspace()

◆ construct_solution()

◆ construct_vectorP()

◆ get_new_working_set()

◆ limit_qspace_size()

◆ max_overlap_with_R()

◆ modified_gram_schmidt()

◆ normalise() [1/2]

◆ normalise() [2/2]

◆ parameter_batches()

◆ propose_rspace()

Outline

◆ redundant_parameters()

◆ resize_qspace()

◆ select_working_set()

◆ update_errors()