molpro::linalg::itsolv::detail::dspace Namespace Reference

Functions
std::vector< std::size_t >	projected_solutions_basis (const subspace::Dimensions &dims, const std::vector< std::size_t > &remove_qspace)
	Returns subspace indices of the vectors u_k that the columns of a projected solutions matrix refer to: the Q vectors moved into Q_{delete}, followed by the current D vectors.
template<typename value_type >
auto	construct_projected_solution (const subspace::Matrix< value_type > &solutions, const subspace::Dimensions &dims, const std::vector< std::size_t > &remove_qspace, Logger &logger)
	Projects solution from the full subspace on to Q_{delete} and current D space.
template<typename value_type >
auto	projected_solutions_overlap (const subspace::Matrix< value_type > &solutions_proj, const subspace::Matrix< value_type > &overlap, const std::vector< std::size_t > &basis, const std::vector< std::size_t > &indices)
	Constructs overlaps of projected solutions with subspace vectors.
template<typename value_type >
auto	projected_solutions_overlap (const subspace::Matrix< value_type > &solutions_proj, const subspace::Matrix< value_type > &overlap, const std::vector< std::size_t > &basis)
	Constructs the overlap matrix of projected solutions among themselves.
template<typename value_type >
auto	construct_projected_solutions_overlap (const subspace::Matrix< value_type > &solutions_proj, const subspace::Matrix< value_type > &overlap, const subspace::Dimensions &dims, const std::vector< std::size_t > &remove_qspace, Logger &logger)
	Constructs overlap matrix for projected solutions.
template<typename value_type , typename value_type_abs >
void	remove_null_norm_and_normalise (subspace::Matrix< value_type > &parameters, subspace::Matrix< value_type > &overlap, const value_type_abs norm_thresh, Logger &logger)
	Removes parameters with norm less than threshold and normalises the rest.
template<typename value_type , typename value_type_abs >
auto	remove_null_projected_solutions (const subspace::Matrix< value_type > &solutions_proj, const subspace::Matrix< value_type > &overlap_proj, const value_type_abs svd_thresh, Logger &logger)
	Transforms to a stable subspace of projected solutions via SVD.
template<typename value_type , typename value_type_abs >
auto	stable_projected_solutions (const subspace::Matrix< value_type > &solutions, const subspace::Matrix< value_type > &overlap, const subspace::Dimensions &dims, const std::vector< std::size_t > &remove_qspace, const value_type_abs norm_thresh, const value_type_abs svd_thresh, Logger &logger)
	Projects solutions onto Q_{delete} and the current D space, and transforms them to a normalised set without null space.
template<typename value_type >
auto	construct_full_subspace_overlap (const subspace::Matrix< value_type > &solutions_proj, const subspace::Dimensions &dims, const std::vector< std::size_t > &remove_qspace, const subspace::Matrix< value_type > &overlap, const size_t nR)
	Constructs overlap matrix of P+Q+R+(projected solutions) subspaces, where Q is without removed parameters.

Function Documentation

construct_full_subspace_overlap()

template<typename value_type >

auto molpro::linalg::itsolv::detail::dspace::construct_full_subspace_overlap	(	const subspace::Matrix< value_type > &	solutions_proj,
		const subspace::Dimensions &	dims,
		const std::vector< std::size_t > &	remove_qspace,
		const subspace::Matrix< value_type > &	overlap,
		const size_t	nR
	)

Constructs overlap matrix of P+Q+R+(projected solutions) subspaces, where Q is without removed parameters.

Parameters

solutions_proj	solutions matrix with Q deleted + current D space as columns
dims	dimensions of the current subspace
remove_qspace	indices of Q parameters to be removed
overlap	overlap of current subspace P+Q+D+R, including all of the current Q space
nR	number of new parameters

Returns

overlap matrix for the subspace P+Q+R+(projected solutions), Q without deleted vectors

construct_projected_solution()

template<typename value_type >

auto molpro::linalg::itsolv::detail::dspace::construct_projected_solution	(	const subspace::Matrix< value_type > &	solutions,
		const subspace::Dimensions &	dims,
		const std::vector< std::size_t > &	remove_qspace,
		Logger &	logger
	)

Projects solution from the full subspace on to Q_{delete} and current D space.

Parameters

solutions	solution matrix in the full subspace
dims	dimensions for partitioning of subspace
remove_qspace	indices to remove from current Q space and move into Q_{delete}
norm_thresh	vectors with norm less than this threshold are considered null

Returns

projected solutions, and their overlap matrix

construct_projected_solutions_overlap()

template<typename value_type >

auto molpro::linalg::itsolv::detail::dspace::construct_projected_solutions_overlap	(	const subspace::Matrix< value_type > &	solutions_proj,
		const subspace::Matrix< value_type > &	overlap,
		const subspace::Dimensions &	dims,
		const std::vector< std::size_t > &	remove_qspace,
		Logger &	logger
	)

Constructs overlap matrix for projected solutions.

Parameters

solutions_proj	solutions matrix projected onto Qd+D space
overlap	overlap matrix of the current subspace
dims	dimensions for partitioning of subspace
remove_qspace	indices to remove from current Q space and move into Q_{delete}
logger	logger

Returns

overlap matrix

projected_solutions_basis()

std::vector< std::size_t > molpro::linalg::itsolv::detail::dspace::projected_solutions_basis ( const subspace::Dimensions &  dims, const std::vector< std::size_t > &  remove_qspace  )

inline

Returns subspace indices of the vectors u_k that the columns of a projected solutions matrix refer to: the Q vectors moved into Q_{delete}, followed by the current D vectors.

Parameters

dims	dimensions for partitioning of subspace
remove_qspace	indices to remove from current Q space and move into Q_{delete}

projected_solutions_overlap() [1/2]

template<typename value_type >

auto molpro::linalg::itsolv::detail::dspace::projected_solutions_overlap	(	const subspace::Matrix< value_type > &	solutions_proj,
		const subspace::Matrix< value_type > &	overlap,
		const std::vector< std::size_t > &	basis
	)

Constructs the overlap matrix of projected solutions among themselves.

x_i = \sum_k C_ik u_k <x_i, x_j> = \sum_kl conj(C_ik) C_jl <u_k, u_l>

Parameters

solutions_proj	projected solutions C, with columns referring to the subspace vectors basis
overlap	overlap matrix of the current subspace
basis	subspace indices of the vectors u_k

Returns

hermitian overlap matrix

projected_solutions_overlap() [2/2]

template<typename value_type >

auto molpro::linalg::itsolv::detail::dspace::projected_solutions_overlap	(	const subspace::Matrix< value_type > &	solutions_proj,
		const subspace::Matrix< value_type > &	overlap,
		const std::vector< std::size_t > &	basis,
		const std::vector< std::size_t > &	indices
	)

Constructs overlaps of projected solutions with subspace vectors.

x_i = \sum_k C_ik u_k <x_i, v_m> = \sum_k conj(C_ik) <u_k, v_m>

Parameters

solutions_proj	projected solutions C, with columns referring to the subspace vectors basis
overlap	overlap matrix of the current subspace, S(k, l) = <v_k, v_l>
basis	subspace indices of the vectors u_k
indices	subspace indices of the vectors v_m

Returns

matrix with projected solutions as rows and the vectors v_m as columns

remove_null_norm_and_normalise()

template<typename value_type , typename value_type_abs >

void molpro::linalg::itsolv::detail::dspace::remove_null_norm_and_normalise	(	subspace::Matrix< value_type > &	parameters,
		subspace::Matrix< value_type > &	overlap,
		const value_type_abs	norm_thresh,
		Logger &	logger
	)

Removes parameters with norm less than threshold and normalises the rest.

Parameters

parameters	row major matrix of parameters
overlap	overlap matrix of parameters
norm_thresh	norm threhsold
logger	logger

remove_null_projected_solutions()

template<typename value_type , typename value_type_abs >

auto molpro::linalg::itsolv::detail::dspace::remove_null_projected_solutions	(	const subspace::Matrix< value_type > &	solutions_proj,
		const subspace::Matrix< value_type > &	overlap_proj,
		const value_type_abs	svd_thresh,
		Logger &	logger
	)

Transforms to a stable subspace of projected solutions via SVD.

Performs SVD and transforms to right-singular vectors with singular values greater than threshold.

Parameters

solutions_proj	solutions projected onto Qd+D space
solutions	solutions in the current subspace
overlap_proj	overlap matrix of projected solutions
norm_thresh
logger

Returns

stable subspace of projected solutions

stable_projected_solutions()

template<typename value_type , typename value_type_abs >

auto molpro::linalg::itsolv::detail::dspace::stable_projected_solutions	(	const subspace::Matrix< value_type > &	solutions,
		const subspace::Matrix< value_type > &	overlap,
		const subspace::Dimensions &	dims,
		const std::vector< std::size_t > &	remove_qspace,
		const value_type_abs	norm_thresh,
		const value_type_abs	svd_thresh,
		Logger &	logger
	)

Projects solutions onto Q_{delete} and the current D space, and transforms them to a normalised set without null space.

Parameters

solutions	solution matrix in the full subspace
overlap	overlap matrix of the current subspace
dims	dimensions for partitioning of subspace
remove_qspace	indices to remove from current Q space and move into Q_{delete}
norm_thresh	projected solutions with norm less than this threshold are considered null
svd_thresh	singular value threshold for marking the null space of projected solutions
logger	logger

Returns

projected solutions as rows, with columns as given by projected_solutions_basis()